[
  {
    "path": ".gitignore",
    "content": "# IDE\n.idea\n.vscode\n.python-version\n\n# Prerequisites\n*.d\n\n# Compiled Object files\n*.slo\n*.lo\n*.o\n*.obj\n\n# Precompiled Headers\n*.gch\n*.pch\n\n# Compiled Dynamic libraries\n*.so\n*.dylib\n*.dll\n\n# Fortran module files\n*.mod\n*.smod\n\n# Compiled Static libraries\n*.lai\n*.la\n*.a\n*.lib\n\n# Executables\n*.exe\n*.out\n*.app\n*.jar\ncmake-build-debug\n\n# Dependencies\nnode_modules\n\n# rust\ntarget/debug\ntarget/package\n\n# C++\nmain\nmain.dSYM"
  },
  {
    "path": "Algorithms-Illuminated/.gitignore",
    "content": "# IDE\n.idea\n.vscode\n.python-version\n\n# Prerequisites\n*.d\n\n# Compiled Object files\n*.slo\n*.lo\n*.o\n*.obj\n\n# Precompiled Headers\n*.gch\n*.pch\n\n# Compiled Dynamic libraries\n*.so\n*.dylib\n*.dll\n\n# Fortran module files\n*.mod\n*.smod\n\n# Compiled Static libraries\n*.lai\n*.la\n*.a\n*.lib\n\n# Executables\n*.exe\n*.out\n*.app\n*.jar\ncmake-build-debug\n\n# Dependencies\nnode_modules\n\n# rust\ntarget/debug\ntarget/package"
  },
  {
    "path": "Algorithms-Illuminated/Algorithms-Illuminated.iml",
    "content": "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<module type=\"RUST_MODULE\" version=\"4\">\n  <component name=\"NewModuleRootManager\" inherit-compiler-output=\"true\">\n    <exclude-output />\n    <content url=\"file://$MODULE_DIR$\">\n      <sourceFolder url=\"file://$MODULE_DIR$/src\" isTestSource=\"false\" />\n      <excludeFolder url=\"file://$MODULE_DIR$/target\" />\n    </content>\n    <orderEntry type=\"inheritedJdk\" />\n    <orderEntry type=\"sourceFolder\" forTests=\"false\" />\n  </component>\n</module>"
  },
  {
    "path": "Algorithms-Illuminated/Cargo.toml",
    "content": "[package]\nname = \"Algorithms-Illuminated\"\nversion = \"0.1.1\"\nedition = \"2021\"\ndescription = \"https://github.com/claytonjwong/Algorithms-Illuminated\"\nlicense = \"MIT\"\n\n# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html\n\n[dependencies]\n"
  },
  {
    "path": "Algorithms-Illuminated/README.md",
    "content": "# Algorithms Illuminated\n\n* [algorithmsilluminated.org](https://www.algorithmsilluminated.org/)\n\nCoincidentally, my [algorithm learning journey](https://github.com/claytonjwong/Algorithms) which began in 2017 has occurred in parallel with the publication of Tim Roughgarden's (TR) 4-book series about algorithms and data structures. Over these years, I've purchased, studied, and provided feedback on TR's books. I was totally stoked when TR sent me a free copy of his 4th book for review before publication in 2020! I'm amazed by what can be done in near-linear time (ie. the amount of time to perform an algorithm is on the order of time to simply read the input), and it's awesome we can leverage these \"for-free primitives\" based upon computationally tractable problems as \"building blocks\" towards more complex solutions to computationally intractable (NP-Hard) problems via selective compromise on generality, correctness, and speed (ie. pick 2 of 3). [`💡` Can we do better?](https://en.wikipedia.org/wiki/Millennium_Prize_Problems#P_versus_NP)\n\n<p>\n    <img src=\"images/TR1.png\" height=\"256\" width=\"400\" />\n    <img src=\"images/TR2.png\" height=\"256\" width=\"400\" />\n</p>\n\n---\n\n# Part 1: The Basics\n\n<br/>\n<a href=\"https://www.amazon.com/dp/0999282905\" target=\"_blank\">\n    <img src=\"images/ai1large.jpg\" />\n</a>\n\n---\n\n### Merge Sort\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [MergeSort: Motivation and Example](https://www.youtube.com/watch?v=kiyRJ7GVWro&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=4) (Section 1.4, part 1)\n* [MergeSort: Pseudocode](https://www.youtube.com/watch?v=rBd5w0rQaFo&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=5) (Section 1.4, part 2)\n* [MergeSort: Analysis](https://www.youtube.com/watch?v=8ArtRiTkYEw&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=6) (Section 1.5)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nfun sort(A: IntArray): IntArray {\n    fun merge(A: IntArray, B: IntArray): IntArray {\n        var C = mutableListOf<Int>()\n        var i = 0\n        var j = 0\n        while (i < A.size && j < B.size)\n            if (A[i] < B[j])\n                C.add(A[i++])\n            else\n                C.add(B[j++])\n        A.slice(i..A.lastIndex).forEach { C.add(it) }\n        B.slice(j..B.lastIndex).forEach { C.add(it) }\n        return C.toIntArray()\n    }\n    fun go(A: IntArray): IntArray {\n        var N = A.size\n        if (N < 2)\n            return A\n        var half = Math.floor(N / 2.0).toInt()\n        var first  = go(A.slice(0 until half).toIntArray())\n        var second = go(A.slice(half until N).toIntArray())\n        return merge(first, second)\n    }\n    return go(A)\n}\n\nfun main(args: Array<String>) {\n    sort(intArrayOf(5,3,8,9,1,7,0,2,6,4)).forEach { print(\"$it \") }  // 0 1 2 3 4 5 6 7 8 9\n    println()\n}\n```\n\n*Javascript*\n```javascript\nlet sort = A => {\n    let go = A => {\n        let N = A.length;\n        if (N < 2)\n            return A;\n        let half = Math.floor(N / 2);\n        let first  = go([...A.slice(0, half)]),\n            second = go([...A.slice(half, N)]);\n        return merge(first, second);\n    };\n    let merge = (A, B, C = []) => {\n        let M = A.length,\n            N = B.length;\n        let i = 0,\n            j = 0;\n        while (i < M && j < N)\n            C.push(A[i] < B[j] ? A[i++] : B[j++]);\n        C.push(...A.slice(i, M));\n        C.push(...B.slice(j, N));\n        return C;\n    };\n    return go(A);\n};\n\nconsole.log(sort([5,3,8,9,1,7,0,2,6,4]));  // (10) [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n```\n\n*Python3*\n```python\nfrom math import floor\n\ndef sort(A):\n    def go(A):\n        N = len(A)\n        if N < 2:\n            return A\n        half = floor(N / 2)\n        first =  go(A[:half])\n        second = go(A[half:])\n        return merge(first, second)\n    def merge(A, B):\n        C = []\n        i = 0\n        j = 0\n        while i < len(A) and j < len(B):\n            if A[i] < B[j]:\n                C.append(A[i]); i += 1\n            else:\n                C.append(B[j]); j += 1\n        C.extend(A[i:])\n        C.extend(B[j:])\n        return C\n    return go(A)\n\nprint(sort([5,3,8,9,1,7,0,2,6,4]))  # [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <vector>\n\nusing namespace std;\n\nclass Solution {\npublic:\n    using VI = vector<int>;\n    VI mergesort(VI& A) {\n        return go(move(A));\n    }\nprivate:\n    VI go(VI&& A) {\n        auto N = A.size();\n        if( N < 2 )\n            return A;\n        auto half = A.begin() + (N / 2);\n        auto first = go({ A.begin(), half }),\n             second = go({ half, A.end() });\n        return merge(first, second);\n    }\n    VI merge(VI& A, VI& B, VI C = {}) {\n        auto i{ 0 },\n             j{ 0 };\n        while (i < A.size() && j < B.size())\n            C.push_back(A[i] < B[j] ? A[i++] : B[j++]);\n        C.insert(C.end(), A.begin() + i, A.end());\n        C.insert(C.end(), B.begin() + j, B.end());\n        return C;\n    }\n};\n\nint main() {\n    Solution::VI A{ 3,5,7,1,3,9,2,0 };\n    auto ans = Solution().mergesort(A);\n    copy(ans.begin(), ans.end(), ostream_iterator<int>(cout, \" \")), cout << endl;  // 0 1 2 3 4 5 6 7 8 9\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Counting Inversions\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [The Divide-and-Conquer Paradigm](https://www.youtube.com/watch?v=7_AJfusC6UQ&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=13) (Section 3.1; part 1 of Section 3.2)\n* [Counting Inversions in O(n log n)](https://www.youtube.com/watch?v=I6ygiW8xN7Y&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=14) Time (Section 3.2, part 2)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.io.File\n\nfun sort(A: IntArray): Pair<IntArray, Long> {\n    fun merge(A: IntArray, B: IntArray): Pair<IntArray, Long> {\n        var C = mutableListOf<Int>()\n        var inv: Long = 0\n        var i = 0\n        var j = 0\n        while (i < A.size && j < B.size)\n            if (A[i] < B[j]) {\n                C.add(A[i++])\n            } else {\n                inv += A.size - i  // ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.add(B[j++])\n            }\n        A.slice(i..A.lastIndex).forEach { C.add(it) }\n        B.slice(j..B.lastIndex).forEach { C.add(it) }\n        return Pair(C.toIntArray(), inv)\n    }\n    fun go(A: IntArray): Pair<IntArray, Long> {\n        var N = A.size\n        if (N < 2)\n            return Pair(A, 0)\n        var half = Math.floor(N / 2.0).toInt()\n        var (first,  inv1) = go(A.slice(0 until half).toIntArray())\n        var (second, inv2) = go(A.slice(half until N).toIntArray())\n        var (third,  inv3) = merge(first, second)\n        return Pair(third, inv1 + inv2 + inv3)\n    }\n    return go(A)\n}\n\nfun run(filename: String): Long {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    var (_, inv) = sort(A.toIntArray())\n    return inv\n}\n\nfun main() {\n    println(\"problem3.5test.txt: \" + run(\"problem3.5test.txt\"))  // problem3.5test.txt: 28\n    println(\"problem3.5.txt: \"     + run(\"problem3.5.txt\"))      // problem3.5.txt: 2407905288\n}\n```\n\n*Javascript*\n```javascript\nlet sort = A => {\n    let go = A => {\n        let N = A.length;\n        if (N < 2)\n            return [A, 0];\n        let half = Math.floor(N / 2);\n        let [first,  inv1] = go([...A.slice(0, half)]),\n            [second, inv2] = go([...A.slice(half, N)]),\n            [third,  inv3] = merge(first, second);\n        return [third, inv1 + inv2 + inv3];\n    };\n    let merge = (A, B, C = [], inv = 0) => {\n        let M = A.length,\n            N = B.length;\n        let i = 0,\n            j = 0;\n        while (i < M && j < N)\n            if (A[i] < B[j])\n                C.push(A[i++]);\n            else\n                inv += M - i,      // ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.push(B[j++]);\n        C.push(...A.slice(i, M));\n        C.push(...B.slice(j, N));\n        return [C, inv];\n    };\n    return go(A);\n};\n\nlet run = filename => {\n    let A = [];\n    require('fs').readFileSync(filename, 'utf-8').split(/\\r?\\n/).forEach(line => A.push(Number(line)));\n    let [_, inv] = sort(A);\n    return inv;\n}\n\nconsole.log(`problem3.5test.txt: ${run('problem3.5test.txt')}`);  // problem3.5test.txt: 28\nconsole.log(`problem3.5.txt: ${run('problem3.5.txt')}`);          // problem3.5.txt: 2407905288\n```\n\n*Python3*\n```python\nfrom math import floor\n\ndef sort(A):\n    def go(A):\n        N = len(A)\n        if N < 2:\n            return [A, 0]\n        half = floor(N / 2)\n        first,  inv1 = go(A[:half])\n        second, inv2 = go(A[half:])\n        third,  inv3 = merge(first, second)\n        return [third, inv1 + inv2 + inv3]\n    def merge(A, B, inv = 0):\n        C = []\n        i = 0\n        j = 0\n        while i < len(A) and j < len(B):\n            if A[i] < B[j]:\n                C.append(A[i]); i += 1\n            else:\n                inv += len(A) - i        # ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.append(B[j]); j += 1\n        C.extend(A[i:])\n        C.extend(B[j:])\n        return [C, inv]\n    return go(A)\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            A.append(int(line))\n    _, inv = sort(A)\n    return inv\n\nprint(f\"problem3.5test.txt: {run('problem3.5test.txt')}\")  # problem3.5test.txt: 28\nprint(f\"problem3.5.txt: {run('problem3.5.txt')}\")          # problem3.5.txt: 2407905288\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <vector>\n#include <fstream>\n\nusing namespace std;\n\nclass Solution {\npublic:\n    using VL = vector<long>;\n    using Pair = pair<VL, long>;\n    using fun = function<Pair(VL&&)>;\n    Pair merge(VL& A, VL& B, VL C = {}, long inv = 0) {\n        auto i = 0,\n             j = 0;\n        while (i < A.size() && j < B.size()) {\n            if (A[i] < B[j]) {\n                C.push_back(A[i++]);\n            } else {\n                inv += A.size() - i; // ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.push_back(B[j++]);\n            }\n        }\n        C.insert(C.end(), A.begin() + i, A.end());\n        C.insert(C.end(), B.begin() + j, B.end());\n        return { C, inv };\n    }\n    Pair inversions(VL& A) {\n        fun go = [&](VL&& A) -> Pair {\n            int N = A.size();\n            if (N < 2)\n                return { A, 0 };\n            int half = N / 2;\n            auto [first,  inv1] = go({ A.begin(), A.begin() + half });\n            auto [second, inv2] = go({ A.begin() + half, A.end() });\n            auto [third,  inv3] = merge(first, second);\n            return { third, inv1 + inv2 + inv3 };\n        };\n        return go(move(A));\n    }\n};\n\nlong run(string filename) {\n    Solution solution;\n    Solution::VL A;\n    fstream fin{ filename };\n    for (string line; fin >> line; A.push_back(stol(line)));\n    auto [_, inv] = solution.inversions(A);\n    return inv;\n}\n\nint main() {\n    cout << \"problem3.5test.txt: \" << run(\"problem3.5test.txt\") << endl   // problem3.5test.txt: 28\n         << \"problem3.5.txt: \"     << run(\"problem3.5.txt\")     << endl;  // problem3.5.txt: 2407905288\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Quick Sort\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [QuickSort: Overview](https://www.youtube.com/watch?v=ETo1cpLN7kk&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=24) (Section 5.1)\n* [Partitioning Around a Pivot Element](https://www.youtube.com/watch?v=LYzdRN5iFdA&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=25) (Section 5.2)\n* [Choosing a Good Pivot](https://www.youtube.com/watch?v=kqO46FOUTbI&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=26) (Sections 5.3 and 5.4)\n* [QuickSort Analysis (Part 1)](https://www.youtube.com/watch?v=sToWtKSYlMw&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=27) (Section 5.5, part 1)\n* [QuickSort Analysis (Part 2)](https://www.youtube.com/watch?v=4t_Y-aGLkok&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=28) (Section 5.5, part 2)\n* [QuickSort Analysis (Part 3)](https://www.youtube.com/watch?v=IBTvneWhFsA&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=29) (Section 5.5, part 3)\n* [Sorting Requires Omega(n log n) Comparisons](https://www.youtube.com/watch?v=aFveIyII5D4&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=30) (Section 5.6)\n* [Proofs by Induction and the Correctness of QuickSort](https://www.youtube.com/watch?v=Colb_4jAy8A&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=36) (Appendix A)\n* [Quick Review of Discrete Probability](https://www.youtube.com/watch?v=uLeIMwMHX5U&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=37) (Appendix B)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.io.File\n\ntypealias PivotFunc = (A: MutableList<Int>, L: Int, R: Int) -> (Int)\nvar pivotLeft: PivotFunc = { _: MutableList<Int>, L: Int, _: Int -> L }\nvar pivotRight: PivotFunc = { _: MutableList<Int>, _: Int, R: Int -> R }\nfun _pivotMedian(A: MutableList<Int>, L: Int, R: Int): Int {\n    var M = L + (R - L) / 2\n    var cand = intArrayOf(A[L], A[M], A[R])\n    cand.sort()\n    var target = cand[1]\n    if (target == A[L]) return L\n    if (target == A[M]) return M\n    if (target == A[R]) return R\n    return -1\n}\nvar pivotMedian: PivotFunc = { A: MutableList<Int>, L: Int, R: Int -> _pivotMedian(A, L, R) }\n\nfun partition(A: MutableList<Int>, L: Int, R: Int, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    var i = L + 1\n    var j = L + 1\n    var k = choosePivot(A, L, R)\n    A[k] = A[L].also { A[L] = A[k] }          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                    // maintain loop invariant A[i] < pivot < A[j]\n            A[i] = A[j].also { A[j] = A[i] }\n            ++i\n        }\n        ++j\n    }\n    A[L] = A[i - 1].also { A[i - 1] = A[L] }  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n}\n\nfun quicksort(A: MutableList<Int>, L: Int, R: Int, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    if (R <= L)\n        return 0\n    var k = partition(A, L, R, choosePivot)\n    return (R - L) + quicksort(A, L, k - 1, choosePivot) + quicksort(A, k + 1, R, choosePivot)\n}\n\nfun run(filename: String, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    return quicksort(A, 0, A.size - 1, choosePivot)\n}\n\nfun main() {\n    var filename = \"problem5.6.txt\"\n    println(\"  left: ${run(filename, pivotLeft)}\")    //   left: 162085\n    println(\" right: ${run(filename, pivotRight)}\")   //  right: 164123\n    println(\"median: ${run(filename, pivotMedian)}\")  // median: 138382\n}\n```\n\n*Javascript*\n```javascript\nlet pivotLeft = (A, L, R) => L;\nlet pivotRight = (A, L, R) => R;\nlet pivotMedian = (A, L, R) => {\n    let M = L + Math.floor((R - L) / 2);\n    let cand = [A[L], A[M], A[R]].sort((a, b) => a - b),\n        target = cand[1];\n    if (target == A[L]) return L;\n    if (target == A[M]) return M;\n    if (target == A[R]) return R;\n};\n\nlet partition = (A, L, R, choosePivot) => {\n    let i = L + 1,\n        j = L + 1,\n        k = choosePivot(A, L, R);\n    [A[L], A[k]] = [A[k], A[L]];          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                // maintain loop invariant A[i] < pivot < A[j]\n            [A[i], A[j]] = [A[j], A[i]];\n            ++i;\n        }\n        ++j;\n    }\n    [A[L], A[i - 1]] = [A[i - 1], A[L]];  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n};\n\nlet quicksort = (A, L, R, choosePivot) => {\n    if (R <= L)\n        return 0;\n    let k = partition(A, L, R, choosePivot);\n    return (R - L) + quicksort(A, L, k - 1, choosePivot)\n                   + quicksort(A, k + 1, R, choosePivot);\n};\n\nlet run = (filename, choosePivot) => {\n    let A = [];\n    let LineByLine = require(\"n-readlines\");\n    let input = new LineByLine(filename);\n    for (let line; line = input.next(); A.push(Number(line)));\n    return quicksort(A, 0, A.length - 1, choosePivot);\n}\n\nlet filename = 'problem5.6.txt';\nconsole.log(`  left: ${run(filename, pivotLeft)}`);    //   left: 162085\nconsole.log(` right: ${run(filename, pivotRight)}`);   //  right: 164123\nconsole.log(`median: ${run(filename, pivotMedian)}`);  // median: 138382\n```\n\n*Python3*\n```python\ndef pivotLeft(A, L, R): return L\ndef pivotRight(A, L, R): return R\ndef pivotMedian(A, L, R):\n    M = L + (R - L) // 2\n    cand = sorted([A[L], A[M], A[R]])\n    target = cand[1]\n    if target == A[L]: return L\n    if target == A[M]: return M\n    if target == A[R]: return R\n\ndef partition(A, L, R, choosePivot):\n    i = L + 1\n    j = L + 1\n    k = choosePivot(A, L, R)\n    A[L], A[k] = A[k], A[L]          # swap pivot A[k] with first element of subarray A[L]\n    while j <= R:\n        if A[j] < A[L]:              # maintain loop invariant A[i] < pivot < A[j]\n            A[i], A[j] = A[j], A[i]\n            i += 1\n        j += 1\n    A[L], A[i - 1] = A[i - 1], A[L]  # swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n\ndef quicksort(A, L, R, choosePivot):\n    if R <= L:\n        return 0\n    k = partition(A, L, R, choosePivot)\n    return (R - L) + quicksort(A, L, k - 1, choosePivot) + quicksort(A, k + 1, R, choosePivot)\n\ndef run(filename, choosePivot):\n    A = []\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            A.append(int(line))\n\n    return quicksort(A, 0, len(A) - 1, choosePivot)\n\nfilename = 'problem5.6.txt'\nprint(f'  left: {run(filename, pivotLeft)}')    #   left: 162085\nprint(f' right: {run(filename, pivotRight)}')   #  right: 164123\nprint(f'median: {run(filename, pivotMedian)}')  # median: 138382\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n\nusing namespace std;\nusing VI = vector<int>;\nusing fun = function<int(VI&, int, int)>;\n\nfun pivotLeft = [](VI& A, int L, int R) { return L; };\nfun pivotRight = [](VI& A, int L, int R) { return R; };\nfun pivotMedian = [](VI& A, int L, int R) {\n    auto M = L + (R - L) / 2;\n    VI cand{ A[L], A[M], A[R] };\n    sort(cand.begin(), cand.end());\n    auto target = cand[1];\n    if (target == A[L]) return L;\n    if (target == A[M]) return M;\n    if (target == A[R]) return R;\n};\n\nint partition(VI& A, int L, int R, fun choosePivot) {\n    auto i = L + 1,\n         j = L + 1,\n         k = choosePivot(A, L, R);\n    swap(A[L], A[k]);          // swap pivot A[k] with first element of the subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {     // maintain loop invariant A[i] < pivot < A[j]\n            swap(A[i], A[j]);\n            ++i;\n        }\n        ++j;\n    }\n    swap(A[L], A[i - 1]);      // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n}\n\nint quicksort(VI& A, int L, int R, fun choosePivot) {\n    if (R <= L)\n        return 0;\n    auto k = partition(A, L, R, choosePivot);\n    return (R - L) + quicksort(A, L, k - 1, choosePivot)\n                   + quicksort(A, k + 1, R, choosePivot);\n}\n\nint run(string& filename, fun choosePivot) {\n    VI A;\n    fstream fin{ filename };\n    for (string line; fin >> line; A.push_back(stoi(line)));\n    int N = A.size();\n    return quicksort(A, 0, N - 1, choosePivot);\n}\n\nint main() {\n    string filename{ \"problem5.6.txt\" };\n    cout << \"  left: \" << run(filename, pivotLeft)   << endl   //   left: 162085\n         << \" right: \" << run(filename, pivotRight)  << endl   //  right: 164123\n         << \"median: \" << run(filename, pivotMedian) << endl;  // median: 138382\n    return 0;\n}\n```\n</details>\n\n---\n\n### Randomized Linear-Time Selection\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Randomized Linear-Time Selection](https://www.youtube.com/watch?v=nFw6x7DoYbs&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=31) (Section 6.1)\n* [Randomized Linear-Time Selection (Analysis)](https://www.youtube.com/watch?v=rX2u2CnpveQ&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=32) (Section 6.2)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.io.File\nimport kotlin.random.Random\n\nfun partition(A: MutableList<Int>, L: Int, R: Int): Int {\n    var i = L + 1\n    var j = L + 1\n    var k = Random.nextInt(L, R + 1)          // +1 for L..R inclusive\n    A[L] = A[k].also { A[k] = A[L] }          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                    // maintain loop invariant A[i] < pivot < A[j]\n            A[i] = A[j].also { A[j] = A[i] }\n            ++i\n        }\n        ++j\n    }\n    A[L] = A[i - 1].also { A[i - 1] = A[L] }  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n}\n\nfun rselect(A: MutableList<Int>, i: Int, L_: Int, R_: Int): Int {\n    var L = L_\n    var R = R_\n    var k = partition(A, L, R)\n    if (i == k)\n        return A[k]  // 🎯 lucky guess\n    if (i < k)\n        R = k - 1\n    else\n        L = k + 1\n    return rselect(A, i, L, R)\n}\n\nfun run(filename: String, i: Int): Int {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    var N = A.size\n    return rselect(A, i - 1, 0 , N - 1)  // -1 for 0-based indexing\n}\n\nfun main() {\n    println(\"problem6.5test1.txt: \" + run(\"problem6.5test1.txt\", 5))   // problem6.5test1.txt: 5469\n    println(\"problem6.5test2.txt: \" + run(\"problem6.5test2.txt\", 50))  // problem6.5test2.txt: 4715\n}\n```\n\n*Javascript*\n```javascript\nlet random = (L, R) => Math.floor(Math.random() * (R + 1 - L) + L);  // +1 for L..R inclusive\n\nlet partition = (A, L, R) => {\n    let i = L + 1,\n        j = L + 1,\n        k = random(L, R);\n    [A[L], A[k]] = [A[k], A[L]];          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                // maintain loop invariant A[i] < pivot < A[j]\n            [A[i], A[j]] = [A[j], A[i]];\n            ++i;\n        }\n        ++j;\n    }\n    [A[L], A[i - 1]] = [A[i - 1], A[L]];  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n};\n\nlet rselect = (A, i, L, R) => {\n    let k = partition(A, L, R);\n    if (i == k)\n        return A[k];  // 🎯 lucky guess\n    if (i < k)\n        R = k - 1;\n    else\n        L = k + 1;\n    return rselect(A, i, L, R);\n}\n\nlet run = (filename, i) => {\n    let A = [];\n    let LineByLine = require(\"n-readlines\");\n    let input = new LineByLine(filename);\n    for (let line; line = input.next(); A.push(Number(line)));\n    let N = A.length;\n    return rselect(A, i - 1, 0, N - 1);  // -1 for 0-based indexing\n};\n\nconsole.log(`problem6.5test1.txt: ${run('problem6.5test1.txt', 5)}`);   // problem6.5test1.txt: 5469\nconsole.log(`problem6.5test2.txt: ${run('problem6.5test2.txt', 50)}`);  // problem6.5test2.txt: 4715\n```\n\n*Python3*\n```python\nfrom random import uniform\nfrom math import floor\n\ndef partition(A, L, R):\n    i = L + 1\n    j = L + 1\n    k = floor(uniform(L, R))\n    A[L], A[k] = A[k], A[L]          # swap pivot A[k] with first element of subarray A[L]\n    while j <= R:\n        if A[j] < A[L]:              # maintain loop invariant A[i] < pivot < A[j]\n            A[i], A[j] = A[j], A[i]\n            i += 1\n        j += 1\n    A[L], A[i - 1] = A[i - 1], A[L]  # swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n\ndef rselect(A, i, L, R):\n    k = partition(A, L, R)\n    if i == k:\n        return A[k]  # 🎯 lucky guess\n    if i < k:\n        R = k - 1\n    else:\n        L = k + 1\n    return rselect(A, i, L, R)\n\ndef run(filename, i):\n    A = []\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            A.append(int(line))\n    N = len(A)\n    return rselect(A, i - 1, 0, N - 1)  # -1 for 0-based indexing\n\nprint('problem6.5test1.txt:', run('problem6.5test1.txt', 5))   # problem6.5test1.txt: 5469\nprint('problem6.5test2.txt:', run('problem6.5test2.txt', 50))  # problem6.5test2.txt: 4715\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <random>\n\nusing namespace std;\nusing VI = vector<int>;\n\nint random(int L, int R) {\n    random_device rd;\n    mt19937 gen{ rd() };\n    uniform_int_distribution dist(L, R);\n    return dist(gen);\n}\n\nint partition(VI& A, int L, int R) {\n    auto i = L + 1,\n         j = L + 1,\n         k = random(L, R);\n    swap(A[L], A[k]);            // swap pivot A[k] with first element of the subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L])         // maintain loop invariant A[i] < pivot < A[j]\n            swap(A[i++], A[j]);\n        ++j;\n    }\n    swap(A[L], A[i - 1]);       // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n}\n\nint rselect(VI& A, int i, int L, int R) {\n    auto k = partition(A, L, R);\n    if (i == k)\n        return A[k];  // 🎯 lucky guess\n    if (i < k)\n        R = k - 1;\n    else\n        L = k + 1;\n    return rselect(A, i, L, R);\n}\n\nint run(string filename, int i, VI A = {}) {\n    fstream fin{ filename };\n    for (string line; fin >> line; A.push_back(stoi(line)));\n    int N = A.size();\n    return rselect(A, i - 1, 0, N - 1);  // -1 for 0-based indexing\n}\n\nint main() {\n    cout << \"problem6.5test1.txt: \" << run(\"problem6.5test1.txt\", 5)  << endl;  // problem6.5test1.txt: 5469\n    cout << \"problem6.5test2.txt: \" << run(\"problem6.5test2.txt\", 50) << endl;  // problem6.5test2.txt: 4715\n    return 0;\n}\n```\n\n</details>\n\n---\n\n# Part 2: Graph Algorithms and Data Structures\n\n<br/>\n<a href=\"https://www.amazon.com/dp/0999282921\" target=\"_blank\">\n    <img src=\"images/ai2large.jpg\" />\n</a>\n\n---\n\n### Topological Sort\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Graphs: The Basics (from 2:06 to 6:39)](https://www.youtube.com/watch?v=4Ih3UhVuEtw&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=1) (Sections 7.1 and 7.2)\n* [Graph Representations](https://www.youtube.com/watch?v=b-Mfu8dPv9U&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=2) (Sections 7.3 and 7.4)\n* [Graph Search Overview](https://www.youtube.com/watch?v=SW6jwg7WS48&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=3) (Section 8.1)\n* [Breadth-First Search](https://www.youtube.com/watch?v=73qCvXsYkfk&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=4) (Section 8.2, Part 1)\n* [Depth-First Search](https://www.youtube.com/watch?v=73qCvXsYkfk&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=4) (Section 8.4)\n* [Topological Sort](https://www.youtube.com/watch?v=ozso3xxkVGU&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=8) (Section 8.5)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.util.Queue\nimport java.util.LinkedList\n\nclass Solution(val adj: MutableMap<Char, List<Char>>) {\n\n    var N: Int\n    var color: Int\n    var m = mutableMapOf<Char, Int>()\n    var seen = mutableSetOf<Char>()\n\n    init {\n        N = adj.size\n        color = 0\n    }\n\n    fun init(start: Int) {\n        color = start\n        m.clear()\n        seen.clear()\n    }\n\n    fun topoSortBFS(): String {\n        init(1)  // 👉 color forward from 1..N\n        bfs()\n        return toString()\n    }\n\n    fun topoSortDFS(): String {\n        init(N)  // 👈 color reverse from N..1 (as the recursive stack unwinds)\n        adj.forEach{ (u, _) -> dfs(u) }\n        return toString()\n    }\n\n    fun bfs() {\n        var degree = mutableMapOf<Char, Int>()\n        adj.forEach{ (_, neighbors) ->\n            neighbors.forEach{ v ->\n                degree[v] = 1 + degree.getOrDefault(v, 0)\n            }\n        }\n        var q: Queue<Char> = LinkedList(adj.map{ (u, _) -> u }.filter{ !degree.contains(it) })\n        while (0 < q.size) {\n            var u = q.poll()\n            m[u] = color++\n            adj[u]!!.forEach{ v ->\n                degree[v] = degree[v]!!.minus(1)\n                if (degree[v] == 0 && !seen.contains(v)) {\n                    q.add(v); seen.add(v)\n                }\n            }\n        }\n    }\n\n    fun dfs(u: Char) {\n        if (seen.contains(u))\n            return\n        seen.add(u)\n        adj[u]!!.forEach{ v ->\n            dfs(v)\n        }\n        m[u] = color--\n    }\n\n    override fun toString(): String {\n        var s = mutableListOf<String>()\n        adj.forEach{ (u, _) ->\n            s.add(\"$u: ${m[u]}\")\n        }\n        return s.joinToString(\"\\n\")\n    }\n}\n\nfun main() {\n    var adj = mutableMapOf<Char, List<Char>>(\n        's' to listOf<Char>('v', 'w'),\n        'v' to listOf<Char>('t'),\n        'w' to listOf<Char>('t'),\n        't' to listOf<Char>()\n    )\n    var solution = Solution(adj)\n    println(\"BFS:\\n${solution.topoSortBFS()}\\n\\nDFS:\\n${solution.topoSortDFS()}\")\n\n//    BFS:\n//    s: 1\n//    v: 2\n//    w: 3\n//    t: 4\n\n//    DFS:\n//    s: 1\n//    v: 3\n//    w: 2\n//    t: 4\n\n}\n```\n\n*Javascript*\n```javascript\nclass Solution {\n    constructor(adj) {\n        this.adj = adj;\n        this.N = this.adj.size;\n    }\n    init(start) {\n        this.color = start;\n        this.seen = new Set();\n        this.m = new Map();\n    }\n    topo_sort_bfs() {\n        this.init(1);       // 👉 color forward from 1..N\n        this.bfs();\n        return this.to_string();\n    }\n    topo_sort_dfs() {\n        this.init(this.N);  // 👈 color reverse from N..1 (as the recursive stack unwinds)\n        for (let [u, _] of [...this.adj])\n            this.dfs(u);\n        return this.to_string();\n    }\n    bfs() {\n        let degree = new Map();\n        for (let [u, _] of [...this.adj]) {\n            degree.set(u, (degree.get(u) || 0));\n            for (let v of this.adj.get(u))\n                degree.set(v, 1 + (degree.get(v) || 0));\n        }\n        let q = [...this.adj].map(([u, _]) => u).filter(u => !degree.get(u));\n        let seen = new Set(q);\n        while (q.length) {\n            let u = q.shift();\n            this.m.set(u, this.color++);\n            for (let v of this.adj.get(u)) {\n                degree.set(v, -1 + degree.get(v));\n                if (!degree.get(v) && !seen.has(v))\n                    q.push(v), seen.add(v);\n            }\n        }\n    }\n    dfs(u) {\n        if (this.seen.has(u))\n            return;\n        this.seen.add(u);\n        for (let v of this.adj.get(u))\n            if (!this.seen.has(v))\n                this.dfs(v);\n        this.m.set(u, this.color--);\n    }\n    to_string() {\n        let s = [];\n        for (let [u, color] of [...this.m])\n            s.push(`${u}: ${color}`);\n        return s.join('\\n');\n    }\n}\n\nlet adj = new Map();\nadj.set('s', ['v', 'w']);\nadj.set('v', ['t']);\nadj.set('w', ['t']);\nadj.set('t', []);\nlet solution = new Solution(adj);\nconsole.log(`BFS:\\n${solution.topo_sort_bfs()}\\n\\nDFS:\\n${solution.topo_sort_dfs()}`);\n\n//    BFS:\n//    s: 1\n//    v: 2\n//    w: 3\n//    t: 4\n\n//    DFS:\n//    t: 4\n//    v: 3\n//    w: 2\n//    s: 1\n```\n\n*Python3*\n```python\nfrom collections import deque\n\nclass Solution:\n    def __init__(self, adj):\n        self.adj = adj\n        self.N = len(adj)\n        self.seen = set()\n        self.m = {}\n\n    def init(self, start):\n        self.color = start\n        self.seen.clear()\n        self.m.clear()\n\n    def topo_sort_bfs(self):\n        self.init(1)         # 👉 color forward from 1..N\n        self.bfs()\n        return self.to_string()\n\n    def topo_sort_dfs(self):\n        self.init(self.N)  # 👈 color reverse from N..1 (as the recursive stack unwinds)\n        for u, _ in self.adj.items():\n            self.dfs(u)\n        return self.to_string()\n\n    def bfs(self):\n        degree = {}\n        for _, neighbors in self.adj.items():\n            for v in neighbors:\n                degree[v] = 1 + (degree[v] if v in degree else 0)\n        q = deque(u for u, _ in self.adj.items() if u not in degree)\n        self.seen.update(*q)\n        while q:\n            u = q.popleft()\n            self.m[u] = self.color; self.color += 1\n            for v in adj[u]:\n                degree[v] -= 1\n                if not degree[v] and v not in self.seen:\n                    q.append(v); self.seen.add(v)\n\n    def dfs(self, u):\n        if u in self.seen:\n            return\n        self.seen.add(u)\n        for v in adj[u]:\n            self.dfs(v)\n        self.m[u] = self.color; self.color -= 1\n\n    def to_string(self):\n        s = []\n        for u, color in self.m.items():\n            s.append(f'{u}: {color}')\n        return '\\n'.join(s)\n\n#\n# graph from Quiz 8.3 on page 45 of Algorithms Illuminated: Part 2\n#\nadj = {\n    's': ['v', 'w'],\n    'v': ['t'],\n    'w': ['t'],\n    't': []\n}\nsolution = Solution(adj)\n\nprint(f'BFS:\\n{solution.topo_sort_bfs()}\\n\\nDFS:\\n{solution.topo_sort_dfs()}')\n\n#    BFS:\n#    s: 1\n#    v: 2\n#    w: 3\n#    t: 4\n\n#    DFS:\n#    t: 4\n#    v: 3\n#    w: 2\n#    s: 1\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n#include <unordered_set>\n#include <queue>\n\nusing namespace std;\n\nusing VI = vector<int>;\nusing AdjList = unordered_map<char, VI>;\nusing Set = unordered_set<char>;\nusing Map = unordered_map<char, int>;\nusing Queue = queue<char>;\nusing fun = function<void(char)>;\n\nclass Solution {\nprivate:\n    AdjList adj;\n    const int N;\n    Map m;\n    Set seen;\n    int color;\npublic:\n    Solution(AdjList& adj) : adj{ adj }, N{ int(adj.size()) } {\n    }\n    void init(int start) {\n        m.clear();\n        seen.clear();\n        color = start;\n    }\n    string topo_sort_bfs() {\n        init(1);  // 👉 color forward from 1..N\n        bfs();\n        return to_string();\n    }\n    string topo_sort_dfs() {\n        init(N);  // 👈 color reverse from N..1 (as the recursive stack unwinds)\n        for (auto [u, _]: adj)\n            dfs(u);\n        return to_string();\n    }\n    void bfs() {\n        Map degree;\n        for (auto [_, neighbors]: adj)\n            for (auto v: neighbors)\n                ++degree[v];\n        Queue q;\n        for (auto [u, _]: adj)\n            if (!degree[u] && seen.insert(u).second)\n                q.push(u);\n        while (q.size()) {\n            auto u = q.front(); q.pop();\n            m[u] = color++;\n            for (auto v: adj[u])\n                if (!--degree[v] && seen.insert(v).second)\n                    q.push(v);\n        }\n    }\n    void dfs(char start) {\n        fun go = [&](auto u) {\n            if (!seen.insert(u).second)\n                return;\n            for (auto v: adj[u])\n                go(v);\n            m[u] = color--;\n        };\n        go(start);\n    }\n    string to_string() {\n        ostringstream os;\n        for (auto [u, color]: m)\n            os << u << \": \" << color << endl;\n        return os.str();\n    }\n};\n\nint main() {\n    //\n    // graph from Quiz 8.3 on page 45 of Algorithms Illuminated: Part 2\n    //\n    AdjList adj{\n        { 's', { 'v', 'w' } },\n        { 'v', { 't' } },\n        { 'w', { 't' } },\n        { 't', {} }\n    };\n    Solution solution{ adj };\n\n    cout << \"BFS:\" << endl << solution.topo_sort_bfs() << endl\n         << \"DFS:\" << endl << solution.topo_sort_dfs() << endl;\n\n//    BFS:\n//    t: 4\n//    w: 3\n//    v: 2\n//    s: 1\n//\n//    DFS:\n//    s: 1\n//    w: 2\n//    v: 3\n//    t: 4\n\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Kosaraju\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Computing Strongly Connected Components (Part 1) (Section 8.6, Part 1)](https://www.youtube.com/watch?v=O98hLTYVN3c&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=9)\n* [Computing Strongly Connected Components (Part 2) (Section 8.6, Part 2)](https://www.youtube.com/watch?v=gbs3UNRJIYk&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=10)\n* [The Structure of the Web (Section 8.7)](https://www.youtube.com/watch?v=7YodysGShlo&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=11)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.util.Stack\nimport java.io.File\n\nclass RecursiveSolution(var adj: MutableMap<Int, MutableList<Int>>, var rev: MutableMap<Int, MutableList<Int>>) {\n    fun topo_sort(): MutableList<Int> {\n        var list = mutableListOf<Int>()\n        var seen = mutableSetOf<Int>()\n        fun go(u: Int) {\n            if (seen.contains(u))\n                return\n            seen.add(u)\n            for (v in rev[u]!!)\n                go(v)\n            list.add(0, u)\n        }\n        for ((u, _) in rev)\n            go(u)\n        return list\n    }\n    fun kosaraju(): MutableList<List<Int>> {\n        var lists = mutableListOf<List<Int>>()\n        var seen = mutableSetOf<Int>()\n        fun go(u: Int, list: MutableList<Int>) {\n            if (seen.contains(u))\n                return\n            list.add(u); seen.add(u)\n            for (v in adj[u]!!)\n                go(v, list)\n        }\n        for (u in topo_sort()) {\n            if (seen.contains(u))\n                continue\n            var list = mutableListOf<Int>()\n            go(u, list)\n            lists.add(list.toList())\n        }\n        return lists\n    }\n}\n\nclass IterativeSolution(var adj: MutableMap<Int, MutableList<Int>>, var rev: MutableMap<Int, MutableList<Int>>) {\n    fun topo_sort(): MutableList<Int> {\n        var list = mutableListOf<Int>()\n        var seen = mutableSetOf<Int>()\n        for ((u, _) in rev) {\n            if (seen.contains(u))\n                continue\n            var stack = Stack<Int>()\n            stack.push(u); seen.add(u)\n            while (!stack.empty()) {\n                var u = stack.last()\n                for (v in rev[u]!!) {\n                    if (!seen.contains(v)) {\n                        stack.push(v); seen.add(v)\n                    }\n                }\n                if (u == stack.last())\n                    list.add(0, stack.pop())\n            }\n        }\n        return list\n    }\n    fun kosaraju(): MutableList<List<Int>> {\n        var lists = mutableListOf<List<Int>>()\n        var seen = mutableSetOf<Int>()\n        for (u in topo_sort()) {\n            if (seen.contains(u))\n                continue\n            var list = mutableListOf<Int>()\n            var stack = Stack<Int>()\n            stack.push(u); seen.add(u)\n            while (!stack.empty()) {\n                var u = stack.last()\n                for (v in adj[u]!!) {\n                    if (!seen.contains(v)) {\n                        stack.push(v); seen.add(v)\n                    }\n                }\n                if (u == stack.last())\n                    list.add(stack.pop())\n            }\n            lists.add(list.toList())\n        }\n        return lists\n    }\n}\n\nfun run(filename: String) {\n    var adj = mutableMapOf<Int, MutableList<Int>>()\n    var rev = mutableMapOf<Int, MutableList<Int>>()\n    File(filename).forEachLine {\n        var (u, v) = it.trim().split(\" \").map{ it.toInt() }\n        if (!adj.contains(u)) adj[u] = mutableListOf(); if (!adj.contains(v)) adj[v] = mutableListOf()\n        if (!rev.contains(u)) rev[u] = mutableListOf(); if (!rev.contains(v)) rev[v] = mutableListOf()\n        adj[u]!!.add(v)\n        rev[v]!!.add(u)\n    }\n    // var solution = RecursiveSolution(adj, rev)\n    var solution = IterativeSolution(adj, rev)\n    var A = solution.kosaraju()\n    A.sortWith(Comparator{ a: List<Int>, b: List<Int> -> b.size - a.size })\n    println(filename + \": \" + A.map{ it.size }.slice(0 until Math.min(A.size, 5)).joinToString(\" \"))\n}\n\nfun main() {\n    run(\"section8.6.5page64.txt\");  // Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\n    run(\"problem8.10test1.txt\");    // Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\n    run(\"problem8.10test2.txt\");    // Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\n    run(\"problem8.10test3.txt\");    // Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\n    run(\"problem8.10test4.txt\");    // Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\n    run(\"problem8.10test5.txt\");    // Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\n    run(\"problem8.10.txt\");         // Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n//    section8.6.5page64.txt: 4 3 3 1\n//    problem8.10test1.txt: 3 3 3\n//    problem8.10test2.txt: 3 3 2\n//    problem8.10test3.txt: 3 3 1 1\n//    problem8.10test4.txt: 7 1\n//    problem8.10test5.txt: 6 3 2 1\n//    problem8.10.txt: 434821 968 459 313 211\n\n}\n```\n\n*Javascript*\n```javascript\nclass BaseSolution {\n    constructor(adj, rev) {\n        this.adj = adj;\n        this.rev = rev;\n    }\n}\n\nclass RecursiveSolution extends BaseSolution {\n    constructor(adj, rev) {\n        super(adj, rev);\n    }\n    topo_sort() {\n        let list = [];\n        let seen = new Set();\n        let go = u => {\n            if (seen.has(u))\n                return;\n            seen.add(u);\n            for (let v of [...this.rev.get(u)])\n                go(v);\n            list.unshift(u);\n        };\n        for (let [u, _] of [...this.rev])\n            go(u);\n        return list;\n    }\n    kosaraju() {\n        let lists = [];\n        let seen = new Set();\n        let go = (u, list) => {\n            if (seen.has(u))\n                return;\n            seen.add(u);\n            list.push(u);\n            for (let v of [...this.adj.get(u)])\n                go(v, list);\n        };\n        for (let u of this.topo_sort()) {\n            let list = [];\n            go(u, list);\n            lists.push([...list]);\n        }\n        lists.sort((a, b) => b.length - a.length);\n        return lists;\n    }\n}\n\nclass IterativeSolution extends BaseSolution {\n    constructor(adj, rev) {\n        super(adj, rev);\n    }\n    topo_sort() {\n        let list = [];\n        let seen = new Set();\n        for (let [u, _] of [...this.rev]) {\n            if (seen.has(u))\n                continue;\n            let stack = [ u ]; seen.add(u);\n            stack.back = () => stack[stack.length - 1];\n            while (stack.length) {\n                let u = stack.back();\n                for (let v of [...this.rev.get(u)])\n                    if (!seen.has(v))\n                        stack.push(v), seen.add(v);\n                if (u == stack.back())\n                    list.unshift(stack.pop());\n            }\n        }\n        return list;\n    }\n    kosaraju() {\n        let lists = [];\n        let seen = new Set();\n        for (let u of this.topo_sort()) {\n            if (seen.has(u))\n                continue;\n            let list = [];\n            let stack = [ u ]; seen.add(u);\n            stack.back = () => stack[stack.length - 1];\n            while (stack.length) {\n                let u = stack.back();\n                for (let v of [...this.adj.get(u)])\n                    if (!seen.has(v))\n                        stack.push(v), seen.add(v);\n                if (u == stack.back())\n                    list.push(stack.pop());\n            }\n            lists.push([...list]);\n        }\n        lists.sort((a, b) => b.length - a.length);\n        return lists;\n    }\n}\n\nlet run = filename => {\n    let adj = new Map(),\n        rev = new Map();\n    let LineByLine = require('n-readlines');\n    let input = new LineByLine(filename);\n    let line;\n    while (line = input.next()) {\n        let [u, v] = String.fromCharCode(...line).split(' ').map(Number);\n        if (!adj.has(u)) adj.set(u, []); if (!adj.has(v)) adj.set(v, []);\n        if (!rev.has(u)) rev.set(u, []); if (!rev.has(v)) rev.set(v, []);\n        adj.get(u).push(v);\n        rev.get(v).push(u);\n    }\n    // let A = new RecursiveSolution(adj, rev).kosaraju();\n    let A = new IterativeSolution(adj, rev).kosaraju();\n    console.log(`${filename}: ${A.slice(0, Math.min(A.length, 5)).map(scc => scc.length).join(' ')}`);\n};\n\nrun('section8.6.5page64.txt')  // Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\nrun('problem8.10test1.txt')    // Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\nrun('problem8.10test2.txt')    // Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\nrun('problem8.10test3.txt')    // Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\nrun('problem8.10test4.txt')    // Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\nrun('problem8.10test5.txt')    // Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\nrun('problem8.10.txt')         // Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n\n//    section8.6.5page64.txt: 4 3 3 1\n//    problem8.10test1.txt: 3 3 3\n//    problem8.10test2.txt: 3 3 2\n//    problem8.10test3.txt: 3 3 1 1\n//    problem8.10test4.txt: 7 1\n//    problem8.10test5.txt: 6 3 2 1\n//    problem8.10.txt: 434821 968 459 313 211\n```\n\n*Python3*\n```python\nfrom collections import deque\nfrom functools import cmp_to_key\n\nclass BaseSolution:\n    def __init__(self, adj, rev):\n        self.adj = adj\n        self.rev = rev\n\nclass RecursiveSolution(BaseSolution):\n    def topo_sort(self):\n        list = deque()\n        seen = set()\n        def go(u):\n            if u in seen:\n                return\n            seen.add(u)\n            for v in self.rev[u]:\n                go(v)\n            list.appendleft(u)\n        for u in self.rev.keys():\n            go(u)\n        return list\n\n    def kosaraju(self):\n        lists = []\n        seen = set()\n        def go(u, list):\n            if u in seen:\n                return\n            seen.add(u)\n            list.append(u)\n            for v in self.adj[u]:\n                go(v, list)\n        for u in self.topo_sort():\n            list = []\n            go(u, list)\n            lists.append(list.copy())\n        lists.sort(key = cmp_to_key(lambda a, b: len(b) - len(a)))\n        return lists\n\nclass IterativeSolution(BaseSolution):\n    def topo_sort(self):\n        list = deque()\n        seen = set()\n        for u in self.rev.keys():\n            if u in seen:\n                continue\n            stack = [ u ]; seen.add(u)\n            while len(stack):\n                u = stack[-1]\n                for v in self.rev[u]:\n                    if v not in seen:\n                        stack.append(v); seen.add(v)\n                if u == stack[-1]:\n                    list.appendleft(stack.pop())\n        return list\n\n    def kosaraju(self):\n        lists = []\n        seen = set()\n        for u in self.topo_sort():\n            if u in seen:\n                continue\n            list = deque()\n            stack = [ u ]; seen.add(u)\n            while len(stack):\n                u = stack[-1]\n                for v in self.adj[u]:\n                    if v not in seen:\n                        stack.append(v); seen.add(v)\n                if u == stack[-1]:\n                    list.appendleft(stack.pop())\n            lists.append(list.copy())\n        lists.sort(key = cmp_to_key(lambda a, b: len(b) - len(a)))\n        return lists\n\ndef run(filename):\n    adj, rev = {}, {}\n    with open(filename) as fin:\n        while True:\n            line = fin.readline().strip()\n            if not line:\n                break\n            u, v = [int(x) for x in line.split()]\n            if u not in adj: adj[u] = []\n            if v not in adj: adj[v] = []\n            if u not in rev: rev[u] = []\n            if v not in rev: rev[v] = []\n            adj[u].append(v)\n            rev[v].append(u)\n    # solution = RecursiveSolution(adj, rev)\n    solution = IterativeSolution(adj, rev)\n    A = solution.kosaraju()\n    print(filename + ': ' + ' '.join(str(len(scc)) for scc in A[:5]))\n\nrun('section8.6.5page64.txt')  # Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\nrun('problem8.10test1.txt')    # Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\nrun('problem8.10test2.txt')    # Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\nrun('problem8.10test3.txt')    # Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\nrun('problem8.10test4.txt')    # Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\nrun('problem8.10test5.txt')    # Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\nrun('problem8.10.txt')         # Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n#    section8.6.5page64.txt: 4 3 3 1\n#    problem8.10test1.txt: 3 3 3\n#    problem8.10test2.txt: 3 3 2\n#    problem8.10test3.txt: 3 3 1 1\n#    problem8.10test4.txt: 7 1\n#    problem8.10test5.txt: 6 3 2 1\n#    problem8.10.txt: 434821 968 459 313 211\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <unordered_map>\n#include <unordered_set>\n#include <queue>\n\nusing namespace std;\n\nusing List = deque<int>;\nusing Lists = deque<List>;\nusing AdjList = unordered_map<int, List>;\nusing Set = unordered_set<int>;\nusing Map = unordered_map<int, int>;\n\nnamespace Base {\n    class Solution {\n    protected:\n        AdjList adj, rev;\n    public:\n        Solution(AdjList& adj, AdjList& rev) : adj{ adj }, rev{ rev } {}\n    };\n}\nnamespace Recursive {\n    struct Solution : public Base::Solution {\n        Solution(AdjList& adj, AdjList& rev) : Base::Solution{ adj, rev } {}\n        Lists kosaraju() {\n            Lists lists;\n            Set seen;\n            using fun = function<void(int, List&)>;\n            fun go = [&](auto u, auto& list) {\n                if (!seen.insert(u).second)\n                    return;\n                list.push_back(u);\n                for (auto v: adj[u])\n                    go(v, list);\n            };\n            for (auto u: topo_sort()) {\n                List list;\n                go(u, list);\n                lists.emplace_back(list);\n            }\n            sort(lists.begin(), lists.end(), [](auto& a, auto& b) { return b.size() < a.size(); });\n            return lists;\n        }\n        List topo_sort() {\n            List list;\n            Set seen;\n            using fun = function<void(int)>;\n            fun go = [&](auto u) {\n                if (!seen.insert(u).second)\n                    return;\n                for (auto v: rev[u])\n                    go(v);\n                list.push_front(u);\n            };\n            for (auto [u, _]: rev)\n                go(u);\n            return list;\n        }\n    };\n}\nnamespace Iterative {\n    struct Solution : public Base::Solution {\n        Solution(AdjList& adj, AdjList& rev) : Base::Solution{ adj, rev } {}\n        Lists kosaraju() {\n            Lists lists;\n            Set seen;\n            for (auto u: topo_sort()) {\n                if (seen.find(u) != seen.end())\n                    continue;\n                List list;\n                List stack{ u }; seen.insert(u);\n                while (stack.size()) {\n                    auto u = stack.back();\n                    for (auto v: adj[u])\n                        if (seen.insert(v).second)\n                            stack.push_back(v);\n                    if (u == stack.back())\n                        list.push_back(u), stack.pop_back();\n                }\n                lists.emplace_back(list);\n            }\n            sort(lists.begin(), lists.end(), [](auto& a, auto& b) { return b.size() < a.size(); });\n            return lists;\n        }\n        List topo_sort() {\n            List list;\n            Set seen;\n            for (auto [u, _]: rev) {\n                if (seen.find(u) != seen.end())\n                    continue;\n                List stack{ u }; seen.insert(u);\n                while (stack.size()) {\n                    auto u = stack.back();\n                    for (auto v: rev[u])\n                        if (seen.insert(v).second)\n                            stack.push_back(v);\n                    if (u == stack.back())\n                        list.push_front(stack.back()), stack.pop_back();\n                }\n            }\n            return list;\n        }\n    };\n}\n\nvoid run(string filename) {\n    int u, v;\n    AdjList adj, rev;\n    fstream fin{ filename };\n    for (string line; fin >> u >> v;) {\n        adj[u].push_back(v);\n        rev[v].push_back(u);\n    }\n    auto A = Iterative::Solution{ adj, rev }.kosaraju();\n    A.resize(min(A.size(), size_t(5)));\n    cout << filename << \": \";\n    for (auto i{ 0 }; i < A.size(); cout << A[i++].size() << \" \");\n    cout << endl;\n}\n\nint main() {\n    run(\"section8.6.5page64.txt\");  // Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\n    run(\"problem8.10test1.txt\");    // Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\n    run(\"problem8.10test2.txt\");    // Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\n    run(\"problem8.10test3.txt\");    // Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\n    run(\"problem8.10test4.txt\");    // Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\n    run(\"problem8.10test5.txt\");    // Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\n    run(\"problem8.10.txt\");         // Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n//    section8.6.5page64.txt: 4 3 3 1\n//    problem8.10test1.txt: 3 3 3\n//    problem8.10test2.txt: 3 3 2\n//    problem8.10test3.txt: 3 3 1 1\n//    problem8.10test4.txt: 7 1\n//    problem8.10test5.txt: 6 3 2 1\n//    problem8.10.txt: 434821 968 459 313 211\n\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Dijkstra\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Shortest Paths and Dijkstra's Algorithm (Sections 9.1 and 9.2, Part 1)](https://www.youtube.com/watch?v=jRlNVmRjdRk&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=12)\n* [Dijkstra's Algorithm: Examples (Section 9.2, Part 2)](https://www.youtube.com/watch?v=ahYhIzLklYo&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=13)\n* [Correctness of Dijkstra's Algorithm (Section 9.3)](https://www.youtube.com/watch?v=sb7j3EW055M&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=14)\n* [Implementation and Running Time of Dijkstra's Algorithm (0:00-4:30) (Section 9.4)](https://www.youtube.com/watch?v=00LtSn_PQjc&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=15)\n* [Data Structures Overview (Section 10.1)](https://www.youtube.com/watch?v=cMrQxxrKg8I&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=16)\n* [Heaps: Operations and Applications (Sections 10.2 and 10.3)](https://www.youtube.com/watch?v=mNYHDv7SbDI&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=17)\n* [Speeding Up Dijkstra's Algorithm With Heaps (4:30-26:27) (Section 10.4)](https://www.youtube.com/watch?v=00LtSn_PQjc&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=15)\n* [Heaps: Implementation Details (Section 10.5)](https://www.youtube.com/watch?v=6VI5kJu8Mv4&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=19&t=0s)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.io.File\nimport java.util.PriorityQueue\n\nvar INF = (1e9 + 7).toInt()\n\ninterface BaseSolution {\n    fun run(filename: String, queries: Array<Int>): String\n}\n\nclass NaiveSolution : BaseSolution {\n    fun dijkstra(E: List<Triple<Int, Int, Int>>): MutableMap<Int, Int> {\n        var dist = mutableMapOf<Int, Int>()\n        var seen = mutableSetOf<Int>()\n        var start = 1\n        dist[start] = 0; seen.add(start)\n        var found: Boolean;\n        do {\n            found = false\n            var best_v = INF\n            var best_w = INF\n            for ((u, v, w) in E) {\n                if (!seen.contains(u) || seen.contains(v))\n                    continue\n                found = true\n                if (best_w > dist[u]!! + w) {\n                    best_v = v\n                    best_w = dist[u]!! + w\n                }\n            }\n            var v = best_v\n            var w = best_w\n            dist[v] = w; seen.add(v)\n        } while (found)\n        return dist\n    }\n    override fun run(filename: String, queries: Array<Int>): String {\n        var E = mutableListOf<Triple<Int, Int, Int>>()\n        File(filename).forEachLine {\n            var words = it.trim().split(\"\\t\")\n            var u = words[0].toInt()\n            for (i in 1 until words.size) {\n                var (v, w) = words[i].split(\",\").map{ it.toInt() }\n                E.add(Triple(u, v, w))\n            }\n        }\n        var dist = dijkstra(E.toList())\n        return queries.map{ dist[it] }.joinToString(\" \")\n    }\n}\n\nclass HeapSolution : BaseSolution {\n    fun dijkstra(adj: MutableMap<Int, MutableList<Pair<Int, Int>>>): MutableMap<Int, Int> {\n        var dist = mutableMapOf<Int, Int>()\n        var seen = mutableSetOf<Int>()\n        var start = 1\n        dist[start] = 0\n        var q = PriorityQueue<Pair<Int, Int>>(Comparator{ a: Pair<Int, Int>, b: Pair<Int, Int> -> a.first.compareTo(b.first) })\n        q.add(Pair(0, start))\n        while (0 < q.size) {\n            var (cost, u) = q.poll()\n            if (seen.contains(u))\n                continue\n            dist[u] = cost; seen.add(u)\n            for ((w, v) in adj[u]!!) {\n                if (seen.contains(v))\n                    continue\n                q.add(Pair(cost + w, v))\n            }\n        }\n        return dist\n    }\n    override fun run(filename: String, queries: Array<Int>): String {\n        var adj = mutableMapOf<Int, MutableList<Pair<Int, Int>>>()\n        File(filename).forEachLine {\n            var words = it.trim().split(\"\\t\")\n            var u = words[0].toInt()\n            if (!adj.contains(u))\n                adj[u] = mutableListOf()\n            for (i in 1 until words.size) {\n                var (v, w) = words[i].split(\",\").map{ it.toInt() }\n                adj[u]!!.add(Pair(w, v))\n            }\n        }\n        var dist = dijkstra(adj)\n        return queries.map{ dist[it] }.joinToString(\" \")\n    }\n}\n\nfun run(solution: BaseSolution) {\n    println(solution.run(\"problem9.8test.txt\", arrayOf(1, 2, 3, 4, 5, 6, 7, 8)))\n    println(solution.run(\"problem9.8.txt\", arrayOf(7, 37, 59, 82, 99, 115, 133, 165, 188, 197)))\n}\n\nfun main() {\n    run(NaiveSolution())\n    //    0 1 2 3 4 4 3 2\n    //    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n    run(HeapSolution())\n    //    0 1 2 3 4 4 3 2\n    //    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n}\n```\n\n*Javascript*\n```javascript\nlet LineByLine = require('n-readlines');\n\nlet INF = Number(1e9 + 7);\n\nclass NaiveSolution {\n    dijkstra(E) {\n        let dist = new Map();\n        let seen = new Set();\n        let start = 1;\n        dist[start] = 0; seen.add(start);\n        for (;;) {\n            let found = false;\n            let best_v = INF,\n                best_w = INF;\n            for (let [u, v, w] of E) {\n                if (!seen.has(u) || seen.has(v))\n                    continue;\n                found = true;\n                if (best_w > dist[u] + w)\n                    best_v = v,\n                    best_w = dist[u] + w;\n            }\n            if (!found)\n                break;\n            let [v, w] = [best_v, best_w];\n            dist[v] = w; seen.add(v);\n        }\n        return dist;\n    }\n    run(filename, queries) {\n        let E = [];\n        let input = new LineByLine(filename);\n        let line;\n        while (line = input.next()) {\n            let words = String.fromCharCode(...line).trim().split(/\\s+/);\n            let u = Number(words[0]);\n            for (let i = 1; i < words.length; ++i) {\n                let [v, w] = words[i].split(',').map(Number);\n                E.push([ u, v, w ]);\n            }\n        }\n        let dist = this.dijkstra(E);\n        return queries.map(x => dist[x]).join(' ');\n    }\n}\n\nlet heapkey = x => Array.isArray(x) ? x[0] : x;\nlet heappush = (A, x, f = Math.min) => {\n    let P = i => Math.floor((i - 1) / 2);  // parent\n    A.push(x);\n    let N = A.length,\n        i = N - 1;\n    while (0 < i && heapkey(A[i]) == f(heapkey(A[i]), heapkey(A[P(i)]))) {\n        [A[i], A[P(i)]] = [A[P(i)], A[i]];\n        i = P(i);\n    }\n};\nlet heappop = (A, f = Math.min) => {\n    let L = i => 2 * i + 1,  // children\n        R = i => 2 * i + 2;\n    let N = A.length,\n        i = 0;\n    let top = A[0];\n    [A[0], A[N - 1]] = [A[N - 1], A[0]], A.pop(), --N;\n    let ok = true;\n    do {\n        ok = true;\n        let left = f == Math.min ? Infinity : -Infinity,\n            right = left;\n        if (L(i) < N && heapkey(A[i]) != f(heapkey(A[i]), heapkey(A[L(i)]))) ok = false, left  = heapkey(A[L(i)]);\n        if (R(i) < N && heapkey(A[i]) != f(heapkey(A[i]), heapkey(A[R(i)]))) ok = false, right = heapkey(A[R(i)]);\n        if (!ok) {\n            let j = left == f(left, right) ? L(i) : R(i);\n            [A[i], A[j]] = [A[j], A[i]];\n            i = j;\n        }\n    } while (!ok);\n    return top;\n};\n\nclass HeapSolution {\n    dijkstra(adj) {\n        let dist = {};\n        let seen = new Set();\n        let start = 1;\n        let q = [[ 0, start ]];\n        while (q.length) {\n            let [cost, u] = heappop(q);\n            if (seen.has(u))\n                continue;\n            dist[u] = cost, seen.add(u);\n            for (let [w, v] of (adj[u] || []))\n                heappush(q, [ dist[u] + w, v ]);\n        }\n        return dist;\n    }\n    run(filename, queries) {\n        let adj = {};\n        let input = new LineByLine(filename);\n        let line;\n        while (line = input.next()) {\n            let words = String.fromCharCode(...line).trim().split('\\t');\n            let u = Number(words[0]);\n            if (!(u in adj))\n                adj[u] = [];\n            for (let i = 1; i < words.length; ++i) {\n                let [v, w] = words[i].split(',').map(Number);\n                adj[u].push([ w, v ]);\n            }\n        }\n        let dist = this.dijkstra(adj);\n        return queries.map(x => dist[x]).join(' ');\n    }\n}\n\nlet run = solution => {\n    console.log(solution.run('problem9.8test.txt', [1, 2, 3, 4, 5, 6, 7, 8]));\n    console.log(solution.run('problem9.8.txt', [7, 37, 59, 82, 99, 115, 133, 165, 188, 197]));\n};\n\nrun(new NaiveSolution());\n//    0 1 2 3 4 4 3 2\n//    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n\nrun(new HeapSolution());\n//    0 1 2 3 4 4 3 2\n//    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n```\n\n*Python3*\n```python\nfrom abc import ABC, abstractmethod\nfrom heapq import heappush, heappop\n\nINF = int(1e9 + 7)\n\nclass BaseSolution(ABC):\n    @abstractmethod\n    def run(self, filename, queries):\n        raise NotImplementedError\n\nclass NaiveSolution(BaseSolution):\n    def dijkstra(self, E):\n        dist = {}\n        seen = set()\n        start = 1\n        dist[start] = 0; seen.add(start)\n        while True:\n            found = False\n            best_v = INF\n            best_w = INF\n            for u, v, w in E:\n                if u not in seen or v in seen:\n                    continue\n                found = True\n                if best_w > dist[u] + w:\n                    best_v = v\n                    best_w = dist[u] + w\n            if not found:\n                break\n            v, w = best_v, best_w\n            dist[v] = w; seen.add(v)\n        return dist\n    def run(self, filename, queries):\n        E = []\n        with open(filename) as fin:\n            while True:\n                line = fin.readline()\n                if not line:\n                    break\n                words = line.split()\n                u = int(words[0])\n                for i in range(1, len(words)):\n                    v, w = map(int, words[i].split(','))\n                    E.append([ u, v, w ])\n        dist = self.dijkstra(E)\n        return ' '.join(str(dist[x]) for x in queries)\n\nclass HeapSolution(BaseSolution):\n    def dijkstra(self, adj, start = 1):\n        dist = {}\n        seen = set()\n        q = [[ 0, start ]]\n        while len(q):\n            cost, u = heappop(q)\n            if u in seen:\n                continue\n            dist[u] = cost; seen.add(u)\n            for w, v in adj[u]:\n                if v not in seen:\n                    heappush(q, [ dist[u] + w, v ])\n        return dist\n    def run(self, filename, queries):\n        adj = {}\n        with open(filename) as fin:\n            while True:\n                line = fin.readline()\n                if not line:\n                    break\n                words = line.split()\n                u = int(words[0])\n                if u not in adj:\n                    adj[u] = []\n                for i in range(1, len(words)):\n                    v, w = map(int, words[i].split(','))\n                    adj[u].append([ w, v ])\n        dist = self.dijkstra(adj)\n        return ' '.join(str(dist[x]) for x in queries)\n\ndef run(solution):\n    print(solution.run('problem9.8test.txt', [1, 2, 3, 4, 5, 6, 7, 8]))\n    print(solution.run('problem9.8.txt', [7, 37, 59, 82, 99, 115, 133, 165, 188, 197]))\n\nrun(NaiveSolution())\n#    0 1 2 3 4 4 3 2\n#    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n\nrun(HeapSolution())\n#    0 1 2 3 4 4 3 2\n#    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n#include <unordered_set>\n#include <queue>\n\nusing namespace std;\n\nusing Queries = vector<int>;\nusing Distance = unordered_map<int, int>;\nusing Set = unordered_set<int>;\n\nclass BaseSolution {\nprotected:\n    static constexpr auto INF = int(1e9 + 7);\npublic:\n    virtual string run(string filename, Queries&& queries) = 0;\n};\n\nclass NaiveSolution : public BaseSolution {\n    using Edge = tuple<int, int, int>;\n    using Edges = vector<Edge>;\npublic:\n    Distance dijkstra(Edges& E) {\n        Distance dist;\n        Set seen;\n        auto start{ 1 };\n        dist[start] = 0, seen.insert(start);\n        for (;;) {\n            auto found = false;\n            auto best_v = INF,\n                 best_w = INF;\n            for (auto [u, v, w]: E) {\n                if (seen.find(u) == seen.end() || seen.find(v) != seen.end())\n                    continue;\n                found = true;\n                if (best_w > dist[u] + w)\n                    best_v = v,\n                    best_w = dist[u] + w;\n            }\n            if (!found)\n                break;\n            auto [v, w] = tie(best_v, best_w);\n            dist[v] = w, seen.insert(v);\n        }\n        return dist;\n    }\n    string run(string filename, Queries&& queries) {\n        Edges E;\n        fstream fin{ filename };\n        string line;\n        int u, v, w;\n        char _;\n        while (getline(fin, line)) {\n            istringstream is{ line };\n            for (is >> u; is >> v >> _ >> w; E.push_back({ u, v, w }));\n        }\n        auto dist = dijkstra(E);\n        ostringstream os;\n        transform(queries.begin(), queries.end(), ostream_iterator<int>(os, \" \"), [&](auto x) { return dist[x]; });\n        return os.str();\n    }\n};\n\nclass HeapSolution : public BaseSolution {\n    using Pair = pair<int, int>;\n    using Pairs = vector<Pair>;\n    using AdjList = unordered_map<int, Pairs>;\n    priority_queue<Pair, Pairs, std::greater<Pair>> q;\npublic:\n    Distance dijkstra(AdjList& adj) {\n        Distance dist;\n        Set seen;\n        for (auto [u, _]: adj)\n            dist[u] = INF;\n        auto start{ 1 };\n        q.push({ 0, start });\n        while (q.size()) {\n            auto [cost, u] = q.top(); q.pop();\n            if (!seen.insert(u).second)\n                continue;\n            dist[u] = cost;\n            for (auto [w, v]: adj[u])\n                if (seen.find(v) == seen.end())\n                    q.push({ dist[u] + w, v });\n        }\n        return dist;\n    }\n    string run(string filename, Queries&& queries) {\n        AdjList adj;\n        fstream fin{ filename };\n        string line;\n        int u, v, w;\n        char _;\n        while (getline(fin, line)) {\n            istringstream is{ line };\n            for (is >> u; is >> v >> _ >> w; adj[u].push_back({ w, v }));\n        }\n        auto dist = dijkstra(adj);\n        ostringstream os;\n        transform(queries.begin(), queries.end(), ostream_iterator<int>(os, \" \"), [&](auto x) { return dist[x]; });\n        return os.str();\n    }\n};\n\nvoid run(BaseSolution&& solution) {\n    cout << \"problem9.8test.txt: \" << solution.run(\"problem9.8test.txt\", Queries{1, 2, 3, 4, 5, 6, 7, 8 }) << endl\n         << \"problem9.8.txt      \" << solution.run(\"problem9.8.txt\", Queries{7, 37, 59, 82, 99, 115, 133, 165, 188, 197 }) << endl;\n}\n\nint main() {\n    run(NaiveSolution());\n//    problem9.8test.txt: 0 1 2 3 4 4 3 2\n//    problem9.8.txt      2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n\n    run(HeapSolution());\n//    problem9.8test.txt: 0 1 2 3 4 4 3 2\n//    problem9.8.txt      2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n    return 0;\n}\n```\n\n</details>\n\n---\n\n# Part 3: Greedy Algorithms and Dynamic Programming\n\n<br/>\n<a href=\"https://www.amazon.com/dp/0999282948\" target=\"_blank\">\n    <img src=\"images/ai3large.jpg\" />\n</a>\n\n---\n\n### Greedy Scheduling\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Introduction to Greedy Algorithms (Section 13.1)](https://www.youtube.com/watch?v=NTFmxA3qgoo&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=4&t=0s)\n* [A Scheduling Problem (Section 13.2)](https://www.youtube.com/watch?v=jK3d_GLzKQA&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=5)\n* [Developing a Greedy Algorithm (Section 13.3)](https://www.youtube.com/watch?v=AJOTgHYjL6A&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=6)\n* [Scheduling: Correctness Proof (Part 1) (Section 13.4, Part 1)](https://www.youtube.com/watch?v=oyLxydVkQwo&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=7)\n* [Scheduling: Correctness Proof (Part 2) (Section 13.4, Part 2)](https://www.youtube.com/watch?v=fmXVPYxmFsU&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=8)\n* [Scheduling: Correctness Proof (Part 3) (Section 13.4, Part 3)](https://www.youtube.com/watch?v=aBFG5PghX68&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=9)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\n\ndata class Job(val weight: Long, val length: Long)\n\nclass Solution {\n    fun minSum(jobs: Array<Job>): Pair<Long, Long> {\n        class Diff: Comparator<Job> {\n            override fun compare(a: Job?, b: Job?): Int {\n                if (a == null || b == null)\n                    return 0\n                var first = a.weight - a.length\n                var second = b.weight - b.length\n                return if (first == second) b.weight.compareTo(a.weight) else second.compareTo(first) // sort by descending difference, break ties in favor of jobs with larger weights\n            }\n        }\n        class Ratio: Comparator<Job> {\n            override fun compare(a: Job?, b: Job?): Int {\n                if (a == null || b == null)\n                    return 0\n                var first = a.weight.toDouble() / a.length\n                var second = b.weight.toDouble() / b.length\n                return if (first == second) b.weight.compareTo(a.weight) else second.compareTo(first) // sort by descending difference, break ties in favor of jobs with larger weights\n            }\n        }\n        return Pair(calcSum(jobs, Diff()), calcSum(jobs, Ratio()))\n    }\n    private fun calcSum(jobs: Array<Job>, comp: Comparator<Job>): Long {\n        jobs.sortWith(comp)\n        var time: Long = 0\n        var total: Long = 0\n        jobs.forEach { job ->\n            time += job.length\n            total += job.weight * time\n        }\n        return total\n    }\n}\n\nfun run(filename: String) {\n    var jobs = mutableListOf<Job>()\n    var first = true\n    File(filename).forEachLine {\n        if (!first) {\n            var words = it.trim().split(\" \").map{ it.toLong() }\n            var (weight, length) = words\n            jobs.add(Job(weight, length))\n        } else {\n            first = false\n        }\n    }\n    var (diff, ratio) = Solution().minSum(jobs.toTypedArray())\n    println(\"$diff, $ratio\") // sub-optimal, optimal\n}\n\nfun main() {\n    run(\"problem13.4test1.txt\") // 23, 22\n    run(\"problem13.4test2.txt\") // 68615, 67247\n    run(\"problem13.4.txt\")      // 69119377652, 67311454237\n}\n```\n\n*Javascript*\n```javascript\nlet LineByLine = require('n-readlines');\n\nclass Job {\n    constructor(weight, length) {\n        this.weight = weight;\n        this.length = length;\n    }\n}\n\nclass Solution {\n    minSum(jobs) {\n        let diff = (a, b) => {\n            let first = a.weight - a.length,\n                second = b.weight - b.length;\n            return first == second ? b.weight - a.weight : second - first; // sort by descending difference, break ties in favor of jobs with larger weights\n        };\n        let ratio = (a, b) => {\n            let first = a.weight / a.length,\n                second = b.weight / b.length;\n            return first == second ? b.weight - a.weight : second - first; // sort by descending ratio, break ties in favor of jobs with larger weights\n        };\n        return [ this._calcSum(jobs, diff), this._calcSum(jobs, ratio) ];\n    }\n    _calcSum(jobs, comp, time = 0) {\n        jobs.sort((a, b) => comp(a, b));\n        return jobs.reduce((total, job) => total + job.weight * (time += job.length), 0);\n    }\n}\n\nlet run = filename => {\n    let jobs = [];\n    let input = new LineByLine(filename);\n    let line = input.next(); // N\n    while (line = input.next()) {\n        let words = String.fromCharCode(...line).trim().split(' ');\n        let [weight, length] = words.map(Number);\n        jobs.push(new Job(weight, length));\n    }\n    let [diff, ratio] = new Solution().minSum(jobs);\n    console.log(`${diff}, ${ratio}`); // sub-optimal, optimal\n};\n\nrun('problem13.4test1.txt'); // 23, 22\nrun('problem13.4test2.txt'); // 68615, 67247\nrun('problem13.4.txt');      // 69119377652, 67311454237\n```\n\n*Python3*\n```python\nfrom functools import cmp_to_key\n\nclass Job:\n    def __init__(self, weight, length):\n        self.weight = weight\n        self.length = length\n\nclass Solution:\n    def minSum(self, jobs):\n        def diff(a, b):\n            first = a.weight - a.length\n            second = b.weight - b.length\n            return b.weight - a.weight if first == second else second - first # sort by descending difference, break ties in favor of jobs with larger weights\n        def ratio(a, b):\n            first = a.weight / a.length\n            second = b.weight / b.length\n            return b.weight - a.weight if first == second else second - first # sort by descending difference, break ties in favor of jobs with larger weights\n        return [ self._calcSum(jobs, diff), self._calcSum(jobs, ratio) ]\n    def _calcSum(self, jobs, comp, time = 0, total = 0):\n        jobs.sort(key = cmp_to_key(lambda a, b: comp(a, b)))\n        for job in jobs:\n            time += job.length\n            total += job.weight * time\n        return total\n\ndef run(filename):\n    jobs = []\n    with open(filename) as fin:\n        line = fin.readline() # N\n        while True:\n            line = fin.readline().strip()\n            if not line:\n                break\n            words = line.split()\n            weight, length = [int(x) for x in words]\n            jobs.append(Job(weight, length))\n    diff, ratio = Solution().minSum(jobs)\n    print(f'{diff}, {ratio}') # sub-optimal, optimal\n\nrun('problem13.4test1.txt') # 23, 22\nrun('problem13.4test2.txt') # 68615, 67247\nrun('problem13.4.txt')      # 69119377652, 67311454237\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <numeric>\n\nusing namespace std;\n\nusing LL = long long;\nstruct Job {\n    LL weight, length;\n    Job(LL weight, LL length) : weight{ weight }, length{ length } {}\n};\nusing Jobs = vector<Job>;\n\nclass Solution {\npublic:\n    using Pair = pair<LL, LL>; // sub-optimal, optimal\n    Pair minSum(Jobs& jobs) {\n        auto diff = [](auto& a, auto& b) {\n            auto first = a.weight - a.length,\n                 second = b.weight - b.length;\n            return first == second ? b.weight < a.weight : second < first; // sort by descending difference, break ties in favor of jobs with larger weights\n        };\n        auto ratio = [](auto& a, auto& b) {\n            auto first = double(a.weight) / a.length,\n                 second = double(b.weight) / b.length;\n            return first == second ? b.weight < a.weight : second < first; // sort by descending ratio, break ties in favor of jobs with larger weights\n        };\n        return { calcSum(jobs, diff), calcSum(jobs, ratio) };\n    }\nprivate:\n    template<typename Comp>\n    LL calcSum(Jobs& jobs, Comp comp, LL time = 0LL) {\n        sort(jobs.begin(), jobs.end(), comp);\n        return accumulate(jobs.begin(), jobs.end(), 0LL, [&](LL total, auto& job) {\n            return total += job.weight * (time += job.length);\n        });\n    }\n};\n\nvoid run(const string& filename) {\n    Jobs jobs;\n    LL N, weight, length;\n    fstream fin{ filename };\n    for (fin >> N; fin >> weight >> length; jobs.emplace_back(Job{ weight, length }));\n    auto [diff, ratio] = Solution().minSum(jobs);\n    cout << diff << \", \" << ratio << endl;\n}\n\nint main() {\n    run(\"problem13.4test1.txt\"); // 23, 22\n    run(\"problem13.4test2.txt\"); // 68615, 67247\n    run(\"problem13.4.txt\");      // 69119377652, 67311454237\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Huffman Codes\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Codes (Section 14.1)](https://www.youtube.com/watch?v=K3WZhFZT6Y0&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=33)\n* [Codes as Trees (Section 14.2)](https://www.youtube.com/watch?v=HESrV5VDu8c&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=34)\n* [Huffman's Greedy Algorithm (Part 1) (Section 14.3, Part 1)](https://www.youtube.com/watch?v=NM6FZB7IfS8&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=35)\n* [Huffman's Greedy Algorithm (Part 2) (Section 14.3, Part 2)](https://www.youtube.com/watch?v=PPmn9osMDyI&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=36)\n* [Huffman's Algorithm: Correctness Proof (Part 1) (Section 14.4, Part 1)](https://www.youtube.com/watch?v=jibgSDjWxdI&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=37)\n* [Huffman's Algorithm: Correctness Proof (Part 2) (Section 14.4, Part 2)](https://www.youtube.com/watch?v=dAjCcqZKYf4&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=38)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\nimport java.util.PriorityQueue\nimport java.util.Queue\nimport java.util.LinkedList\n\nvar INF = (1e9 + 7).toInt()\n\ndata class Tree(val weight: Int, val left: Tree? = null, val right: Tree? = null)\n\n/*\nfun encode(A: List<Int>): Tree {\n    var q = PriorityQueue<Tree>(Comparator{ a: Tree, b: Tree -> a.weight.compareTo(b.weight) })\n    for (weight in A)\n        q.add(Tree(weight))\n    while (1 < q.size) {\n        var a = q.poll()\n        var b = q.poll()\n        var c = Tree(a.weight + b.weight, a, b)\n        q.add(c)\n    }\n    return q.poll()\n}\n*/\n\n/*\n * Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n * of a sorting subroutine, followed by a linear amount of additional work.\n */\nfun encode(A: MutableList<Int>): Tree {\n    A.sort()\n    var first: Queue<Tree> = LinkedList<Tree>(A.map{ weight -> Tree(weight) }.toList())\n    var second: Queue<Tree> = LinkedList<Tree>()\n    var next = mutableListOf<Tree>()\n    while (1 < first.size + second.size) {\n        next.clear()\n        do {\n            if (0 < first.size && 0 < second.size) {\n                if (first.peek().weight < second.peek().weight) next.add(first.poll()) else next.add(second.poll())\n            }\n            else if (0 < first.size) next.add(first.poll())\n            else if (0 < second.size) next.add(second.poll())\n        } while (next.size < 2)\n        var (a, b) = next\n        var c = Tree(a.weight + b.weight, a, b)\n        second.add(c)\n    }\n    return second.poll()\n}\n\nfun run(filename: String): Pair<Int, Int> {\n    var A = mutableListOf<Int>()\n    var first = true\n    File(filename).forEachLine {\n        if (!first) {\n            var weight = it.trim().toInt()\n            A.add(weight)\n        } else {\n            first = false\n        }\n    }\n    var tree = encode(A.toMutableList())\n    var lo = INF\n    var hi = -INF\n    fun go(root: Tree? = tree, depth: Int = 0) {\n        if (root == null)\n            return\n        var isLeaf = { node: Tree? -> node?.left == null && node?.right == null }\n        if (isLeaf(root)) {\n            lo = Math.min(lo, depth)\n            hi = Math.max(hi, depth)\n        } else {\n            go(root.left, depth + 1)\n            go(root.right, depth + 1)\n        }\n    }\n    go()\n    return Pair(lo, hi)\n}\n\nfun main() {\n    for (filename in listOf(\"problem14.6test1.txt\", \"problem14.6test2.txt\", \"problem14.6.txt\")) {\n        var (lo, hi) = run(filename)\n        println(\"$filename: $lo, $hi\") // min, max encoding length in the corresponding optimal prefix-free tree\n    }\n}\n\n//    problem14.6test1.txt: 2, 5\n//    problem14.6test2.txt: 3, 6\n//    problem14.6.txt: 9, 19\n```\n\n*Javascript*\n```javascript\nlet LineByLine = require('n-readlines');\n\nclass Tree {\n    constructor(weight, left = null, right = null) {\n        this.weight = weight;\n        this.left = left;\n        this.right = right;\n    }\n}\n\n/*\nlet key = x => Array.isArray(x) ? x[0] : x;\nlet heappush = (A, x, f = Math.min) => {\n    let P = i => Math.floor((i - 1) / 2);  // parent\n    A.push(x);\n    let N = A.length,\n        i = N - 1;\n    while (0 < i && key(A[i]) == f(key(A[i]), key(A[P(i)]))) {\n        [A[i], A[P(i)]] = [A[P(i)], A[i]];\n        i = P(i);\n    }\n};\nlet heappop = (A, f = Math.min) => {\n    let L = i => 2 * i + 1,  // children\n        R = i => 2 * i + 2;\n    let N = A.length,\n        i = 0;\n    let top = A[0];\n    [A[0], A[N - 1]] = [A[N - 1], A[0]], A.pop(), --N;\n    let ok;\n    do {\n        ok = true;\n        let left = f == Math.min ? Infinity : -Infinity,\n            right = left;\n        if (L(i) < N && key(A[i]) != f(key(A[i]), key(A[L(i)]))) ok = false, left  = key(A[L(i)]);\n        if (R(i) < N && key(A[i]) != f(key(A[i]), key(A[R(i)]))) ok = false, right = key(A[R(i)]);\n        if (!ok) {\n            let j = left == f(left, right) ? L(i) : R(i);\n            [A[i], A[j]] = [A[j], A[i]];\n            i = j;\n        }\n    } while (!ok);\n    return top;\n};\n\nlet encode = A => {\n    let T = [];\n    for (let weight of A)\n        heappush(T, [ weight, new Tree(weight) ]);\n    while (1 < T.length) {\n        let [ a, b ] = [ heappop(T), heappop(T) ];\n        let c = [ a[0] + b[0], new Tree(a[0] + b[0], a[1], b[1]) ];\n        heappush(T, c);\n    }\n    return T[0][1];\n};\n*/\n\n/*\n * Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n * of a sorting subroutine, followed by a linear amount of additional work.\n */\nlet encode = A => {\n    A.sort((a, b) => a - b)\n    let first = A.map(weight => new Tree(weight)),\n        second = [];\n    while (1 < first.length + second.length) {\n        let next = [];\n        while (next.length < 2) {\n            if (first.length && second.length) {\n                next.push(first[0].weight < second[0].weight ? first.shift() : second.shift());\n            }\n            else if (first.length) next.push(first.shift());\n            else if (second.length) next.push(second.shift());\n        }\n        let [a, b] = next;\n        let c = new Tree(a.weight + b.weight, a, b);\n        second.push(c);\n    }\n    return second.shift();\n};\n\nlet run = filename => {\n    let A = [];\n    let input = new LineByLine(filename);\n    let line;\n    line = input.next(); // N\n    while (line = input.next()) {\n        let weight = Number(String.fromCharCode(...line).trim());\n        A.push(weight);\n    }\n    let tree = encode(A);\n    let [lo, hi] = [Infinity, -Infinity];\n    let go = (root = tree, depth = 0) => {\n        if (!root)\n            return;\n        let isLeaf = root => !root.left && !root.right;\n        if (isLeaf(root))\n            lo = Math.min(lo, depth),\n            hi = Math.max(hi, depth);\n        else\n            go(root.left, depth + 1),\n            go(root.right, depth + 1);\n    };\n    go();\n    return [ lo, hi ];\n}\n\nfor (let filename of [ 'problem14.6test1.txt', 'problem14.6test2.txt', 'problem14.6.txt' ]) {\n    let [lo, hi] = run(filename);\n    console.log(`${filename}: ${lo}, ${hi}`); // min, max encoding length in the corresponding optimal prefix-free tree\n}\n\n//    problem14.6test1.txt: 2, 5\n//    problem14.6test2.txt: 3, 6\n//    problem14.6.txt: 9, 19\n```\n\n*Python3*\n```python\nclass Tree:\n    def __init__(self, weight, left = None, right = None):\n        self.weight = weight\n        self.left = left\n        self.right = right\n    def __lt__(self, other):\n        return self.weight < other.weight\n\n#\n# priority queue\n#\n\n# from heapq import heappush\n# from heapq import heappop\n# def encode(A):\n#     T = []\n#     for weight in A:\n#         heappush(T, Tree(weight))\n#     while 1 < len(T):\n#         a, b = heappop(T), heappop(T)\n#         c = Tree(a.weight + b.weight, a, b)\n#         heappush(T, c)\n#     return heappop(T)\n\n#\n# Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n# of a sorting subroutine, followed by a linear amount of additional work.\n#\nfrom collections import deque\ndef encode(A):\n    A.sort()\n    first, second = deque([Tree(weight) for weight in A]), deque()\n    while 1 < len(first) + len(second):\n        next = []\n        while len(next) < 2:\n            if len(first) and len(second):\n                next.append(first.popleft() if first[0].weight < second[0].weight else second.popleft())\n            elif len(first): next.append(first.popleft())\n            elif len(second): next.append(second.popleft())\n        a, b = next\n        c = Tree(a.weight + b.weight, a, b)\n        second.append(c)\n    return second.popleft()\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        N = int(fin.readline())\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            weight = int(line.strip())\n            A.append(weight)\n    tree = encode(A)\n    lo, hi = float('inf'), float('-inf')\n    def go(root = tree, depth = 0):\n        nonlocal lo, hi\n        if not root:\n            return\n        isLeaf = lambda root: not root.left and not root.right\n        if isLeaf(root):\n            lo = min(lo, depth)\n            hi = max(hi, depth)\n        else:\n            go(root.left, depth + 1)\n            go(root.right, depth + 1)\n    go()\n    return [ lo, hi ]\n\nfor filename in [ 'problem14.6test1.txt', 'problem14.6test2.txt', 'problem14.6.txt' ]:\n    lo, hi = run(filename)\n    print(f'{filename}: {lo}, {hi}') # min, max encoding length in the corresponding optimal prefix-free tree\n\n#    problem14.6test1.txt: 2, 5\n#    problem14.6test2.txt: 3, 6\n#    problem14.6.txt: 9, 19\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <queue>\n#include <list>\n\n#define PRIORITY_QUEUE    // O(N * logN)\n#ifndef PRIORITY_QUEUE\n#define TWO_QUEUES        // O(N)\n#endif\n\nusing namespace std;\nusing LL = long long;\nusing Weight = LL;\nusing Weights = vector<Weight>;\n\nstruct Tree;\nusing TreePtr = shared_ptr<Tree>;\nstruct Tree {\n    Weight weight;\n    TreePtr left, right;\n    Tree(Weight weight, TreePtr left = nullptr, TreePtr right = nullptr) :\n            weight{ weight }, left{ left }, right{ right } {}\n};\nusing TreePtrs = vector<TreePtr>;\n\n#ifdef PRIORITY_QUEUE\nstruct Comp {\n    size_t operator()(const TreePtr& a, const TreePtr& b) const {\n        return b->weight < a->weight;\n    }\n};\nusing Queue = priority_queue<TreePtr, TreePtrs, Comp>;\nTreePtr encode(const Weights& A, Queue q = {}) {\n    for (auto weight: A)\n        q.emplace(make_shared<Tree>(weight));\n    while (1 < q.size()) {\n        auto a = q.top(); q.pop();\n        auto b = q.top(); q.pop();\n        auto c = make_shared<Tree>(a->weight + b->weight, a, b);\n        q.emplace(c);\n    }\n    return q.top();\n}\n#else // TWO_QUEUES\n/*\n * Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n * of a sorting subroutine, followed by a linear amount of additional work.\n */\nusing Queue = queue<TreePtr>;\nTreePtr encode(Weights& A, Queue first = {}, Queue second = {}) {\n    sort(A.begin(), A.end());\n    for (auto weight: A)\n        first.push(make_shared<Tree>(weight));\n    TreePtrs next;\n    auto takeFirst = [&]() { next.push_back(first.front()), first.pop(); };\n    auto takeSecond = [&]() { next.push_back(second.front()), second.pop(); };\n    while (1 < first.size() + second.size()) {\n        next.clear();\n        do {\n            if (first.size() && second.size()) {\n                if (first.front()->weight < second.front()->weight) takeFirst(); else takeSecond();\n            }\n            else if (first.size()) takeFirst();\n            else if (second.size()) takeSecond();\n        } while (next.size() < 2);\n        auto [a, b] = tie(next[0], next[1]);\n        auto c = make_shared<Tree>(a->weight + b->weight, a, b);\n        second.emplace(c);\n    }\n    return second.front();\n}\n#endif\n\nusing MinMax = pair<LL, LL>;\nconstexpr auto Min = numeric_limits<LL>::min();\nconstexpr auto Max = numeric_limits<LL>::max();\nMinMax run(const string& filename) {\n    Weights A; // weight of each symbol\n    fstream fin{ filename };\n    LL N, weight;\n    for (fin >> N; fin >> weight; A.push_back(weight));\n    auto tree = encode(A);\n    LL lo = Max,\n       hi = Min;\n    using fun = function<void(TreePtr, int)>;\n    fun go = [&](auto root, LL depth) {\n        if (!root)\n            return;\n        auto isLeaf = [](auto root) { return !root->left && !root->right; };\n        if (isLeaf(root))\n            lo = min(lo, depth),\n            hi = max(hi, depth);\n        else\n            go(root->left, depth + 1),\n            go(root->right, depth + 1);\n    };\n    go(tree, 0);\n    return make_pair(lo, hi);\n}\n\nint main() {\n    for (auto& filename: { \"problem14.6test1.txt\", \"problem14.6test2.txt\", \"problem14.6.txt\" }) {\n        auto [lo, hi] = run(filename);\n        cout << filename << \": \" << lo << \", \" << hi << endl; // min, max encoding length in the corresponding optimal prefix-free tree\n    }\n//    problem14.6test1.txt: 2, 5\n//    problem14.6test2.txt: 3, 6\n//    problem14.6.txt: 9, 19\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Prim's MST\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Minimum Spanning Trees: Problem Definition (Section 15.1)](https://www.youtube.com/watch?v=tDj9BkaQDO8&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=10)\n* [Prim's MST Algorithm (Section 15.2)](https://www.youtube.com/watch?v=jsvOPssDVJA&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=11)\n* [Speeding Up Prim's Algorithm via Heaps (Part 1) (Section 15.3, Part 1)](https://www.youtube.com/watch?v=cDtQnXMZGtg&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=15)\n* [Speeding Up Prim's Algorithm via Heaps (Part 2) (Section 15.3, Part 2)](https://www.youtube.com/watch?v=jGR_LAwGLGk&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=16)\n* [Prim's Algorithm: Correctness Proof (Part 1) (Section 15.4, Part 1) [Note: this video provides an alternative treatment to that in the book.]](https://www.youtube.com/watch?v=pGUzn3S7bp4&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=12)\n* [Prim's Algorithm: Correctness Proof (Part 2) (Section 15.4, Part 2) [Note: this video provides an alternative treatment to that in the book.]](https://www.youtube.com/watch?v=199ItGt4mE8&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=13)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\nimport java.util.PriorityQueue\nimport java.util.Random\n\nfun prim(N: Int, adj: MutableMap<Int, MutableList<Pair<Int, Int>>>): Int {\n    var total: Int = 0\n    var start = Random().nextInt(N) + 1\n    var q = PriorityQueue<Pair<Int, Int>>(Comparator{ a: Pair<Int, Int>, b: Pair<Int, Int> -> a.first.compareTo(b.first) })\n    var seen = mutableSetOf<Int>(start)\n    for ((w, v) in adj[start]!!)\n        q.add(Pair(w, v))\n    while (0 < q.size) {\n        var (cost, u) = q.poll()\n        if (seen.contains(u))\n            continue\n        total += cost; seen.add(u)\n        for ((w, v) in adj[u]!!)\n            if (!seen.contains(v))\n                q.add(Pair(w, v))\n    }\n    return total\n}\n\nfun run(filename: String) {\n    var N: Int = 0\n    var adj = mutableMapOf<Int, MutableList<Pair<Int, Int>>>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (u, v, w) = line.split(\" \").map{ it.toInt() }\n            if (!adj.contains(u)) adj[u] = mutableListOf<Pair<Int, Int>>()\n            if (!adj.contains(v)) adj[v] = mutableListOf<Pair<Int, Int>>()\n            adj[u]!!.add(Pair(w, v))\n            adj[v]!!.add(Pair(w, u))\n        } else {\n            var (numVertex, _) = line.split(\" \").map{ it.toInt() }\n            N = numVertex\n            first = false\n        }\n    }\n    var cost = prim(N, adj)\n    println(\"$filename: $cost\")\n}\n\nfun main() {\n    run(\"problem15.9test.txt\") // problem15.9test.txt: 14\n    run(\"problem15.9.txt\")     // problem15.9.txt: -3612829\n}\n```\n\n*Javascript*\n```javascript\nlet LineByLine = require('n-readlines');\n\nlet key = x => Array.isArray(x) ? x[0] : x;\nlet heappush = (A, x, f = Math.min) => {\n    let P = i => Math.floor((i - 1) / 2);  // parent\n    A.push(x);\n    let N = A.length,\n        i = N - 1;\n    while (0 < i && key(A[i]) == f(key(A[i]), key(A[P(i)]))) {\n        [A[i], A[P(i)]] = [A[P(i)], A[i]];\n        i = P(i);\n    }\n};\nlet heappop = (A, f = Math.min) => {\n    let L = i => 2 * i + 1,  // children\n        R = i => 2 * i + 2;\n    let N = A.length,\n        i = 0;\n    let top = A[0];\n    [A[0], A[N - 1]] = [A[N - 1], A[0]], A.pop(), --N;\n    let ok;\n    do {\n        ok = true;\n        let left = f == Math.min ? Infinity : -Infinity,\n            right = left;\n        if (L(i) < N && key(A[i]) != f(key(A[i]), key(A[L(i)]))) ok = false, left  = key(A[L(i)]);\n        if (R(i) < N && key(A[i]) != f(key(A[i]), key(A[R(i)]))) ok = false, right = key(A[R(i)]);\n        if (!ok) {\n            let j = left == f(left, right) ? L(i) : R(i);\n            [A[i], A[j]] = [A[j], A[i]];\n            i = j;\n        }\n    } while (!ok);\n    return top;\n};\n\nlet prim = (N, adj, q = [], seen = new Set(), total = 0) => {\n    let start = Math.ceil(N * Math.random());\n    seen.add(start);\n    for (let [w, v] of adj.get(start))\n        heappush(q, [w, v]);\n    while (q.length) {\n        let [cost, u] = heappop(q);\n        if (seen.has(u))\n            continue;\n        total += cost; seen.add(u);\n        for (let [w, v] of adj.get(u))\n            if (!seen.has(v))\n                heappush(q, [w, v]);\n    }\n    return total;\n};\n\nlet run = filename => {\n    let adj = new Map();\n    let input = new LineByLine(filename);\n    let line = input.next();\n    let [N, M] = String.fromCharCode(...line).trim().split(' ').map(Number);\n    while (line = input.next()) {\n        let [u, v, w] = String.fromCharCode(...line).trim().split(' ').map(Number);\n        if (!adj.has(u)) adj.set(u, []);\n        if (!adj.has(v)) adj.set(v, []);\n        adj.get(u).push([w, v]);\n        adj.get(v).push([w, u]);\n    }\n    let cost = prim(N, adj);\n    console.log(`${filename}: ${cost}`);\n}\n\nrun('problem15.9test.txt') // problem15.9test.txt: 14\nrun('problem15.9.txt')     // problem15.9.txt: -3612829\n```\n\n*Python3*\n```python\nfrom random import randint\nfrom heapq import heappush, heappop\n\ndef prim(N, adj, total = 0):\n    q = []\n    seen = set()\n    start = randint(1, N); seen.add(start)\n    for w, v in adj[start]:\n        heappush(q, [w, v])\n    while q:\n        cost, u = heappop(q)\n        if u in seen:\n            continue\n        total += cost; seen.add(u)\n        for w, v in adj[u]:\n            if v not in seen:\n                heappush(q, [w, v])\n    return total\n\ndef run(filename):\n    adj = {}\n    first = True\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            words = line.split()\n            if not first:\n                u, v, w = [int(x) for x in words]\n                if u not in adj: adj[u] = []\n                if v not in adj: adj[v] = []\n                adj[u].append([w, v])\n                adj[v].append([w, u])\n            else:\n                N, M = [int(x) for x in words]\n                first = False\n    cost = prim(N, adj)\n    print(f'{filename}: {cost}')\n\nrun('problem15.9test.txt') # problem15.9test.txt: 14\nrun('problem15.9.txt')     # problem15.9.txt: -3612829\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <unordered_set>\n#include <unordered_map>\n#include <queue>\n#include <random>\n\nusing namespace std;\nusing Pair = pair<int, int>;\nusing Pairs = vector<Pair>;\nusing AdjList = unordered_map<int, Pairs>;\nusing Queue = priority_queue<Pair, Pairs, std::greater<Pair>>;\nusing Set = unordered_set<int>;\n\nconstexpr auto INF = int(1e9 + 7);\n\nint getRandom(int N) {\n    default_random_engine generator;\n    uniform_int_distribution<int> distribution(1, N);\n    return distribution(generator);\n}\n\nint prim(int N, AdjList& adj, Queue q = {}, Set seen = {}, int total = 0) {\n    auto start = getRandom(N);\n    seen.insert(start);\n    for (auto [w, v]: adj[start])\n        q.push({ w, v });\n    while (q.size()) {\n        auto [cost, u] = q.top(); q.pop();\n        if (!seen.insert(u).second)\n            continue;\n        total += cost;\n        for (auto [w, v]: adj[u])\n            if (seen.find(v) == seen.end())\n                q.push({ w, v });\n    }\n    return total;\n}\n\nvoid run(const string& filename) {\n    AdjList adj;\n    fstream fin{ filename };\n    int N, M; fin >> N >> M; // N vertices and M edges\n    int u, v, w;             // edge u -> v of weight w\n    while (fin >> u >> v >> w) {\n        adj[u].emplace_back(w, v);\n        adj[v].emplace_back(w, u);\n    }\n    auto cost = prim(N, adj);\n    cout << filename << \": \" << cost << endl;\n}\n\nint main() {\n    run(\"problem15.9test.txt\"); // problem15.9test.txt: 14\n    run(\"problem15.9.txt\");     // problem15.9.txt: -3612829\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Kruskal's MST\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Minimum Spanning Trees: Problem Definition (Section 15.1)](https://www.youtube.com/watch?v=tDj9BkaQDO8&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=10)\n* [Kruskal's MST Algorithm (Section 15.5)](https://www.youtube.com/watch?v=SZuCspj5AJc&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=17)\n* [Speeding Up Kruskal's Algorithm via Union-Find (Part 1) (Section 15.6, Part 1)](https://www.youtube.com/watch?v=fItEZEVyJKE&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=19)\n* [Speeding Up Kruskal's Algorithm via Union-Find (Part 2) (Section 15.6, Part 2) [Note: this video provides an alternative treatment to that in the book.]](https://www.youtube.com/watch?v=jY-vY6d18W4&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=20)\n* [Lazy Unions (Section 15.6, Part 3) [Note: this video is closer to the union-find implementation in the book.]](https://www.youtube.com/watch?v=bRwTSPIEI9k&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=24)\n* [Kruskal's Algorithm: Correctness Proof (Section 15.7) [Note: this video provides an alternative treatment to that in the book.]](https://www.youtube.com/watch?v=AjLjL0Rp10g&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=18)\n* [Application: Single-Link Clustering (Section 15.8)](https://www.youtube.com/watch?v=MSSzOs1X4K8&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=22)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\n\nfun kruskal(E: MutableList<Triple<Int, Int, Int>>): Int {\n    var total: Int = 0\n    var M = E.size\n    var P = IntArray(M) { it } // 🙂 parent representatives of 1..M disjoint sets\n    fun find(x: Int): Int {\n        P[x] = if (P[x] == x) x else find(P[x])\n        return P[x]\n    }\n    fun union(a: Int, b: Int): Boolean {\n        var x = find(a)\n        var y = find(b)\n        if (x == y)\n            return false\n        P[x] = y // 🎲 arbitrary choice\n        return true\n    }\n    E.sortWith(Comparator{ a, b -> a.third.compareTo(b.third) }) // sort edges by nondecreasing weight\n    for ((u, v, w) in E)\n        if (union(u, v))\n            total += w\n    return total\n}\n\nfun run(filename: String) {\n    var E = mutableListOf<Triple<Int, Int, Int>>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (u, v, w) = line.trim().split(\" \").map{ it.toInt() }\n            E.add(Triple(u, v, w))\n        } else {\n            first = false // ignore first line with N vertices and M edges\n        }\n    }\n    var cost = kruskal(E)\n    println(\"$filename: $cost\")\n}\n\nfun main() {\n    run(\"problem15.9test.txt\") // problem15.9test.txt: 14\n    run(\"problem15.9.txt\")     // problem15.9.txt: -3612829\n}\n```\n\n*Javascipt*\n```javascript\nlet LineByLine = require('n-readlines');\n\nlet kruskal = E => {\n    let total = 0;\n    let M = E.length;\n    let P = [...Array(M).keys()]; // 🙂 parent representatives of 1..M disjoint sets\n    let find = x => P[x] = P[x] == x ? x : find(P[x]);\n    let union = (a, b) => {\n        a = find(a);\n        b = find(b);\n        if (a == b)\n            return false;\n        P[a] = b; // 🎲 arbitrary choice\n        return true;\n    };\n    E.sort((first, second) => { // sort edges by nondecreasing weight\n        let [u1, v1, w1] = first,\n            [u2, v2, w2] = second;\n        return w1 - w2;\n    });\n    for (let [u, v, w] of E)\n        if (union(u, v))\n            total += w;\n    return total;\n};\n\nlet run = filename => {\n    let E = [];\n    let input = new LineByLine(filename);\n    let line = input.next(); // ignore first line with N vertices and M edges\n    while (line = input.next()) {\n        let [u, v, w] = String.fromCharCode(...line).trim().split(' ').map(Number);\n        E.push([ u, v, w ]);\n    }\n    let cost = kruskal(E);\n    console.log(`${filename}: ${cost}`);\n};\n\nrun('problem15.9test.txt'); // problem15.9test.txt: 14\nrun('problem15.9.txt');     // problem15.9.txt: -3612829\n```\n\n*Python3*\n```python\nfrom functools import cmp_to_key\n\ndef kruskal(E, total = 0):\n    M = len(E)\n    P = [i for i in range(M)] # 🙂 parent representatives of 1..M disjoint sets\n    def find(x):\n        P[x] = P[x] if P[x] == x else find(P[x])\n        return P[x]\n    def union(a, b):\n        a = find(a)\n        b = find(b)\n        if a == b:\n            return False\n        P[a] = b # 🎲 arbitary choice\n        return True\n    E.sort(key = cmp_to_key(lambda first, second: first[2] - second[2])) # sort edges by nondecreasing weight\n    for u, v, w in E:\n        if union(u, v):\n            total += w\n    return total\n\ndef run(filename):\n    E = []\n    first = True\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            values = [int(x) for x in line.strip().split()]\n            if not first:\n                u, v, w = values # edge u -> v of weight w\n                E.append([ u, v, w ])\n            else:\n                first = False # ignore first line with N vertices and M edges\n    cost = kruskal(E)\n    print(f'{filename}: {cost}')\n\nrun('problem15.9test.txt') # problem15.9test.txt: 14\nrun('problem15.9.txt')     # problem15.9.txt: -3612829\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <unordered_map>\n#include <numeric>\n\nusing namespace std;\nusing Edge = tuple<int, int, int>;\nusing Edges = vector<Edge>;\nusing Parents = vector<int>;\nusing fun = function<int(int)>;\n\nint kruskal(Edges& E, int total = 0) {\n    auto M = E.size();\n    Parents P(M); iota(P.begin(), P.end(), 0); // 🙂 parent representatives of 1..M disjoint sets\n    fun find = [&](auto x) {\n         return P[x] = P[x] == x ? x : find(P[x]);\n    };\n    auto join = [&](auto a, auto b) {\n        a = find(a);\n        b = find(b);\n        if (a == b)\n            return false;\n        P[a] = b; // 🎲 arbitrary choice\n        return true;\n    };\n    sort(E.begin(), E.end(), [](auto& first, auto& second) { // sort edges by nondecreasing weight\n        auto [u1, v1, w1] = first;\n        auto [u2, v2, w2] = second;\n        return w1 < w2;\n    });\n    for (auto [u, v, w]: E)\n        if (join(u, v))\n            total += w;\n    return total;\n}\n\nvoid run(const string& filename, Edges E = {}) {\n    fstream fin{ filename };\n    int N, M; fin >> N >> M; // ignore first line with N vertices and M edges\n    int u, v, w;             // edge u -> v of weight w\n    while (fin >> u >> v >> w)\n        E.emplace_back(u, v, w);\n    auto cost = kruskal(E);\n    cout << filename << \": \" << cost << endl;\n}\n\nint main() {\n    run(\"problem15.9test.txt\"); // problem15.9test.txt: 14\n    run(\"problem15.9.txt\");     // problem15.9.txt: -3612829\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Weighted Independent Set\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [The Weighted Independent Set Problem (Section 16.1)](https://www.youtube.com/watch?v=0awkct8SkxA&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=39)\n* [A Linear-Time Algorithm for WIS in Path Graphs (Part 1) (Section 16.2, Part 1)](https://www.youtube.com/watch?v=pLOkbHGRsv0&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=40)\n* [A Linear-Time Algorithm for WIS in Path Graphs (Part 2) (Section 16.2, Part 2)](https://www.youtube.com/watch?v=Im_zjFkZDCY&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=41)\n* [A Reconstruction Algorithm (Section 16.3)](https://www.youtube.com/watch?v=W2ncNfksRqo&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=42)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\n\nfun topDown(A: MutableList<Long>): Long {\n    var N = A.size\n    var m = mutableMapOf<Int, Long>()\n    fun go(i: Int = N - 1): Long {\n        if (m.contains(i))                    // 🤔 memo\n            return m[i]!!\n        if (i < 0) {                          // 🛑 empty set\n            m[i] = 0\n            return 0\n        }\n        if (i == 0) {                         // 🛑 single set\n            m[i] = A[0]\n            return A[0]\n        }\n        var include = go(i - 2) + A[i]        // ✅ include A[i]\n        var exclude = go(i - 1)               // 🚫 exclude A[i]\n        m[i] = Math.max(include, exclude)     // 🎯 best\n        return m[i]!!\n    }\n    return go()\n}\n\nfun bottomUp(A: MutableList<Long>): Long {\n    var N = A.size\n    var dp = LongArray(N + 1)                 // 🤔 memo\n    dp[0] = 0                                 // 🛑 empty set\n    dp[1] = A[0]                              // 🛑 single set\n    for (i in 2..N) {\n        var include = dp[i - 2] + A[i - 1]    // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        var exclude = dp[i - 1]               // 🚫 exclude A[i]\n        dp[i] = Math.max(include, exclude)    // 🎯 best\n    }\n    return dp[N]\n}\n\nfun bottomUpMemOpt(A: MutableList<Long>): Long {\n    var N = A.size\n    var a: Long = 0                     // 🤔 memo + 🛑 empty set\n    var b: Long = A[0]                  // 🤔 memo + 🛑 single set\n    var c: Long = -1\n    for (i in 2..N) {\n        var include = a + A[i - 1]      // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        var exclude = b                 // 🚫 exclude A[i]\n        c = Math.max(include, exclude)  // 🎯 best\n        a = b; b = c                    // 👈 slide window\n    }\n    return c\n}\n\nfun run(filename: String) {\n    var A = mutableListOf<Long>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            A.add(line.toLong())\n        } else {\n            first = false\n        }\n    }\n    var a = topDown(A)\n    var b = bottomUp(A)\n    var c = bottomUpMemOpt(A)\n    assert(a == b && b == c) // 💩 sanity check\n    println(\"$filename: $a\")\n}\n\nfun main() {\n    run(\"problem16.6test.txt\")  // problem16.6test.txt: 2617\n    run(\"problem16.6.txt\")      // problem16.6.txt: 2955353732\n}\n```\n\n*Javascript*\n```javascript\nconst assert = require('assert');\nconst LineByLine = require('n-readlines');\n\nlet top_down = (A, m = {}) => {\n    let N = A.length;\n    let go = (i = N - 1) => {\n        if (m[i])                                     // 🤔 memo\n            return m[i];\n        if (i < 0) return m[i] = 0;                   // 🛑 empty set\n        if (!i) return m[i] = A[0];                   // 🛑 single set\n        let include = go(i - 2) + A[i],               // ✅ include A[i]\n            exclude = go(i - 1);                      // 🚫 exclude A[i]\n        return m[i] = Math.max(include, exclude);     // 🎯 best\n    };\n    return go();\n};\n\nlet bottom_up = A => {\n    let N = A.length;\n    let dp = Array(N + 1);                    // 🤔 memo\n    dp[0] = 0;                                // 🛑 empty set\n    dp[1] = A[0];                             // 🛑 single set\n    for (let i = 2; i <= N; ++i) {\n        let include = dp[i - 2] + A[i - 1],   // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n            exclude = dp[i - 1];              // 🚫 exclude A[i]\n        dp[i] = Math.max(include, exclude);   // 🎯 best\n    }\n    return dp[N];\n};\n\nlet bottom_up_memopt = A => {\n    let N = A.length;\n    let a = 0,                           // 🤔 memo + 🛑 empty set\n        b = A[0],                        // 🤔 memo + 🛑 single set\n        c = -1;\n    for (let i = 2; i <= N; ++i) {\n        let include = a + A[i - 1],      // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n            exclude = b;                 // 🚫 exclude A[i]\n        c = Math.max(include, exclude);  // 🎯 best\n        a = b, b = c;                    // 👈 slide window\n    }\n    return c;\n};\n\nlet run = filename => {\n    let A = [];\n    let input = new LineByLine(filename);\n    let line;\n    let first = true;\n    while (line = input.next()) {\n        if (!first) {\n            A.push(Number(line.toString('ascii')));\n        } else {\n            first = false;\n        }\n    }\n    let a = top_down(A),\n        b = bottom_up(A),\n        c = bottom_up_memopt(A);\n    assert(a == b && b == c); // 💩 sanity check\n    console.log(`${filename}: ${a}`);\n};\n\nrun('problem16.6test.txt');  // problem16.6test.txt: 2617\nrun('problem16.6.txt');      // problem16.6.txt: 2955353732\n```\n\n*Python3*\n```python\nfrom functools import lru_cache\n\ndef top_down(A):\n    N = len(A)\n    @lru_cache                        # 🤔 memo\n    def go(i = N - 1):\n        if i < 0: return 0            # 🛑 empty set\n        if i == 0: return A[0]        # 🛑 single set\n        include = go(i - 2) + A[i]    # ✅ include A[i]\n        exclude = go(i - 1)           # 🚫 exclude A[i]\n        return max(include, exclude)  # 🎯 best\n    return go()\n\ndef bottom_up(A):\n    N = len(A)\n    dp = [0] * (N + 1)                  # 🤔 memo\n    dp[0] = 0                           # 🛑 empty set\n    dp[1] = A[0]                        # 🛑 single set\n    for i in range(2, N + 1):\n        include = dp[i - 2] + A[i - 1]  # ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        exclude = dp[i - 1]             # 🚫 exclude A[i]\n        dp[i] = max(include, exclude)   # 🎯 best\n    return dp[N]\n\ndef bottom_up_memopt(A):\n    N = len(A)\n    a = 0                          # 🤔 memo + 🛑 empty set\n    b = A[0]                       # 🤔 memo + 🛑 single set\n    c = -1\n    for i in range(2, N + 1):\n        include = a + A[i - 1]     # ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        exclude = b                # 🚫 exclude A[i]\n        c = max(include, exclude)  # 🎯 best\n        a = b; b = c               # 👈 slide window\n    return c\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        first = True\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            x = int(line)\n            if not first:\n                A.append(x)\n            else:\n                first = False\n                N = x\n    a = top_down(A)\n    b = bottom_up(A)\n    c = bottom_up_memopt(A)\n    assert(a == b and b == c) # 💩 sanity check\n    print(f'{filename}: {a}')\n\nrun('problem16.6test.txt')     # problem16.6test.txt: 2617\nrun('problem16.6.txt')         # problem16.6.txt: 2955353732\n```\n\n*C++*\n```cpp\n#include <cassert>\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <unordered_map>\n\nusing namespace std;\nusing LL = long long;\nusing List = vector<LL>;\nusing Map = unordered_map<int, LL>;\n\nnamespace TopDown {\n    LL best(List& A, Map m = {}) {\n        int N = A.size();\n        using fun = function<LL(int)>;\n        fun go = [&](auto i) {\n            if (m[i]) return m[i];                // 🤔 memo\n            if (i < 0) return m[i] = 0LL;         // 🛑 empty set\n            if (!i) return m[i] = A[0];           // 🛑 single set\n            auto include = go(i - 2) + A[i],      // ✅ include A[i]\n                 exclude = go(i - 1);             // 🚫 exclude A[i]\n            return m[i] = max(include, exclude);  // 🎯 best\n        };\n        return go(N - 1);\n    }\n}\nnamespace BottomUp {\n    LL best(List& A, Map m = {}) {\n        int N = A.size();\n        List dp(N + 1);                           // 🤔 memo\n        dp[0] = 0LL;                              // 🛑 empty set\n        dp[1] = A[0];                             // 🛑 single set\n        for (auto i{ 2 }; i <= N; ++i) {\n            auto include = dp[i - 2] + A[i - 1],  // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n                 exclude = dp[i - 1];             // 🚫 exclude A[i]\n            dp[i] = max(include, exclude);        // 🎯 best\n        }\n        return dp[N];\n    }\n}\n\nnamespace BottomUpMemOpt {\n    LL best(List& A) {\n        int N = A.size();\n        LL a = 0LL,                       // 🤔 memo + 🛑 empty set\n           b = A[0],                      // 🤔 memo + 🛑 single set\n           c = -1;\n        for (auto i{ 2 }; i <= N; ++i) {\n            auto include = a + A[i - 1],  // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n                 exclude = b;             // 🚫 exclude A[i]\n            c = max(include, exclude);    // 🎯 best\n            a = b, b = c;                 // 👈 slide window\n        }\n        return c;\n    }\n}\n\nvoid run(const string& filename) {\n    List A;\n    fstream fin{ filename };\n    int N; fin >> N;\n    copy_n(istream_iterator<LL>(fin), N, back_inserter(A));\n    auto a = TopDown::best(A),\n         b = BottomUp::best(A),\n         c = BottomUpMemOpt::best(A);\n    assert(a == b && b == c); // 💩 sanity check\n    cout << filename << \": \" << a << endl;\n}\n\nint main() {\n    run(\"problem16.6test.txt\");  // problem16.6test.txt: 2617\n    run(\"problem16.6.txt\");      // problem16.6.txt: 2955353732\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Knapsack\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Principles of Dynamic Programming (Section 16.4)](https://www.youtube.com/watch?v=27nK8C-GCPM&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=43)\n* [The Knapsack Problem (Part 1) (Section 16.5, Part 1)](https://www.youtube.com/watch?v=jlHIBaUizOU&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=44)\n* [The Knapsack Problem (Part 2) (Section 16.5, Part 2)](https://www.youtube.com/watch?v=KX_6OF8X6HQ&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=45)\n* [The Knapsack Problem (Part 3) (Section 16.5, Part 3)](https://www.youtube.com/watch?v=1dRUOZKcvYs&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=46)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\n\nvar INF = (1e9 + 7).toInt()\n\nfun top_down(A: List<Pair<Int, Int>>, K: Int): Int {\n    var N = A.size\n    var m = mutableMapOf<String, Int>()\n    fun go(i: Int = 0, k: Int = K): Int {\n        if (i == N)                                                                 // 🛑 empty set\n            return 0\n        var key = \"$i,$k\"\n        if (m.contains(key))                                                        // 🤔 memo\n            return m[key]!!\n        var (value, weight) = A[i]\n        var include = if (0 <= k - weight) go(i + 1, k - weight) + value else -INF  // ✅ include A[i]\n        var exclude = go(i + 1, k)                                                  // 🚫 exclude A[i]\n        m[key] = Math.max(include, exclude)                                         // 🎯 best\n        return m[key]!!\n    }\n    return go()\n}\n\nfun bottom_up(A: List<Pair<Int, Int>>, K: Int): Int {\n    var N = A.size\n    var dp = Array(N + 1){ Array(K + 1){ -INF } }                                       // 🤔 memo\n    for (k in 0..K)                                                                     // 🛑 empty set\n        dp[0][k] = 0\n    for (i in 1..N) {\n        for (k in 0..K) {\n            var (value, weight) = A[i - 1]\n            var include = if (0 <= k - weight) dp[i - 1][k - weight] + value else -INF  // ✅ include A[i]\n            var exclude = dp[i - 1][k]                                                  // 🚫 exclude A[i]\n            dp[i][k] = Math.max(include, exclude)                                       // 🎯 best\n        }\n    }\n    return dp[N][K]\n}\n\nfun bottom_up_memopt(A: List<Pair<Int, Int>>, K: Int): Int {\n    var N = A.size\n    var pre = Array(K + 1) { 0 }                                                  // 🤔 memo + 🛑 empty set\n    for (i in 1..N) {\n        var cur = Array(K + 1) { -INF }\n        for (k in 0..K) {\n            var (value, weight) = A[i - 1]\n            var include = if (0 <= k - weight) pre[k - weight] + value else -INF  // ✅ include A[i]\n            var exclude = pre[k]                                                  // 🚫 exclude A[i]\n            cur[k] = Math.max(include, exclude)                                   // 🎯 best\n        }\n        pre = cur.also { cur = pre }\n    }\n    return pre[K]\n}\n\nfun run(filename: String) {\n    var A = mutableListOf<Pair<Int, Int>>()\n    var K = 0\n    var N = 0\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (value, weight) = line.trim().split(\" \").map{ it -> it.toInt() }\n            A.add(Pair(value, weight))\n        } else {\n            var (a, b) = line.trim().split(\" \").map{ it -> it.toInt() }\n            K = a\n            N = b\n            first = false\n        }\n    }\n    var a = top_down(A, K)\n    var b = bottom_up(A, K)\n    var c = bottom_up_memopt(A, K)\n    assert(a == b && b == c) // 💩 sanity check\n    println(\"$filename: $a\")\n}\n\nfun main() {\n    run(\"problem16.7test.txt\")  // problem16.7test.txt: 2493893\n}\n```\n\n*Javascript*\n```javascript\nconst assert = require('assert');\nconst LineByLine = require('n-readlines');\n\nlet top_down = (A, K, m = new Map()) => {\n    let N = A.length;\n    let go = (i = 0, k = K) => {\n        if (i == N)                                                                 // 🛑 empty set\n            return 0;\n        let key = `${i},${k}`;\n        if (m.has(key))                                                             // 🤔 memo\n            return m.get(key);\n        let [value, weight] = A[i];\n        let include = 0 <= k - weight ? go(i + 1, k - weight) + value : -Infinity,  // ✅ include A[i]\n            exclude = go(i + 1, k);                                                 // 🚫 exclude A[i]\n        return m.set(key, Math.max(include, exclude))                               // 🎯 best\n                .get(key);\n    };\n    return go();\n};\n\nlet bottom_up = (A, K) => {\n    let N = A.length;\n    let dp = [...Array(N + 1)].map(_ => Array(K + 1).fill(-Infinity));                  // 🤔 memo\n    for (let k = 0; k < K; dp[0][k++] = 0);                                             // 🛑 empty set\n    for (let i = 1; i <= N; ++i) {\n        for (let k = 0; k <= K; ++k) {\n            let [value, weight] = A[i - 1];\n            let include = 0 <= k - weight ? dp[i - 1][k - weight] + value : -Infinity,  // ✅ include A[i]\n                exclude = dp[i - 1][k];                                                 // 🚫 exclude A[i]\n            dp[i][k] = Math.max(include, exclude);                                      // 🎯 best\n        }\n    }\n    return dp[N][K];\n};\n\nlet bottom_up_memopt = (A, K) => {\n    let N = A.length;\n    let pre = Array(K + 1).fill(0);                                               // 🤔 memo + 🛑 empty set\n    for (let i = 1; i <= N; ++i) {\n        let cur = Array(K + 1).fill(-Infinity);\n        for (let k = 0; k <= K; ++k) {\n            let [value, weight] = A[i - 1];\n            let include = 0 <= k - weight ? pre[k - weight] + value : -Infinity,  // ✅ include A[i]\n                exclude = pre[k];                                                 // 🚫 exclude A[i]\n            cur[k] = Math.max(include, exclude);                                  // 🎯 best\n        }\n        [pre, cur] = [cur, pre];\n    }\n    return pre[K];\n};\n\nlet run = filename => {\n    let A = [];\n    const input = new LineByLine(filename)\n    let [K, N] = input.next().toString().split(' ').map(Number);  // K capacity, N items\n    let line;\n    while (line = input.next()) {\n        let [value, weight] = line.toString().split(' ').map(Number);\n        A.push([value, weight]);\n    }\n    let a = top_down(A, K),\n        b = bottom_up(A, K),\n        c = bottom_up_memopt(A, K);\n    assert(a == b && b == c); // 💩 sanity check\n    console.log(`${filename}: ${a}`);\n};\n\nrun('problem16.7test.txt')  // problem16.7test.txt: 2493893\n```\n\n*Python3*\n```python\nfrom functools import lru_cache\n\ndef top_down(A, K):\n    N = len(A)\n    total = [0] * N\n    @lru_cache(maxsize = None)                                                          # 🤔 memo\n    def go(i = 0, k = K):\n        if i == N:                                                                      # 🛑 empty set\n            return 0\n        value, weight = A[i]\n        include = go(i + 1, k - weight) + value if 0 <= k - weight else float('-inf')  # ✅ include A[i]\n        exclude = go(i + 1, k)                                                         # 🚫 exclude A[i]\n        return max(include, exclude)                                                   # 🎯 best\n    return go()\n\ndef bottom_up(A, K):\n    N = len(A)\n    dp = [[float('-inf')] * (K + 1) for _ in range(N + 1)]                                 # 🤔 memo\n    for j in range(K):                                                                     # 🛑 empty set\n        dp[0][j] = 0\n    for i in range(1, N + 1):\n        for k in range(1, K + 1):\n            value, weight = A[i - 1]\n            include = dp[i - 1][k - weight] + value if 0 <= k - weight else float('-inf')  # ✅ include A[i]\n            exclude = dp[i - 1][k]                                                         # 🚫 exclude A[i]\n            dp[i][k] = max(include, exclude)                                               # 🎯 best\n    return dp[N][K]\n\ndef bottom_up_memopt(A, K):\n    N = len(A)\n    pre = [0] * (K + 1)                                                              # 🤔 memo + 🛑 empty set\n    for i in range(1, N + 1):\n        cur = [float('-inf')] * (K + 1)\n        for k in range(1, K + 1):\n            value, weight = A[i - 1]\n            include = pre[k - weight] + value if 0 <= k - weight else float('-inf')  # ✅ include A[i]\n            exclude = pre[k]                                                         # 🚫 exclude A[i]\n            cur[k] = max(include, exclude)                                           # 🎯 best\n        pre, cur = cur, pre\n    return pre[K]\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        line = fin.readline()\n        [K, N] = [int(word) for word in line.split()]  # K capacity, N items\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            value, weight = [int(word) for word in line.split()]\n            A.append([value, weight])\n    a = top_down(A, K)\n    b = bottom_up(A, K)\n    c = bottom_up_memopt(A, K)\n    assert(a == b and b == c) # 💩 sanity check\n    print(f'{filename}: {a}')\n\nrun('problem16.7test.txt')  # problem16.7test.txt: 2493893\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n\nusing namespace std;\nusing Pair = pair<int, int>;  // value, weight\nusing Pairs = vector<Pair>;\nusing fun = function<int(int, int)>;\nusing Map = unordered_map<string, int>;\n\nint INF = 1e9 + 7;\n\nint top_down(Pairs& A, int K, Map m = {}) {\n    auto N = A.size();\n    fun go = [&](auto i, auto k) {\n        if (i == N)                                                             // 🛑 empty set\n            return 0;\n        stringstream key; key << i << \",\" << k;\n        if (m.find(key.str()) != m.end())                                       // 🤔 memo\n            return m[key.str()];\n        auto [value, weight] = A[i];\n        auto include = 0 <= k - weight ? go(i + 1, k - weight) + value : -INF,  // ✅ include A[i]\n             exclude = go(i + 1, k);                                            // 🚫 exclude A[i]\n        return m[key.str()] = max(include, exclude);                            // 🎯 best\n    };\n    return go(0, K);\n}\n\nint bottom_up(Pairs& A, int K) {\n    auto N = A.size();\n    using VI = vector<int>;\n    using VVI = vector<VI>;\n    VVI dp(N + 1, VI(K + 1, -INF));                                                // 🤔 memo\n    for (auto k{ 0 }; k < K; dp[0][k++] = 0);                                      // 🛑 empty set\n    for (auto i{ 1 }; i <= N; ++i) {\n        for (auto k{ 0 }; k <= K; ++k) {\n            auto [value, weight] = A[i - 1];\n            auto include = 0 <= k - weight ? dp[i - 1][k - weight] +value : -INF,  // ✅ include A[i]\n                 exclude = dp[i - 1][k];                                           // 🚫 exclude A[i]\n            dp[i][k] = max(include, exclude);                                      // 🎯 best\n        }\n    }\n    return dp[N][K];\n}\n\nint bottom_up_memopt(Pairs& A, int K) {\n    auto N = A.size();\n    using VI = vector<int>;\n    VI pre(K + 1, 0);                                                        // 🤔 memo + 🛑 empty set\n    for (auto i{ 1 }; i <= N; ++i) {\n        VI cur(K + 1, -INF);\n        for (auto k{ 0 }; k <= K; ++k) {\n            auto [value, weight] = A[i - 1];\n            auto include = 0 <= k - weight ? pre[k - weight] +value : -INF,  // ✅ include A[i]\n            exclude = pre[k];                                                // 🚫 exclude A[i]\n            cur[k] = max(include, exclude);                                  // 🎯 best\n        }\n        swap(pre, cur);\n    }\n    return pre[K];\n}\n\nvoid run(const string& filename) {\n    Pairs A;\n    fstream fin{ filename };\n    int K, N;                // K capacity, N items\n    fin >> K >> N;\n    for (int value, weight; fin >> value >> weight; A.emplace_back(value, weight));\n    auto a = top_down(A, K),\n         b = bottom_up(A, K),\n         c = bottom_up_memopt(A, K);\n    assert(a == b && b == c); // 💩 sanity check\n    cout << filename << \": \" << a << endl;\n}\n\nint main() {\n    run(\"problem16.7test.txt\");  // problem16.7test.txt: 2493893\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Bellman-Ford\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Shortest Paths with Negative Edge Lengths (Section 18.1)](https://www.youtube.com/watch?v=oyHoqtxHiOs&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=54)\n* [The Bellman-Ford Algorithm (Part 1) (Section 18.2, Part 1)](https://www.youtube.com/watch?v=06OK99Aak60&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=55)\n* [The Bellman-Ford Algorithm (Part 2) (Section 18.2, Part 2)](https://www.youtube.com/watch?v=d1TWZa20Mkw&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=56)\n* [The Bellman-Ford Algorithm (Part 3) (Section 18.2, Part 3)](https://www.youtube.com/watch?v=HaXTsC8eOfo&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=57)\n* [The Bellman-Ford Algorithm (Part 4) (Section 18.2, Part 4)](https://www.youtube.com/watch?v=Otn0kbliRUQ&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=58)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\nimport java.util.LinkedList\nimport java.util.Queue\n\n// bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\nfun bell(E: Array<Triple<Int, Int, Int>>, N: Int, start: Int = 1, INF: Int = (1e6).toInt()): IntArray {\n    var dist = IntArray(N) { INF }\n    dist[start] = 0\n    var K = N - 1\n    while (0 < K--)\n        E.forEach{ (u, v, w) -> dist[v] = Math.min(dist[v], dist[u] + w)}\n    return dist\n}\n\n// shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\nfun spfa(E: Array<Triple<Int, Int, Int>>, N: Int, start: Int = 1, INF: Int = (1e6).toInt()): IntArray {\n    var dist = IntArray(N) { INF }\n    dist[start] = 0\n    var adj = Array<MutableList<Pair<Int, Int>>>(N) { mutableListOf<Pair<Int, Int>>() }\n    for ((u, v, w) in E)\n        adj[u].add(Pair(v, w))\n    var q: Queue<Int> = LinkedList<Int>(listOf(start))\n    while (0 < q.size) {\n        var u = q.poll()\n        for ((v, w) in adj[u]) {\n            if (dist[v] > dist[u] + w) {\n                dist[v] = dist[u] + w; q.add(v)\n            }\n        }\n    }\n    return dist\n}\n\nfun run(filename: String): IntArray {\n    var N = 0\n    var E = mutableListOf<Triple<Int, Int, Int>>()\n    File(filename).forEachLine {\n        var A = ArrayDeque(it.trim().split(\"\\t\"))\n        var u = A.removeFirst().toInt()\n        for ((v, w) in A.map{ it.split(\",\").map{ it.toInt() } })\n            E.add(Triple(u, v, w))\n        ++N;\n    }\n    var A = E.toTypedArray()\n    var a = bell(A, N + 1)  // +1 for 1-based indexing\n    var b = spfa(A, N + 1)\n    assert(a == b)          // 💩 sanity check: single source shortest paths are the same\n    return b\n}\n\nfun main() {\n    var dist = run(\"test.txt\")\n    println(listOf(7, 37, 59, 82, 99, 115, 133, 165, 188, 197).map{ dist[it] }.joinToString(\",\"))  // 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068\n}\n```\n\n*Javascript*\n```javascript\nconst assert = require('assert');\nconst zip = require('lodash/zip');\nconst LineByLine = require('n-readlines');\n\n// bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\nlet bell = (E, N, start = 1, INF = Number(1e6)) => {\n    let dist = Array(N).fill(INF);\n    dist[start] = 0;\n    let K = N - 1;\n    while (K--)\n        E.forEach(([u, v, w]) => dist[v] = Math.min(dist[v], dist[u] + w));\n    return dist;\n};\n\n// shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\nlet spfa = (E, N, start = 1, INF = Number(1e6)) => {\n    let dist = Array(N).fill(INF);\n    dist[start] = 0;\n    let adj = [...Array(N)].map(_ => []);\n    E.forEach(([u, v, w]) => adj[u].push([v, w]));\n    let q = [start];\n    while (q.length) {\n        let u = q.shift();\n        for (let [v, w] of adj[u])\n            if (dist[v] > dist[u] + w)\n                dist[v] = dist[u] + w, q.push(v);\n    }\n    return dist;\n};\n\nlet run = filename => {\n    let N = 0;\n    let E = [];\n    let input = new LineByLine(filename);\n    let line;\n    while (line = input.next()) {\n        let A = line.toString('ascii').split('\\t').filter(it => it.length);\n        let u = Number(A.shift());\n        A.map(pair => pair.split(',').map(Number)).forEach(([v, w]) => E.push([u, v, w]));\n        ++N;\n    }\n    let a = bell(E, N + 1),  // +1 for 1-based indexing\n        b = spfa(E, N + 1);\n    zip(a, b).forEach(([x, y]) => assert(x == y));  // 💩 sanity check: single source shortest paths are the same\n    return a;\n};\n\nlet dist = run('test.txt');\nconsole.log([7, 37, 59, 82, 99, 115, 133, 165, 188, 197].map(x => dist[x]).join(','));  // 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068\n```\n\n*Python3*\n```python\nfrom collections import deque\n\n# bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\ndef bell(E, N, start = 1, INF = int(1e6)):\n    dist = [INF] * N\n    dist[start] = 0\n    k = N - 1\n    while k:\n        for u, v, w in E:\n            dist[v] = min(dist[v], dist[u] + w)\n        k -= 1\n    return dist\n\n# shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\ndef spfa(E, N, start = 1, INF = int(1e6)):\n    dist = [INF] * N\n    dist[start] = 0\n    adj = {i: [] for i in range(N)}\n    for u, v, w in E:\n        adj[u].append([v, w])\n    q = deque([start])\n    while q:\n        u = q.popleft()\n        for v, w in adj[u]:\n            if dist[v] > dist[u] + w:\n                dist[v] = dist[u] + w; q.append(v)\n    return dist\n\ndef run(filename):\n    E = []\n    N = 0\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            line = line.strip()\n            A = [word for word in line.split('\\t') if len(word)]\n            u = int(A[0])\n            for i in range(1, len(A)):\n                v, w = [int(x) for x in A[i].split(',')]\n                E.append([u, v, w])\n            N += 1\n    a = bell(E, N + 1)  # +1 for 1-based indexing\n    b = spfa(E, N + 1)\n    assert(a == b)\n    return b\n\ndist = run('test.txt')\nprint(','.join(str(dist[x]) for x in [7, 37, 59, 82, 99, 115, 133, 165, 188, 197]))  # 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n#include <queue>\n\nusing namespace std;\nusing VI = vector<int>;\nusing VS = vector<string>;\nusing Edge = tuple<int, int, int>;\nusing Edges = vector<Edge>;\nusing Pair = pair<int, int>;\nusing Pairs = vector<Pair>;\nusing AdjList = unordered_map<int, Pairs>;\nusing Queue = queue<int>;\n\n// bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\nVI bell(Edges& E, int N, int start = 1, int INF = 1e6) {\n    VI dist(N, INF);\n    dist[start] = 0;\n    auto K = N - 1;\n    while (K--)\n        for (auto [u, v, w]: E)\n            dist[v] = min(dist[v], dist[u] + w);\n    return dist;\n}\n\n// shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\nVI spfa(Edges& E, int N, int start = 1, int INF = 1e6, AdjList adj = {}) {\n    VI dist(N, INF);\n    dist[start] = 0;\n    for (auto [u, v, w]: E)\n        adj[u].emplace_back(v, w);\n    Queue q{{ start }};\n    while (q.size()) {\n        auto u = q.front(); q.pop();\n        for (auto [v, w]: adj[u])\n            if (dist[v] > dist[u] + w)\n                dist[v] = dist[u] + w, q.push(v);\n    }\n    return dist;\n}\n\nVI run(const string& filename) {\n    auto N = 0;\n    Edges E;\n    fstream fin{ filename };\n    VS A;\n    for (string line; getline(fin, line); A.emplace_back(line));\n    for (auto& s: A) {\n        transform(s.begin(), s.end(), s.begin(), [](auto c) { return c == ',' ? ' ' : c; });\n        stringstream ss{ s };\n        auto [u, v, w] = make_tuple(0, 0, 0);\n        ss >> u;\n        while (ss >> v >> w)\n            E.emplace_back(u, v, w);\n        ++N;\n    }\n    auto a = bell(E, N + 1),  // +1 for 1-based indexing\n         b = spfa(E, N + 1);\n    assert(a == b);\n    return b;\n}\n\nint main() {\n    auto dist = run(\"test.txt\");\n    VI A{ 7, 37, 59, 82, 99, 115, 133, 165, 188, 197 };\n    transform(A.begin(), A.end(), A.begin(), [&](auto x) { return dist[x]; });\n    copy(A.begin(), A.end(), ostream_iterator<int>(cout, \",\"));  // 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068,\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Floyd-Warshall\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [The All-Pairs Shortest Path Problem (Section 18.3)](https://www.youtube.com/watch?v=TENbWZPz3Ho&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=62)\n* [The Floyd-Warshall Algorithm (Part 1) (Section 18.4, Part 1)](https://www.youtube.com/watch?v=ogcvCr02gqM&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=63)\n* [The Floyd-Warshall Algorithm (Part 2) (Section 18.4, Part 2)](https://www.youtube.com/watch?v=3cBHwPjDZxg&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=64)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\n\nvar key = { i: Int, j: Int -> \"$i,$j\" }\nvar INF = (1e9 + 7).toInt()\n\nfun floyd_warshall(E: MutableMap<String, Int>, N: Int): Array<IntArray> {\n    var dp = Array(N + 1) { Array(N + 1) { IntArray(N + 1) { INF } } }\n    for (i in 0..N)\n        for (j in 0..N)\n            if (i == j)\n                dp[0][i][j] = 0\n            else\n            if (E.contains(key(i, j)))\n                dp[0][i][j] = E[key(i, j)]!!\n    for (k in 1..N)\n        for (i in 1..N)\n            for (j in 1..N)\n                dp[k][i][j] = Math.min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j])\n    return dp[N]\n}\n\nfun floyd_warshall_memopt(E: MutableMap<String, Int>, N: Int): Array<IntArray> {\n    var pre = Array(N + 1) { IntArray(N + 1) { INF } }\n    for (i in 0..N)\n        for (j in 0..N)\n            if (i == j)\n                pre[i][j] = 0\n            else\n            if (E.contains(key(i, j)))\n                pre[i][j] = E[key(i, j)]!!\n    for (k in 1..N) {\n        var cur = Array(N + 1) { IntArray(N + 1) { INF } }\n        for (i in 1..N)\n            for (j in 1..N)\n                cur[i][j] = Math.min(pre[i][j], pre[i][k] + pre[k][j])\n        pre = cur.also{ cur = pre }\n    }\n    return pre\n}\n\nfun run(filename: String) {\n    var N = 0\n    var E = mutableMapOf<String, Int>()\n    var first = true\n    File(filename).forEachLine {\n        if (!first) {\n            var (u, v, w) = it.trim().split(\" \").map{ it.toInt() }\n            E[key(u, v)] = w\n        } else {\n            N = it.trim().split(\" \").map{ it.toInt() }[0]\n            first = false\n        }\n    }\n    var a = floyd_warshall_memopt(E, N)\n    var b = floyd_warshall(E, N)\n    for (i in 1..N)\n        for (j in 1..N)\n            assert(a[i][j] == b[i][j])  // 💩 sanity check\n    var cycle = false\n    for (i in 1..N)\n        if (a[i][i] < 0)\n            cycle = true\n    if (cycle) {\n        println(\"$filename: contains a negative cycle\")\n        return\n    }\n    var best = INF\n    for (i in 1..N)\n        for (j in 1..N)\n            best = Math.min(best, a[i][j])\n    println(\"$filename: $best\")\n}\n\nfun main() {\n    run(\"problem18.8test1.txt\");  // problem18.8test1.txt: -2\n    run(\"problem18.8test2.txt\");  // problem18.8test2.txt: contains a negative cycle\n    run(\"problem18.8file1.txt\");  // problem18.8file1.txt: contains a negative cycle\n    run(\"problem18.8file2.txt\");  // problem18.8file2.txt: contains a negative cycle\n    run(\"problem18.8file3.txt\");  // problem18.8file3.txt: -19\n    // run(\"problem18.8file4.txt\");\n}\n```\n\n*Javascript*\n```javascript\nconst LineByLine = require('n-readlines');\nconst assert = require('assert');\n\nlet key = (i, j) => `${i},${j}`;\n\nlet floyd_warshall = (E, N) => {\n    let dp = [...Array(N + 1)].map(_ => [...Array(N + 1)].map(_ => Array(N + 1).fill(Infinity)));\n    for (let i = 1; i <= N; ++i)\n        for (let j = 1; j <= N; ++j)\n            if (i == j)\n                dp[0][i][j] = 0;\n            else\n            if (E.has(key(i, j)))\n                dp[0][i][j] = E.get(key(i, j));\n    for (let k = 1; k <= N; ++k)\n        for (let i = 1; i <= N; ++i)\n            for (let j = 1; j <= N; ++j)\n                dp[k][i][j] = Math.min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j]);\n    return dp[N];\n};\n\nlet floyd_warshall_memopt = (E, N) => {\n    let pre = [...Array(N + 1)].map(_ => Array(N + 1).fill(Infinity));\n    for (let i = 1; i <= N; ++i)\n        for (let j = 1; j <= N; ++j)\n            if (i == j)\n                pre[i][j] = 0;\n            else\n            if (E.has(key(i, j)))\n                pre[i][j] = E.get(key(i, j));\n    for (let k = 1; k <= N; ++k) {\n        let cur = [...Array(N + 1)].map(_ => Array(N + 1).fill(Infinity));\n        for (let i = 1; i <= N; ++i)\n            for (let j = 1; j <= N; ++j)\n                cur[i][j] = Math.min(pre[i][j], pre[i][k] + pre[k][j]);\n        [pre, cur] = [cur, pre];\n    }\n    return pre;\n};\n\nlet run = filename => {\n    let E = new Map();\n    let input = new LineByLine(filename);\n    let [N, _] = input.next().toString('ascii').split(' ').map(Number);\n    let line;\n    while (line = input.next()) {\n        let [u, v, w] = line.toString('ascii').split(' ').map(Number);\n        E.set(key(u, v), w);\n    }\n    let a = floyd_warshall_memopt(E, N),\n        b = floyd_warshall(E, N);\n    for (let i = 1; i <= N; ++i)\n        for (let j = 1; j <= N; ++j)\n            assert(a[i][j] == b[i][j]);\n    let cycle = false;\n    for (let i = 1; i <= N; ++i)\n        if (a[i][i] < 0)\n            cycle = true;\n    if (cycle) {\n        console.log(`${filename}: contains a negative cycle`);\n        return;\n    }\n    var best = Infinity;\n    for (row of a)\n        best = Math.min(best, ...row);\n    console.log(`${filename}: ${best}`);\n};\n\nrun('problem18.8test1.txt');  // problem18.8test1.txt: -2\nrun('problem18.8test2.txt');  // problem18.8test2.txt: contains a negative cycle\nrun('problem18.8file1.txt');  // problem18.8file1.txt: contains a negative cycle\nrun('problem18.8file2.txt');  // problem18.8file2.txt: contains a negative cycle\nrun('problem18.8file3.txt');  // problem18.8file3.txt: -19\n// run('problem18.8file4.txt');\n```\n\n*Python3*\n```python\nkey = lambda i, j: f'{i},{j}'\n\ndef floyd_warshall(E, N):\n    dp = [[[float('inf')] * (N + 1) for _ in range(N + 1)] for _ in range(N + 1)]\n    for i in range(1, N + 1):\n        for j in range(1, N + 1):\n            if i == j:\n                dp[0][i][j] = 0\n            elif key(i, j) in E:\n                dp[0][i][j] = E[key(i, j)]\n    for k in range(1, N + 1):\n        for i in range(1, N + 1):\n            for j in range(1, N + 1):\n                dp[k][i][j] = min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j])\n    return dp[N]\n\ndef floyd_warshall_memopt(E, N):\n    pre = [[float('inf')] * (N + 1) for _ in range(N + 1)]\n    for i in range(1, N + 1):\n        for j in range(1, N + 1):\n            if i == j:\n                pre[i][j] = 0\n            elif key(i, j) in E:\n                pre[i][j] = E[key(i, j)]\n    for k in range(1, N + 1):\n        cur = [[float('inf')] * (N + 1) for _ in range(N + 1)]\n        for i in range(1, N + 1):\n            for j in range(1, N + 1):\n                cur[i][j] = min(pre[i][j], pre[i][k] + pre[k][j])\n        pre, cur = cur, pre\n    return pre\n\ndef run(filename):\n    E = {}\n    N = 0\n    first = True\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            if not first:\n                u, v, w = [int(x) for x in line.strip().split(' ')]\n                E[key(u, v)] = w\n            else:\n                N = [int(x) for x in line.strip().split(' ')][0]\n                first = False\n    a = floyd_warshall_memopt(E, N)\n    b = floyd_warshall(E, N)\n    for i in range(1, N + 1):\n        for j in range(1, N + 1):\n            assert(a[i][j] == b[i][j])  # 💩 sanity check\n    cycle = False\n    for i in range(1, N + 1):\n        if a[i][i] < 0:\n            cycle = True\n    if cycle:\n        print(f'{filename}: contains a negative cycle')\n        return\n    best = float('inf')\n    for row in a:\n        best = min(best, *row)\n    print(f'{filename}: {best}')\n\nrun('problem18.8test1.txt')  # problem18.8test1.txt: -2\nrun('problem18.8test2.txt')  # problem18.8test2.txt: contains a negative cycle\nrun('problem18.8file1.txt')  # problem18.8file1.txt: contains a negative cycle\nrun('problem18.8file2.txt')  # problem18.8file2.txt: contains a negative cycle\nrun('problem18.8file3.txt')  # problem18.8file3.txt: -19\n# run('problem18.8file4.txt')\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n\n#define PERF_TEST\n\nusing namespace std;\n\nusing LL = long long;\nusing VL = vector<LL>;\nusing VVL = vector<VL>;\nusing VVVL = vector<VVL>;\nusing Edges = unordered_map<string, LL>;\n\nLL INF = 1e9 + 7;\n\nstring key(int i, int j) {\n    stringstream ss; ss << i << \",\" << j;\n    return ss.str();\n}\n\nVVL floyd_warshall(Edges& E, int N) {\n    VVVL dp(N + 1, VVL(N + 1, VL(N + 1, INF)));\n    for (auto i{ 1 }; i <= N; ++i)\n        for (auto j{ 1 }; j <= N; ++j)\n            if (i == j)\n                dp[0][i][j] = 0;\n            else\n            if (E.find(key(i, j)) != E.end())\n                dp[0][i][j] = E[key(i, j)];\n    for (auto k{ 1 }; k <= N; ++k)\n        for (auto i{ 1 }; i <= N; ++i)\n            for (auto j{ 1 }; j <= N; ++j)\n                dp[k][i][j] = min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j]);\n    return dp[N];\n}\n\nVVL floyd_warshall_memopt(Edges& E, int N) {\n    VVL pre(N + 1, VL(N + 1, INF));\n    for (auto i{ 1 }; i <= N; ++i)\n        for (auto j{ 1 }; j <= N; ++j)\n            if (i == j)\n                pre[i][j] = 0;\n            else\n            if (E.find(key(i, j)) != E.end())\n                pre[i][j] = E[key(i, j)];\n    for (auto k{ 1 }; k <= N; ++k) {\n        VVL cur(N + 1, VL(N + 1, INF));\n        for (auto i{ 1 }; i <= N; ++i)\n            for (auto j{ 1 }; j <= N; ++j)\n                cur[i][j] = min(pre[i][j], pre[i][k] + pre[k][j]);\n        swap(pre, cur);\n    }\n    return pre;\n}\n\nvoid run(const string& filename) {\n    Edges E;\n    fstream fin{ filename };\n    int N, M; fin >> N >> M;\n    for (int u, v, w; fin >> u >> v >> w; E[key(u, v)] = w);\n#ifdef PERF_TEST\n    auto a = floyd_warshall_memopt(E, N);\n#else\n    auto a = floyd_warshall_memopt(E, N),\n         b = floyd_warshall(E, N);\n    assert(a == b);  // 💩 sanity check\n#endif\n    auto cycle = false;\n    for (auto i{ 1 }; i <= N && !cycle; ++i)\n        cycle = a[i][i] < 0;\n    if (cycle) {\n        cout << filename << \": contains a negative cycle\" << endl;\n        return;\n    }\n    auto best = INF;\n    for (auto& row: a)\n        best = min(best, *min_element(row.begin(), row.end()));\n    cout << filename << \": \" << best << endl;\n}\n\nint main() {\n    run(\"problem18.8test1.txt\");  // problem18.8test1.txt: -2\n    run(\"problem18.8test2.txt\");  // problem18.8test2.txt: contains a negative cycle\n    run(\"problem18.8file1.txt\");  // problem18.8file1.txt: contains a negative cycle\n    run(\"problem18.8file2.txt\");  // problem18.8file2.txt: contains a negative cycle\n    run(\"problem18.8file3.txt\");  // problem18.8file3.txt: -19\n//    run(\"problem18.8file4.txt\");\n    return 0;\n}\n```\n\n</details>\n\n---\n\n# Part 4: Algorithms for NP-Hard Problems\n\n<br/>\n<a href=\"https://www.amazon.com/dp/0999282964\" target=\"_blank\">\n    <img src=\"images/ai4large.jpg\" />\n</a>\n\n---\n"
  },
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    "path": "Algorithms-Illuminated/src/main.rs",
    "content": "fn main() {\n    println!(\"Hello, world!\");\n}\n"
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    "path": "Algorithms-Illuminated/target/.rustc_info.json",
    "content": "{\"rustc_fingerprint\":10491184667718451318,\"outputs\":{\"17598535894874457435\":{\"success\":true,\"status\":\"\",\"code\":0,\"stdout\":\"rustc 1.57.0 (f1edd0429 2021-11-29)\\nbinary: rustc\\ncommit-hash: f1edd0429582dd29cccacaf50fd134b05593bd9c\\ncommit-date: 2021-11-29\\nhost: x86_64-apple-darwin\\nrelease: 1.57.0\\nLLVM version: 13.0.0\\n\",\"stderr\":\"\"},\"2797684049618456168\":{\"success\":true,\"status\":\"\",\"code\":0,\"stdout\":\"___\\nlib___.rlib\\nlib___.dylib\\nlib___.dylib\\nlib___.a\\nlib___.dylib\\n\",\"stderr\":\"\"},\"931469667778813386\":{\"success\":true,\"status\":\"\",\"code\":0,\"stdout\":\"___\\nlib___.rlib\\nlib___.dylib\\nlib___.dylib\\nlib___.a\\nlib___.dylib\\n/Users/clayton.wonng/.rustup/toolchains/stable-x86_64-apple-darwin\\ndebug_assertions\\nproc_macro\\ntarget_arch=\\\"x86_64\\\"\\ntarget_endian=\\\"little\\\"\\ntarget_env=\\\"\\\"\\ntarget_family=\\\"unix\\\"\\ntarget_feature=\\\"fxsr\\\"\\ntarget_feature=\\\"sse\\\"\\ntarget_feature=\\\"sse2\\\"\\ntarget_feature=\\\"sse3\\\"\\ntarget_feature=\\\"ssse3\\\"\\ntarget_os=\\\"macos\\\"\\ntarget_pointer_width=\\\"64\\\"\\ntarget_vendor=\\\"apple\\\"\\nunix\\n\",\"stderr\":\"\"},\"15537503139010883884\":{\"success\":true,\"status\":\"\",\"code\":0,\"stdout\":\"___\\nlib___.rlib\\nlib___.dylib\\nlib___.dylib\\nlib___.a\\nlib___.dylib\\n\",\"stderr\":\"\"}},\"successes\":{}}"
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    "path": "Algorithms-Illuminated/target/CACHEDIR.TAG",
    "content": "Signature: 8a477f597d28d172789f06886806bc55\n# This file is a cache directory tag created by cargo.\n# For information about cache directory tags see https://bford.info/cachedir/\n"
  },
  {
    "path": "README.md",
    "content": "# Algorithms Illuminated\n\n* [algorithmsilluminated.org](https://www.algorithmsilluminated.org/)\n\nCoincidentally, my [algorithm learning journey](https://github.com/claytonjwong/Algorithms) which began in 2017 has occurred in parallel with the publication of Tim Roughgarden's (TR) 4-book series about algorithms and data structures. Over these years, I've purchased, studied, and provided feedback on TR's books. I was totally stoked when TR sent me a free copy of his 4th book for review before publication in 2020! I'm amazed by what can be done in near-linear time (ie. the amount of time to perform an algorithm is on the order of time to simply read the input), and it's awesome we can leverage these \"for-free primitives\" based upon computationally tractable problems as \"building blocks\" towards more complex solutions to computationally intractable (NP-Hard) problems via selective compromise on generality, correctness, and speed (ie. pick 2 of 3). [`💡` Can we do better?](https://en.wikipedia.org/wiki/Millennium_Prize_Problems#P_versus_NP)\n\n<p>\n    <img src=\"images/TR1.png\" height=\"256\" width=\"400\" />\n    <img src=\"images/TR2.png\" height=\"256\" width=\"400\" />\n</p>\n\n---\n\n# Part 1: The Basics\n\n<br/>\n<a href=\"https://www.amazon.com/dp/0999282905\" target=\"_blank\">\n    <img src=\"images/ai1large.jpg\" />\n</a>\n\n<details><summary>⚡️ TL;DR ⚡️</summary>\n<br/>\n\n> A \"fast algorithm\" is an algorithm whose worst-case runtime grows slowly with the input size.\n\n* **Recursion Tree:** each child node corresponds to recusive invocations by its parent node\n  * helpful visualization of work done by recursive algorithms to quantify aymptotic bounds\n* **Algorithm Analysis Principles**\n  1. Worst-Case\n     * no input assumptions for general-purpose analysis\n  2. Big-Picture\n     * drop constant factors and lower-order terms for runtime upper bound\n       * mathematical tractability\n       * primitive operation runtime depends on environmental factors\n       * retains accurate predictions for slow/fast algorithms\n  3. Asymptotic Analysis\n     * focus on the runtime growth for large inputs\n       * only large inputs require algorithmic ingenuity\n* **For-Free Primitives**\n  * Linear-time algorithms (the \"holy grail\")\n    * Runtime is proportional to the input size\n    * \"Free\" since the time to perform the algorithm is on the order of time to simply read the input\n* **Asymptotic Notation**: suppress constant factors and lower-order terms to focus on how an algorithm's runtime scales with input size\n  * constant factors are too system dependent\n  * lower-order terms are irrelevant for large inputs\n* **Big-O Notation:** `T(n) = O(f(n))` if-and-only-if `T(n)` is eventually bounded above by a constant multiple of `f(n)`\n  * `T(n) = O(f(n))` if-and-only-if there exists positive constants *c* and *n*<sub>0</sub> such that `T(n) <= c * O(f(n))` for all *n* greater-than-or-equal-to *n*<sub>0</sub>\n</details>\n\n---\n\n### Integer Multiplication\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Introduction: Why Study Algorithms?](https://www.youtube.com/watch?v=yRM3sc57q0c&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=1)\n* [Introduction: Integer Multiplication](https://www.youtube.com/watch?v=6u0Vaj4nn54&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=2)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Python3*\n```python\ndef go(x, y):\n    if x < 10 or y < 10:\n        return x * y\n    n = max(len(str(x)), len(str(y)))\n    if n & 1:\n        n += 1  # +1 is n is odd\n    m = 10 ** (n // 2)\n    a, b = x // m, x % m\n    c, d = y // m, y % m\n    p, q = a + b, c + d\n\n    ac = go(a, c)\n    bd = go(b, d)\n    pq = go(p, q)\n    adbc = pq - ac - bd\n    return 10**n * ac + 10**(n//2) * adbc + bd\n\nx = 3141592653589793238462643383279502884197169399375105820974944592\ny = 2718281828459045235360287471352662497757247093699959574966967627\nassert(x * y == go(x, y))\n```\n\n*Julia*\n```julia\nusing Test, Random\n\nfunction go(x, y)\n  if x < 10 || y < 10\n    return x * y\n  end\n\n  n = max(length(string(x)), length(string(y)))\n  if isodd(n)\n    n += 1\n  end\n\n  m = 10 ^ div(n, 2) # middle decimal value\n  a, b = div(x, m), mod(x, m)\n  c, d = div(y, m), mod(y, m)\n\n  ac = go(a, c)\n  ad = go(a, d)\n  bc = go(b, c)\n  bd = go(b, d)\n  return 10^n * ac + 10^div(n, 2) * (ad + bc) + bd\nend\n\nRandom.seed!(123456789)\n\n@testset \"Recursive Integer Multiplication tests\" begin\n    for _ in 1:100\n        n = rand((1, 2, 4, 8, 16))\n\n        lo = 10^(n-1)\n        hi = 10^n - 1\n\n        x = rand(lo:hi)\n        y = rand(lo:hi)\n\n        expect, actual = x * y, go(x, y)\n        @test expect == actual\n        println(\"($x x $y)\\nexpect: $expect\\nactual: $actual\\n\")\n    end\nend\n```\n\n</details>\n\n---\n\n### Karatsuba Multiplication\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Introduction: Karatsuba Multiplication](https://www.youtube.com/watch?v=JCbZayFr9RE&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=3)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Julia*\n```julia\nusing Test, Random\n\nfunction go(x, y)\n  if x < 10 || y < 10\n    return x * y\n  end\n\n  n = max(length(string(x)), length(string(y)))\n  if isodd(n)\n    n += 1\n  end\n\n  m = 10 ^ div(n, 2) # middle decimal value\n  a, b = div(x, m), mod(x, m)\n  c, d = div(y, m), mod(y, m)\n  p, q = a + b, c + d\n\n  ac = go(a, c)\n  bd = go(b, d)\n  pq = go(p, q)\n  adbc = pq - ac - bd\n  return 10^n * ac + 10^div(n, 2) * adbc + bd\nend\n\nRandom.seed!(123456789)\n\n@testset \"Karatsuba Multiplication tests\" begin\n    for _ in 1:100\n        n = rand((1, 2, 4, 8, 16))\n\n        lo = 10^(n-1)\n        hi = 10^n - 1\n\n        x = rand(lo:hi)\n        y = rand(lo:hi)\n\n        expect, actual = x * y, go(x, y)\n        @test expect == actual\n        println(\"($x x $y)\\nexpect: $expect\\nactual: $actual\\n\")\n    end\nend\n```\n\n</details>\n\n---\n\n### Merge Sort\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [MergeSort: Motivation and Example](https://www.youtube.com/watch?v=kiyRJ7GVWro&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=4) (Section 1.4, part 1)\n* [MergeSort: Pseudocode](https://www.youtube.com/watch?v=rBd5w0rQaFo&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=5) (Section 1.4, part 2)\n* [MergeSort: Analysis](https://www.youtube.com/watch?v=8ArtRiTkYEw&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=6) (Section 1.5)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nfun sort(A: IntArray): IntArray {\n    fun merge(A: IntArray, B: IntArray): IntArray {\n        var C = mutableListOf<Int>()\n        var i = 0\n        var j = 0\n        while (i < A.size && j < B.size)\n            if (A[i] < B[j])\n                C.add(A[i++])\n            else\n                C.add(B[j++])\n        A.slice(i..A.lastIndex).forEach { C.add(it) }\n        B.slice(j..B.lastIndex).forEach { C.add(it) }\n        return C.toIntArray()\n    }\n    fun go(A: IntArray): IntArray {\n        var N = A.size\n        if (N < 2)\n            return A\n        var half = Math.floor(N / 2.0).toInt()\n        var first  = go(A.slice(0 until half).toIntArray())\n        var second = go(A.slice(half until N).toIntArray())\n        return merge(first, second)\n    }\n    return go(A)\n}\n\nfun main(args: Array<String>) {\n    sort(intArrayOf(5,3,8,9,1,7,0,2,6,4)).forEach { print(\"$it \") }  // 0 1 2 3 4 5 6 7 8 9\n    println()\n}\n```\n\n*Javascript*\n```javascript\nlet sort = A => {\n    let go = A => {\n        let N = A.length;\n        if (N < 2)\n            return A;\n        let half = Math.floor(N / 2);\n        let first  = go([...A.slice(0, half)]),\n            second = go([...A.slice(half, N)]);\n        return merge(first, second);\n    };\n    let merge = (A, B, C = []) => {\n        let M = A.length,\n            N = B.length;\n        let i = 0,\n            j = 0;\n        while (i < M && j < N)\n            C.push(A[i] < B[j] ? A[i++] : B[j++]);\n        C.push(...A.slice(i, M));\n        C.push(...B.slice(j, N));\n        return C;\n    };\n    return go(A);\n};\n\nconsole.log(sort([5,3,8,9,1,7,0,2,6,4]));  // (10) [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n```\n\n```julia\nfunction go(A)\n  N = length(A)\n  if N < 2\n    return A\n  end\n  half = div(N, 2)\n  first = go(A[begin:half])\n  second = go(A[half+1:end])\n  return merge(first, second)\nend\n\nfunction merge(A, B)\n  C = []\n  i, j, k = 1, 1, 1\n  while i <= length(A) && j <= length(B)\n    if A[i] < B[j]\n      push!(C, A[i])\n      i += 1\n    else\n      push!(C, B[j])\n      j += 1\n    end\n    k += 1\n  end\n  append!(C, @view A[i:end])\n  append!(C, @view B[j:end])\n  return C\nend\n\nprintln(go([5, 3, 8, 9, 1, 7, 0, 2, 6, 4]))  # Any[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n```\n\n*Python3*\n```python\nfrom math import floor\n\ndef sort(A):\n    def go(A):\n        N = len(A)\n        if N < 2:\n            return A\n        half = floor(N / 2)\n        first =  go(A[:half])\n        second = go(A[half:])\n        return merge(first, second)\n    def merge(A, B):\n        C = []\n        i = 0\n        j = 0\n        while i < len(A) and j < len(B):\n            if A[i] < B[j]:\n                C.append(A[i]); i += 1\n            else:\n                C.append(B[j]); j += 1\n        C.extend(A[i:])\n        C.extend(B[j:])\n        return C\n    return go(A)\n\nprint(sort([5,3,8,9,1,7,0,2,6,4]))  # [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <vector>\n\nusing namespace std;\n\nclass Solution {\npublic:\n    using VI = vector<int>;\n    VI mergesort(VI& A) {\n        return go(move(A));\n    }\nprivate:\n    VI go(VI&& A) {\n        auto N = A.size();\n        if( N < 2 )\n            return A;\n        auto half = A.begin() + (N / 2);\n        auto first = go({ A.begin(), half }),\n             second = go({ half, A.end() });\n        return merge(first, second);\n    }\n    VI merge(VI& A, VI& B, VI C = {}) {\n        auto i{ 0 },\n             j{ 0 };\n        while (i < A.size() && j < B.size())\n            C.push_back(A[i] < B[j] ? A[i++] : B[j++]);\n        C.insert(C.end(), A.begin() + i, A.end());\n        C.insert(C.end(), B.begin() + j, B.end());\n        return C;\n    }\n};\n\nint main() {\n    Solution::VI A{ 3,5,7,1,3,9,2,0 };\n    auto ans = Solution().mergesort(A);\n    copy(ans.begin(), ans.end(), ostream_iterator<int>(cout, \" \")), cout << endl;  // 0 1 2 3 4 5 6 7 8 9\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Counting Inversions\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [The Divide-and-Conquer Paradigm](https://www.youtube.com/watch?v=7_AJfusC6UQ&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=13) (Section 3.1; part 1 of Section 3.2)\n* [Counting Inversions in O(n log n)](https://www.youtube.com/watch?v=I6ygiW8xN7Y&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=14) Time (Section 3.2, part 2)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.io.File\n\nfun sort(A: IntArray): Pair<IntArray, Long> {\n    fun merge(A: IntArray, B: IntArray): Pair<IntArray, Long> {\n        var C = mutableListOf<Int>()\n        var inv: Long = 0\n        var i = 0\n        var j = 0\n        while (i < A.size && j < B.size)\n            if (A[i] < B[j]) {\n                C.add(A[i++])\n            } else {\n                inv += A.size - i  // ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.add(B[j++])\n            }\n        A.slice(i..A.lastIndex).forEach { C.add(it) }\n        B.slice(j..B.lastIndex).forEach { C.add(it) }\n        return Pair(C.toIntArray(), inv)\n    }\n    fun go(A: IntArray): Pair<IntArray, Long> {\n        var N = A.size\n        if (N < 2)\n            return Pair(A, 0)\n        var half = Math.floor(N / 2.0).toInt()\n        var (first,  inv1) = go(A.slice(0 until half).toIntArray())\n        var (second, inv2) = go(A.slice(half until N).toIntArray())\n        var (third,  inv3) = merge(first, second)\n        return Pair(third, inv1 + inv2 + inv3)\n    }\n    return go(A)\n}\n\nfun run(filename: String): Long {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    var (_, inv) = sort(A.toIntArray())\n    return inv\n}\n\nfun main() {\n    println(\"problem3.5test.txt: \" + run(\"problem3.5test.txt\"))  // problem3.5test.txt: 28\n    println(\"problem3.5.txt: \"     + run(\"problem3.5.txt\"))      // problem3.5.txt: 2407905288\n}\n```\n\n*Javascript*\n```javascript\nlet sort = A => {\n    let go = A => {\n        let N = A.length;\n        if (N < 2)\n            return [A, 0];\n        let half = Math.floor(N / 2);\n        let [first,  inv1] = go([...A.slice(0, half)]),\n            [second, inv2] = go([...A.slice(half, N)]),\n            [third,  inv3] = merge(first, second);\n        return [third, inv1 + inv2 + inv3];\n    };\n    let merge = (A, B, C = [], inv = 0) => {\n        let M = A.length,\n            N = B.length;\n        let i = 0,\n            j = 0;\n        while (i < M && j < N)\n            if (A[i] < B[j])\n                C.push(A[i++]);\n            else\n                inv += M - i,      // ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.push(B[j++]);\n        C.push(...A.slice(i, M));\n        C.push(...B.slice(j, N));\n        return [C, inv];\n    };\n    return go(A);\n};\n\nlet run = filename => {\n    let A = [];\n    require('fs').readFileSync(filename, 'utf-8').split(/\\r?\\n/).forEach(line => A.push(Number(line)));\n    let [_, inv] = sort(A);\n    return inv;\n}\n\nconsole.log(`problem3.5test.txt: ${run('problem3.5test.txt')}`);  // problem3.5test.txt: 28\nconsole.log(`problem3.5.txt: ${run('problem3.5.txt')}`);          // problem3.5.txt: 2407905288\n```\n\n*Julia*\n```julia\nfunction go(A)\n  N = length(A)\n  if N < 2\n    return A, 0\n  end\n  half = div(N, 2)\n  first, inv1 = go(A[begin:half])\n  second, inv2 = go(A[half+1:end])\n  third, inv3 = merge(first, second)\n  return third, inv1 + inv2 + inv3\nend\n\nfunction merge(A, B)\n  C, inv = [], 0\n  i, j, k = 1, 1, 1\n  while i <= length(A) && j <= length(B)\n    if A[i] < B[j]\n      push!(C, A[i])\n      i += 1\n    else\n      push!(C, B[j]); inv += length(A) - i + 1  # ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n      j += 1\n    end\n    k += 1\n  end\n  append!(C, @view A[i:end])\n  append!(C, @view B[j:end])\n  return C, inv\nend\n\nfunction run(filename)\n  input = Int[]\n  open(filename, \"r\") do file\n    for line in eachline(file)\n      push!(input, parse(Int, strip(line)))\n    end\n  end\n  _, inv = go(input)\n  return inv\nend\n\nprintln(run(\"problem3.5test.txt\"))  # 28\nprintln(run(\"problem3.5.txt\"))      # 2407905288\n```\n\n*Python3*\n```python\nfrom math import floor\n\ndef sort(A):\n    def go(A):\n        N = len(A)\n        if N < 2:\n            return [A, 0]\n        half = floor(N / 2)\n        first,  inv1 = go(A[:half])\n        second, inv2 = go(A[half:])\n        third,  inv3 = merge(first, second)\n        return [third, inv1 + inv2 + inv3]\n    def merge(A, B, inv = 0):\n        C = []\n        i = 0\n        j = 0\n        while i < len(A) and j < len(B):\n            if A[i] < B[j]:\n                C.append(A[i]); i += 1\n            else:\n                inv += len(A) - i        # ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.append(B[j]); j += 1\n        C.extend(A[i:])\n        C.extend(B[j:])\n        return [C, inv]\n    return go(A)\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            A.append(int(line))\n    _, inv = sort(A)\n    return inv\n\nprint(f\"problem3.5test.txt: {run('problem3.5test.txt')}\")  # problem3.5test.txt: 28\nprint(f\"problem3.5.txt: {run('problem3.5.txt')}\")          # problem3.5.txt: 2407905288\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <vector>\n#include <fstream>\n\nusing namespace std;\n\nclass Solution {\npublic:\n    using VL = vector<long>;\n    using Pair = pair<VL, long>;\n    using fun = function<Pair(VL&&)>;\n    Pair merge(VL& A, VL& B, VL C = {}, long inv = 0) {\n        auto i = 0,\n             j = 0;\n        while (i < A.size() && j < B.size()) {\n            if (A[i] < B[j]) {\n                C.push_back(A[i++]);\n            } else {\n                inv += A.size() - i; // ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.push_back(B[j++]);\n            }\n        }\n        C.insert(C.end(), A.begin() + i, A.end());\n        C.insert(C.end(), B.begin() + j, B.end());\n        return { C, inv };\n    }\n    Pair inversions(VL& A) {\n        fun go = [&](VL&& A) -> Pair {\n            int N = A.size();\n            if (N < 2)\n                return { A, 0 };\n            int half = N / 2;\n            auto [first,  inv1] = go({ A.begin(), A.begin() + half });\n            auto [second, inv2] = go({ A.begin() + half, A.end() });\n            auto [third,  inv3] = merge(first, second);\n            return { third, inv1 + inv2 + inv3 };\n        };\n        return go(move(A));\n    }\n};\n\nlong run(string filename) {\n    Solution solution;\n    Solution::VL A;\n    fstream fin{ filename };\n    for (string line; fin >> line; A.push_back(stol(line)));\n    auto [_, inv] = solution.inversions(A);\n    return inv;\n}\n\nint main() {\n    cout << \"problem3.5test.txt: \" << run(\"problem3.5test.txt\") << endl   // problem3.5test.txt: 28\n         << \"problem3.5.txt: \"     << run(\"problem3.5.txt\")     << endl;  // problem3.5.txt: 2407905288\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Recursive Matrix Multiplication\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Strassen 's Subcubic Matrix Multiplication Algorithm](https://www.youtube.com/watch?v=ORrM-aSNZUs&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=15)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n* Assume N is a power of 2 for simplicity\n\n#### Iterative Matrix Multiplication\n\n* **Cubic runtime:** O(N<sup>3</sup>)\n\n*Python3*\n```python\nN = 2\n\nX = [[1, 2],\n     [3, 4]]\n\nY = [[5, 6],\n     [7, 8]]\n\nZ = [[0] * N for _ in range(N)]\n\nfor i in range(N):\n    for j in range(N):\n        for k in range(N):\n            Z[i][j] += X[i][k] * Y[k][j]\n```\n\n#### Standard Recursive Matrix Multiplication\n\n* **Cubic runtime:** O(N<sup>3</sup>)\n\n*Python3*\n```python\nimport numpy as np\n\ndef go(X, Y):\n    n = X.shape[0]\n\n    # Base case: 1x1 matrix\n    if n == 1:\n        return X * Y\n\n    # Divide: Partition A and B into n/2 x n/2 submatrices\n    k = n // 2\n\n    A, B = X[:k, :k], X[:k, k:]\n    C, D = X[k:, :k], X[k:, k:]\n\n    E, F = Y[:k, :k], Y[:k, k:]\n    G, H = Y[k:, :k], Y[k:, k:]\n\n    # Combine: Reconstruct the full matrix from quadrants\n    Z = np.zeros((n, n), dtype=X.dtype)\n    Z[:k, :k], Z[:k, k:] = go(A, E) + go(B, G), go(A, F) + go(B, H)\n    Z[k:, :k], Z[k:, k:] = go(C, E) + go(D, G), go(C, F) + go(D, H)\n    return Z\n```\n\n#### Strassen's Matrix Multiplication\n\n* **Sub-cubic runtime:** O(N<sup>log<sub>2</sub>(7)</sup>)\n\n*Python3*\n```python\nimport numpy as np\n\ndef go(X, Y):\n    n = X.shape[0]\n\n    # Base case: 1x1 matrix\n    if n == 1:\n        return X * Y\n\n    # Divide: Partition A and B into n/2 x n/2 submatrices\n    k = n // 2\n\n    A, B = X[:k, :k], X[:k, k:]\n    C, D = X[k:, :k], X[k:, k:]\n\n    E, F = Y[:k, :k], Y[:k, k:]\n    G, H = Y[k:, :k], Y[k:, k:]\n\n    # Combine: Reconstruct the full matrix from quadrants\n    Z = np.zeros((n, n), dtype=X.dtype)\n    P1 = go(A, F - H)\n    P2 = go(A + B, H)\n    P3 = go(C + D, E)\n    P4 = go(D, G - E)\n    P5 = go(A + D, E + H)\n    P6 = go(B - D, G + H)\n    P7 = go(A - C, E + F)\n    Z[:k, :k], Z[:k, k:] = (P5 + P4 - P2 + P6), (P1 + P2)\n    Z[k:, :k], Z[k:, k:] = (P3 + P4), (P1 + P5 - P3 - P7)\n    return Z\n```\n\n#### Strassen's Matrix Multiplication (Variants)\n\n* **Sub-cubic runtime:** O(N<sup>log<sub>2</sub>(7)</sup>)\n\n*Python3*\n```python\n#\n# Strassen-family Recursive Matrix Multiplication (2x2 block form)\n#\n# Methods:\n#   - \"strassen\"  : classical Strassen scheme (7 recursive multiplies)\n#   - \"winograd\"  : Winograd rearrangement of Strassen (7 multiplies, fewer additions)\n#   - \"basis2017\" : alternative-basis 7-multiply scheme (basis change + recombination)\n#\n# All methods:\n#   - Recursively split X and Y into 2x2 blocks\n#   - Perform 7 recursive multiplications\n#   - Recombine into result blocks\n#\n# Assumption: n is a power of 2\n#\ndef go(X: np.ndarray, Y: np.ndarray, method: str = \"strassen\") -> np.ndarray:\n    n = X.shape[0]\n\n    # Base case: 1x1 matrix multiply\n    if n == 1:\n        return X * Y\n\n    k = n // 2\n\n    # Partition X into 2x2 block matrix\n    # X = [[A11 A12]\n    #      [A21 A22]]\n    A11, A12 = X[:k, :k], X[:k, k:]\n    A21, A22 = X[k:, :k], X[k:, k:]\n\n    # Partition Y into 2x2 block matrix\n    # Y = [[B11 B12]\n    #      [B21 B22]]\n    B11, B12 = Y[:k, :k], Y[:k, k:]\n    B21, B22 = Y[k:, :k], Y[k:, k:]\n\n    # Allocate result matrix\n    Z = np.zeros((n, n), dtype=X.dtype)\n\n    # ============================================================\n    # Classical Strassen scheme\n    # ============================================================\n    if method == \"strassen\":\n\n        # 7 recursive multiplications\n        M1 = go(A11 + A22, B11 + B22, method)\n        M2 = go(A21 + A22, B11, method)\n        M3 = go(A11, B12 - B22, method)\n        M4 = go(A22, B21 - B11, method)\n        M5 = go(A11 + A12, B22, method)\n        M6 = go(A21 - A11, B11 + B12, method)\n        M7 = go(A12 - A22, B21 + B22, method)\n\n        # Recombine into C blocks\n        C11 = M1 + M4 - M5 + M7\n        C12 = M3 + M5\n        C21 = M2 + M4\n        C22 = M1 - M2 + M3 + M6\n\n        Z[:k, :k] = C11\n        Z[:k, k:] = C12\n        Z[k:, :k] = C21\n        Z[k:, k:] = C22\n        return Z\n\n    # ============================================================\n    # Winograd rearrangement of Strassen\n    # Same 7 multiplies, different additive structure\n    # ============================================================\n    if method == \"winograd\":\n\n        # Core recursive products\n        t = go(A11, B11, method)\n        u = go(A21 - A11, B12 - B22, method)\n        v = go(A21 + A22, B12 - B11, method)\n\n        # w reuses t to reduce total additions\n        w = t + go(A21 + A22 - A11, B11 + B22 - B12, method)\n\n        # Recombine result blocks\n        C11 = t + go(A12, B21, method)\n        C12 = w + v + go(A11 + A12 - A21 - A22, B22, method)\n        C21 = w + u + go(A22, B21 + B12 - B11 - B22, method)\n        C22 = w + u + v\n\n        Z[:k, :k] = C11\n        Z[:k, k:] = C12\n        Z[k:, :k] = C21\n        Z[k:, k:] = C22\n        return Z\n\n    # ============================================================\n    # 2017 alternative-basis 7-multiply scheme\n    # Performs a basis change on A22 and B22 blocks\n    # ============================================================\n    if method == \"basis2017\":\n\n        # Basis transformation of lower-right blocks\n        A22p = A12 - A21 + A22\n        B22p = B12 - B21 + B22\n\n        # Linear combinations used by recursive multiplies\n        t1 = A21 + A22p\n        t2 = A22p - A12\n        t3 = A22p - A11\n        t4 = B22p - B11\n        t5 = B21 + B22p\n        t6 = B22p - B12\n\n        # 7 recursive multiplications\n        M1 = go(A11, B11, method)\n        M2 = go(A12, B21, method)\n        M3 = go(A21, t4, method)\n        M4 = go(A22p, B22p, method)\n        M5 = go(t1, t5, method)\n        M6 = go(t2, t6, method)\n        M7 = go(t3, B12, method)\n\n        # Initial recombination\n        C11 = M1 + M2\n        C12 = M5 - M7\n        C21 = M3 + M6\n        C22 = M5 + M6 - M2 - M4\n\n        # Final correction step required by basis change\n        C12 = C12 - C22\n        C21 = C22 - C21\n\n        Z[:k, :k] = C11\n        Z[:k, k:] = C12\n        Z[k:, :k] = C21\n        Z[k:, k:] = C22\n        return Z\n```\n\n</details>\n\n\n---\n\n### Closest Pair\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [O(nlogn) Algorithm for Closest Pair: Part One](https://www.youtube.com/watch?v=3pUOv_ocJyA&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=16)\n* [O(nlogn) Algorithm for Closest Pair: Part Two](https://www.youtube.com/watch?v=7tiafUFrlBw&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=17)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n* **Input:** `n >= 2` points p<sub>1</sub>=(x<sub>1</sub>,y<sub>1</sub>), p2=(x<sub>2</sub>,y<sub>2</sub>), ... , p<sub>n</sub>=(x<sub>n</sub>,y<sub>n</sub>)\n* **Output:** The pair p<sub>i</sub>,p<sub>j</sub> of distinct points with smallest Euclidean distance d(p<sub>i</sub>,p<sub>j</sub>)\n\n#### Brute-Force\n\n* **Quadratic runtime:** O(N<sup>2</sup>)\n\n*Python3*\n```python\nP = [(1, 8), (2, 5), (4, 7), (6, 3)]\nN = len(P)\nINF = 1234567890  # arbitary choice for infinity\n\ndef dist(i, j):\n    x1, y1 = P[i]\n    x2, y2 = P[j]\n    return (x1 - x2) ** 2 \\\n         + (y1 - y2) ** 2\n\nbest_dist = 123456789\nbest_pair = None\n\nD = [[INF] * N for _ in range(N)]\nfor i in range(N):\n    for j in range(N):\n        D[i][j] = dist(i, j)\n        if i != j:  # candidates for best pair cannot be the same point\n            if best_dist >= D[i][j]:\n                best_dist = D[i][j]\n                best_pair = (i, j)\n\ni, j = best_pair\nprint(f'best pair: {P[i]}, {P[j]}')\n```\n\n#### Recursive\n\n* **Super-linear runtime:** O(NlogN)\n\n```python\nINF = 1234567890  # arbitary choice for infinity\n\ndef distance(a, b):\n    x1, y1 = a\n    x2, y2 = b\n    return (x1 - x2) ** 2 \\\n         + (y1 - y2) ** 2\n\ndef split(Px, Py, d):\n    # median x-coordinate\n    median = Px[len(Px) // 2][0]\n\n    # identify points near left/right boundary\n    Sy = [(x, y) for x, y in Py if median - d <= x <= median + d]\n\n    # return the best split pair (if it exists)\n    best_dist, best_pairs = INF, set()\n    for i in range(len(Sy) - 1):\n        for j in range(i + 1, min(i + 1 + 7, len(Sy))):\n            cand = distance(Sy[i], Sy[j])\n            if best_dist > cand:\n                best_dist = cand\n                best_pairs = set()\n            if best_dist == cand:\n                best_pairs.add((Sy[i], Sy[j]))\n    return best_dist, best_pairs\n\ndef best(P):\n    best_dist, best_pairs = INF, set()\n    for i in range(len(P)):\n        for j in range(i + 1, len(P)):\n            cand = distance(P[i], P[j]) if P[i] != P[j] else INF\n            if best_dist > cand:\n                best_dist = cand\n                best_pairs = set()\n            if best_dist == cand:\n                best_pairs.add((P[i], P[j]))\n    return best_dist, best_pairs\n\ndef go(Px, Py):\n    if len(Px) <= 3:  # Base case\n        return best(Px)\n\n    Lx, Rx = Px[:len(Px) // 2], Px[len(Px) // 2:]\n    Ly, Ry = [], []\n    for x, y in Py:\n        if x <= Lx[-1][0]:\n            Ly.append((x, y))\n        else:\n            Ry.append((x, y))\n\n    dist_left, best_left = go(Lx, Ly)\n    dist_right, best_right = go(Rx, Ry)\n    dist_split, best_split = split(Px, Py, min(dist_left, dist_right))\n\n    cands = sorted([(dist_left, best_left), (dist_right, best_right), (dist_split, best_split)], key=lambda it: it[0])\n    best_dist, best_pairs = cands[0][0], set()\n    for dist, pairs in cands:\n        if dist == best_dist:\n            for a, b in pairs:\n                best_pairs.add((a, b) if a < b else (b, a))\n    return best_dist, best_pairs\n\ndef run(points, expected_best_pair):\n    Px = sorted(points, key=lambda it: it[0])\n    Py = sorted(points, key=lambda it: it[1])\n    _, best_pair = go(Px, Py)\n    print(f'points: {points}')\n    print(f'actual: {sorted(best_pair)}')\n    print(f'expect: {sorted(expected_best_pair)}')\n    print()\n    assert(sorted(best_pair) == sorted(expected_best_pair))\n```\n\n</details>\n\n\n---\n\n### Quick Sort\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [QuickSort: Overview](https://www.youtube.com/watch?v=ETo1cpLN7kk&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=24) (Section 5.1)\n* [Partitioning Around a Pivot Element](https://www.youtube.com/watch?v=LYzdRN5iFdA&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=25) (Section 5.2)\n* [Choosing a Good Pivot](https://www.youtube.com/watch?v=kqO46FOUTbI&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=26) (Sections 5.3 and 5.4)\n* [QuickSort Analysis (Part 1)](https://www.youtube.com/watch?v=sToWtKSYlMw&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=27) (Section 5.5, part 1)\n* [QuickSort Analysis (Part 2)](https://www.youtube.com/watch?v=4t_Y-aGLkok&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=28) (Section 5.5, part 2)\n* [QuickSort Analysis (Part 3)](https://www.youtube.com/watch?v=IBTvneWhFsA&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=29) (Section 5.5, part 3)\n* [Sorting Requires Omega(n log n) Comparisons](https://www.youtube.com/watch?v=aFveIyII5D4&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=30) (Section 5.6)\n* [Proofs by Induction and the Correctness of QuickSort](https://www.youtube.com/watch?v=Colb_4jAy8A&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=36) (Appendix A)\n* [Quick Review of Discrete Probability](https://www.youtube.com/watch?v=uLeIMwMHX5U&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=37) (Appendix B)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.io.File\n\ntypealias PivotFunc = (A: MutableList<Int>, L: Int, R: Int) -> (Int)\nvar pivotLeft: PivotFunc = { _: MutableList<Int>, L: Int, _: Int -> L }\nvar pivotRight: PivotFunc = { _: MutableList<Int>, _: Int, R: Int -> R }\nfun _pivotMedian(A: MutableList<Int>, L: Int, R: Int): Int {\n    var M = L + (R - L) / 2\n    var cand = intArrayOf(A[L], A[M], A[R])\n    cand.sort()\n    var target = cand[1]\n    if (target == A[L]) return L\n    if (target == A[M]) return M\n    if (target == A[R]) return R\n    return -1\n}\nvar pivotMedian: PivotFunc = { A: MutableList<Int>, L: Int, R: Int -> _pivotMedian(A, L, R) }\n\nfun partition(A: MutableList<Int>, L: Int, R: Int, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    var i = L + 1\n    var j = L + 1\n    var k = choosePivot(A, L, R)\n    A[k] = A[L].also { A[L] = A[k] }          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                    // maintain loop invariant A[i] < pivot < A[j]\n            A[i] = A[j].also { A[j] = A[i] }\n            ++i\n        }\n        ++j\n    }\n    A[L] = A[i - 1].also { A[i - 1] = A[L] }  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n}\n\nfun quicksort(A: MutableList<Int>, L: Int, R: Int, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    if (R <= L)\n        return 0\n    var k = partition(A, L, R, choosePivot)\n    return (R - L) + quicksort(A, L, k - 1, choosePivot) + quicksort(A, k + 1, R, choosePivot)\n}\n\nfun run(filename: String, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    return quicksort(A, 0, A.size - 1, choosePivot)\n}\n\nfun main() {\n    var filename = \"problem5.6.txt\"\n    println(\"  left: ${run(filename, pivotLeft)}\")    //   left: 162085\n    println(\" right: ${run(filename, pivotRight)}\")   //  right: 164123\n    println(\"median: ${run(filename, pivotMedian)}\")  // median: 138382\n}\n```\n\n*Javascript*\n```javascript\nlet pivotLeft = (A, L, R) => L;\nlet pivotRight = (A, L, R) => R;\nlet pivotMedian = (A, L, R) => {\n    let M = L + Math.floor((R - L) / 2);\n    let cand = [A[L], A[M], A[R]].sort((a, b) => a - b),\n        target = cand[1];\n    if (target == A[L]) return L;\n    if (target == A[M]) return M;\n    if (target == A[R]) return R;\n};\n\nlet partition = (A, L, R, choosePivot) => {\n    let i = L + 1,\n        j = L + 1,\n        k = choosePivot(A, L, R);\n    [A[L], A[k]] = [A[k], A[L]];          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                // maintain loop invariant A[i] < pivot < A[j]\n            [A[i], A[j]] = [A[j], A[i]];\n            ++i;\n        }\n        ++j;\n    }\n    [A[L], A[i - 1]] = [A[i - 1], A[L]];  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n};\n\nlet quicksort = (A, L, R, choosePivot) => {\n    if (R <= L)\n        return 0;\n    let k = partition(A, L, R, choosePivot);\n    return (R - L) + quicksort(A, L, k - 1, choosePivot)\n                   + quicksort(A, k + 1, R, choosePivot);\n};\n\nlet run = (filename, choosePivot) => {\n    let A = [];\n    let LineByLine = require(\"n-readlines\");\n    let input = new LineByLine(filename);\n    for (let line; line = input.next(); A.push(Number(line)));\n    return quicksort(A, 0, A.length - 1, choosePivot);\n}\n\nlet filename = 'problem5.6.txt';\nconsole.log(`  left: ${run(filename, pivotLeft)}`);    //   left: 162085\nconsole.log(` right: ${run(filename, pivotRight)}`);   //  right: 164123\nconsole.log(`median: ${run(filename, pivotMedian)}`);  // median: 138382\n```\n\n*Python3*\n```python\ndef pivotLeft(A, L, R): return L\ndef pivotRight(A, L, R): return R\ndef pivotMedian(A, L, R):\n    M = L + (R - L) // 2\n    cand = sorted([A[L], A[M], A[R]])\n    target = cand[1]\n    if target == A[L]: return L\n    if target == A[M]: return M\n    if target == A[R]: return R\n\ndef partition(A, L, R, choosePivot):\n    i = L + 1\n    j = L + 1\n    k = choosePivot(A, L, R)\n    A[L], A[k] = A[k], A[L]          # swap pivot A[k] with first element of subarray A[L]\n    while j <= R:\n        if A[j] < A[L]:              # maintain loop invariant A[i] < pivot < A[j]\n            A[i], A[j] = A[j], A[i]\n            i += 1\n        j += 1\n    A[L], A[i - 1] = A[i - 1], A[L]  # swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n\ndef quicksort(A, L, R, choosePivot):\n    if R <= L:\n        return 0\n    k = partition(A, L, R, choosePivot)\n    return (R - L) + quicksort(A, L, k - 1, choosePivot) + quicksort(A, k + 1, R, choosePivot)\n\ndef run(filename, choosePivot):\n    A = []\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            A.append(int(line))\n\n    return quicksort(A, 0, len(A) - 1, choosePivot)\n\nfilename = 'problem5.6.txt'\nprint(f'  left: {run(filename, pivotLeft)}')    #   left: 162085\nprint(f' right: {run(filename, pivotRight)}')   #  right: 164123\nprint(f'median: {run(filename, pivotMedian)}')  # median: 138382\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n\nusing namespace std;\nusing VI = vector<int>;\nusing fun = function<int(VI&, int, int)>;\n\nfun pivotLeft = [](VI& A, int L, int R) { return L; };\nfun pivotRight = [](VI& A, int L, int R) { return R; };\nfun pivotMedian = [](VI& A, int L, int R) {\n    auto M = L + (R - L) / 2;\n    VI cand{ A[L], A[M], A[R] };\n    sort(cand.begin(), cand.end());\n    auto target = cand[1];\n    if (target == A[L]) return L;\n    if (target == A[M]) return M;\n    if (target == A[R]) return R;\n};\n\nint partition(VI& A, int L, int R, fun choosePivot) {\n    auto i = L + 1,\n         j = L + 1,\n         k = choosePivot(A, L, R);\n    swap(A[L], A[k]);          // swap pivot A[k] with first element of the subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {     // maintain loop invariant A[i] < pivot < A[j]\n            swap(A[i], A[j]);\n            ++i;\n        }\n        ++j;\n    }\n    swap(A[L], A[i - 1]);      // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n}\n\nint quicksort(VI& A, int L, int R, fun choosePivot) {\n    if (R <= L)\n        return 0;\n    auto k = partition(A, L, R, choosePivot);\n    return (R - L) + quicksort(A, L, k - 1, choosePivot)\n                   + quicksort(A, k + 1, R, choosePivot);\n}\n\nint run(string& filename, fun choosePivot) {\n    VI A;\n    fstream fin{ filename };\n    for (string line; fin >> line; A.push_back(stoi(line)));\n    int N = A.size();\n    return quicksort(A, 0, N - 1, choosePivot);\n}\n\nint main() {\n    string filename{ \"problem5.6.txt\" };\n    cout << \"  left: \" << run(filename, pivotLeft)   << endl   //   left: 162085\n         << \" right: \" << run(filename, pivotRight)  << endl   //  right: 164123\n         << \"median: \" << run(filename, pivotMedian) << endl;  // median: 138382\n    return 0;\n}\n```\n</details>\n\n---\n\n### Randomized Linear-Time Selection\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Randomized Linear-Time Selection](https://www.youtube.com/watch?v=nFw6x7DoYbs&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=31) (Section 6.1)\n* [Randomized Linear-Time Selection (Analysis)](https://www.youtube.com/watch?v=rX2u2CnpveQ&list=PLEGCF-WLh2RLHqXx6-GZr_w7LgqKDXxN_&index=32) (Section 6.2)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.io.File\nimport kotlin.random.Random\n\nfun partition(A: MutableList<Int>, L: Int, R: Int): Int {\n    var i = L + 1\n    var j = L + 1\n    var k = Random.nextInt(L, R + 1)          // +1 for L..R inclusive\n    A[L] = A[k].also { A[k] = A[L] }          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                    // maintain loop invariant A[i] < pivot < A[j]\n            A[i] = A[j].also { A[j] = A[i] }\n            ++i\n        }\n        ++j\n    }\n    A[L] = A[i - 1].also { A[i - 1] = A[L] }  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n}\n\nfun rselect(A: MutableList<Int>, i: Int, L_: Int, R_: Int): Int {\n    var L = L_\n    var R = R_\n    var k = partition(A, L, R)\n    if (i == k)\n        return A[k]  // 🎯 lucky guess\n    if (i < k)\n        R = k - 1\n    else\n        L = k + 1\n    return rselect(A, i, L, R)\n}\n\nfun run(filename: String, i: Int): Int {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    var N = A.size\n    return rselect(A, i - 1, 0 , N - 1)  // -1 for 0-based indexing\n}\n\nfun main() {\n    println(\"problem6.5test1.txt: \" + run(\"problem6.5test1.txt\", 5))   // problem6.5test1.txt: 5469\n    println(\"problem6.5test2.txt: \" + run(\"problem6.5test2.txt\", 50))  // problem6.5test2.txt: 4715\n}\n```\n\n*Javascript*\n```javascript\nlet random = (L, R) => Math.floor(Math.random() * (R + 1 - L) + L);  // +1 for L..R inclusive\n\nlet partition = (A, L, R) => {\n    let i = L + 1,\n        j = L + 1,\n        k = random(L, R);\n    [A[L], A[k]] = [A[k], A[L]];          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                // maintain loop invariant A[i] < pivot < A[j]\n            [A[i], A[j]] = [A[j], A[i]];\n            ++i;\n        }\n        ++j;\n    }\n    [A[L], A[i - 1]] = [A[i - 1], A[L]];  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n};\n\nlet rselect = (A, i, L, R) => {\n    let k = partition(A, L, R);\n    if (i == k)\n        return A[k];  // 🎯 lucky guess\n    if (i < k)\n        R = k - 1;\n    else\n        L = k + 1;\n    return rselect(A, i, L, R);\n}\n\nlet run = (filename, i) => {\n    let A = [];\n    let LineByLine = require(\"n-readlines\");\n    let input = new LineByLine(filename);\n    for (let line; line = input.next(); A.push(Number(line)));\n    let N = A.length;\n    return rselect(A, i - 1, 0, N - 1);  // -1 for 0-based indexing\n};\n\nconsole.log(`problem6.5test1.txt: ${run('problem6.5test1.txt', 5)}`);   // problem6.5test1.txt: 5469\nconsole.log(`problem6.5test2.txt: ${run('problem6.5test2.txt', 50)}`);  // problem6.5test2.txt: 4715\n```\n\n*Python3*\n```python\nfrom random import uniform\nfrom math import floor\n\ndef partition(A, L, R):\n    i = L + 1\n    j = L + 1\n    k = floor(uniform(L, R))\n    A[L], A[k] = A[k], A[L]          # swap pivot A[k] with first element of subarray A[L]\n    while j <= R:\n        if A[j] < A[L]:              # maintain loop invariant A[i] < pivot < A[j]\n            A[i], A[j] = A[j], A[i]\n            i += 1\n        j += 1\n    A[L], A[i - 1] = A[i - 1], A[L]  # swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n\ndef rselect(A, i, L, R):\n    k = partition(A, L, R)\n    if i == k:\n        return A[k]  # 🎯 lucky guess\n    if i < k:\n        R = k - 1\n    else:\n        L = k + 1\n    return rselect(A, i, L, R)\n\ndef run(filename, i):\n    A = []\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            A.append(int(line))\n    N = len(A)\n    return rselect(A, i - 1, 0, N - 1)  # -1 for 0-based indexing\n\nprint('problem6.5test1.txt:', run('problem6.5test1.txt', 5))   # problem6.5test1.txt: 5469\nprint('problem6.5test2.txt:', run('problem6.5test2.txt', 50))  # problem6.5test2.txt: 4715\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <random>\n\nusing namespace std;\nusing VI = vector<int>;\n\nint random(int L, int R) {\n    random_device rd;\n    mt19937 gen{ rd() };\n    uniform_int_distribution dist(L, R);\n    return dist(gen);\n}\n\nint partition(VI& A, int L, int R) {\n    auto i = L + 1,\n         j = L + 1,\n         k = random(L, R);\n    swap(A[L], A[k]);            // swap pivot A[k] with first element of the subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L])         // maintain loop invariant A[i] < pivot < A[j]\n            swap(A[i++], A[j]);\n        ++j;\n    }\n    swap(A[L], A[i - 1]);       // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n}\n\nint rselect(VI& A, int i, int L, int R) {\n    auto k = partition(A, L, R);\n    if (i == k)\n        return A[k];  // 🎯 lucky guess\n    if (i < k)\n        R = k - 1;\n    else\n        L = k + 1;\n    return rselect(A, i, L, R);\n}\n\nint run(string filename, int i, VI A = {}) {\n    fstream fin{ filename };\n    for (string line; fin >> line; A.push_back(stoi(line)));\n    int N = A.size();\n    return rselect(A, i - 1, 0, N - 1);  // -1 for 0-based indexing\n}\n\nint main() {\n    cout << \"problem6.5test1.txt: \" << run(\"problem6.5test1.txt\", 5)  << endl;  // problem6.5test1.txt: 5469\n    cout << \"problem6.5test2.txt: \" << run(\"problem6.5test2.txt\", 50) << endl;  // problem6.5test2.txt: 4715\n    return 0;\n}\n```\n\n</details>\n\n---\n\n# Part 2: Graph Algorithms and Data Structures\n\n<br/>\n<a href=\"https://www.amazon.com/dp/0999282921\" target=\"_blank\">\n    <img src=\"images/ai2large.jpg\" />\n</a>\n\n---\n\n### Topological Sort\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Graphs: The Basics (from 2:06 to 6:39)](https://www.youtube.com/watch?v=4Ih3UhVuEtw&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=1) (Sections 7.1 and 7.2)\n* [Graph Representations](https://www.youtube.com/watch?v=b-Mfu8dPv9U&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=2) (Sections 7.3 and 7.4)\n* [Graph Search Overview](https://www.youtube.com/watch?v=SW6jwg7WS48&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=3) (Section 8.1)\n* [Breadth-First Search](https://www.youtube.com/watch?v=73qCvXsYkfk&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=4) (Section 8.2, Part 1)\n* [Depth-First Search](https://www.youtube.com/watch?v=73qCvXsYkfk&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=4) (Section 8.4)\n* [Topological Sort](https://www.youtube.com/watch?v=ozso3xxkVGU&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=8) (Section 8.5)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.util.Queue\nimport java.util.LinkedList\n\nclass Solution(val adj: MutableMap<Char, List<Char>>) {\n\n    var N: Int\n    var color: Int\n    var m = mutableMapOf<Char, Int>()\n    var seen = mutableSetOf<Char>()\n\n    init {\n        N = adj.size\n        color = 0\n    }\n\n    fun init(start: Int) {\n        color = start\n        m.clear()\n        seen.clear()\n    }\n\n    fun topoSortBFS(): String {\n        init(1)  // 👉 color forward from 1..N\n        bfs()\n        return toString()\n    }\n\n    fun topoSortDFS(): String {\n        init(N)  // 👈 color reverse from N..1 (as the recursive stack unwinds)\n        adj.forEach{ (u, _) -> dfs(u) }\n        return toString()\n    }\n\n    fun bfs() {\n        var degree = mutableMapOf<Char, Int>()\n        adj.forEach{ (_, neighbors) ->\n            neighbors.forEach{ v ->\n                degree[v] = 1 + degree.getOrDefault(v, 0)\n            }\n        }\n        var q: Queue<Char> = LinkedList(adj.map{ (u, _) -> u }.filter{ !degree.contains(it) })\n        while (0 < q.size) {\n            var u = q.poll()\n            m[u] = color++\n            adj[u]!!.forEach{ v ->\n                degree[v] = degree[v]!!.minus(1)\n                if (degree[v] == 0 && !seen.contains(v)) {\n                    q.add(v); seen.add(v)\n                }\n            }\n        }\n    }\n\n    fun dfs(u: Char) {\n        if (seen.contains(u))\n            return\n        seen.add(u)\n        adj[u]!!.forEach{ v ->\n            dfs(v)\n        }\n        m[u] = color--\n    }\n\n    override fun toString(): String {\n        var s = mutableListOf<String>()\n        adj.forEach{ (u, _) ->\n            s.add(\"$u: ${m[u]}\")\n        }\n        return s.joinToString(\"\\n\")\n    }\n}\n\nfun main() {\n    var adj = mutableMapOf<Char, List<Char>>(\n        's' to listOf<Char>('v', 'w'),\n        'v' to listOf<Char>('t'),\n        'w' to listOf<Char>('t'),\n        't' to listOf<Char>()\n    )\n    var solution = Solution(adj)\n    println(\"BFS:\\n${solution.topoSortBFS()}\\n\\nDFS:\\n${solution.topoSortDFS()}\")\n\n//    BFS:\n//    s: 1\n//    v: 2\n//    w: 3\n//    t: 4\n\n//    DFS:\n//    s: 1\n//    v: 3\n//    w: 2\n//    t: 4\n\n}\n```\n\n*Javascript*\n```javascript\nclass Solution {\n    constructor(adj) {\n        this.adj = adj;\n        this.N = this.adj.size;\n    }\n    init(start) {\n        this.color = start;\n        this.seen = new Set();\n        this.m = new Map();\n    }\n    topo_sort_bfs() {\n        this.init(1);       // 👉 color forward from 1..N\n        this.bfs();\n        return this.to_string();\n    }\n    topo_sort_dfs() {\n        this.init(this.N);  // 👈 color reverse from N..1 (as the recursive stack unwinds)\n        for (let [u, _] of [...this.adj])\n            this.dfs(u);\n        return this.to_string();\n    }\n    bfs() {\n        let degree = new Map();\n        for (let [u, _] of [...this.adj]) {\n            degree.set(u, (degree.get(u) || 0));\n            for (let v of this.adj.get(u))\n                degree.set(v, 1 + (degree.get(v) || 0));\n        }\n        let q = [...this.adj].map(([u, _]) => u).filter(u => !degree.get(u));\n        let seen = new Set(q);\n        while (q.length) {\n            let u = q.shift();\n            this.m.set(u, this.color++);\n            for (let v of this.adj.get(u)) {\n                degree.set(v, -1 + degree.get(v));\n                if (!degree.get(v) && !seen.has(v))\n                    q.push(v), seen.add(v);\n            }\n        }\n    }\n    dfs(u) {\n        if (this.seen.has(u))\n            return;\n        this.seen.add(u);\n        for (let v of this.adj.get(u))\n            if (!this.seen.has(v))\n                this.dfs(v);\n        this.m.set(u, this.color--);\n    }\n    to_string() {\n        let s = [];\n        for (let [u, color] of [...this.m])\n            s.push(`${u}: ${color}`);\n        return s.join('\\n');\n    }\n}\n\nlet adj = new Map();\nadj.set('s', ['v', 'w']);\nadj.set('v', ['t']);\nadj.set('w', ['t']);\nadj.set('t', []);\nlet solution = new Solution(adj);\nconsole.log(`BFS:\\n${solution.topo_sort_bfs()}\\n\\nDFS:\\n${solution.topo_sort_dfs()}`);\n\n//    BFS:\n//    s: 1\n//    v: 2\n//    w: 3\n//    t: 4\n\n//    DFS:\n//    t: 4\n//    v: 3\n//    w: 2\n//    s: 1\n```\n\n*Python3*\n```python\nfrom collections import deque\n\nclass Solution:\n    def __init__(self, adj):\n        self.adj = adj\n        self.N = len(adj)\n        self.seen = set()\n        self.m = {}\n\n    def init(self, start):\n        self.color = start\n        self.seen.clear()\n        self.m.clear()\n\n    def topo_sort_bfs(self):\n        self.init(1)         # 👉 color forward from 1..N\n        self.bfs()\n        return self.to_string()\n\n    def topo_sort_dfs(self):\n        self.init(self.N)  # 👈 color reverse from N..1 (as the recursive stack unwinds)\n        for u, _ in self.adj.items():\n            self.dfs(u)\n        return self.to_string()\n\n    def bfs(self):\n        degree = {}\n        for _, neighbors in self.adj.items():\n            for v in neighbors:\n                degree[v] = 1 + (degree[v] if v in degree else 0)\n        q = deque(u for u, _ in self.adj.items() if u not in degree)\n        self.seen.update(*q)\n        while q:\n            u = q.popleft()\n            self.m[u] = self.color; self.color += 1\n            for v in adj[u]:\n                degree[v] -= 1\n                if not degree[v] and v not in self.seen:\n                    q.append(v); self.seen.add(v)\n\n    def dfs(self, u):\n        if u in self.seen:\n            return\n        self.seen.add(u)\n        for v in adj[u]:\n            self.dfs(v)\n        self.m[u] = self.color; self.color -= 1\n\n    def to_string(self):\n        s = []\n        for u, color in self.m.items():\n            s.append(f'{u}: {color}')\n        return '\\n'.join(s)\n\n#\n# graph from Quiz 8.3 on page 45 of Algorithms Illuminated: Part 2\n#\nadj = {\n    's': ['v', 'w'],\n    'v': ['t'],\n    'w': ['t'],\n    't': []\n}\nsolution = Solution(adj)\n\nprint(f'BFS:\\n{solution.topo_sort_bfs()}\\n\\nDFS:\\n{solution.topo_sort_dfs()}')\n\n#    BFS:\n#    s: 1\n#    v: 2\n#    w: 3\n#    t: 4\n\n#    DFS:\n#    t: 4\n#    v: 3\n#    w: 2\n#    s: 1\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n#include <unordered_set>\n#include <queue>\n\nusing namespace std;\n\nusing VI = vector<int>;\nusing AdjList = unordered_map<char, VI>;\nusing Set = unordered_set<char>;\nusing Map = unordered_map<char, int>;\nusing Queue = queue<char>;\nusing fun = function<void(char)>;\n\nclass Solution {\nprivate:\n    AdjList adj;\n    const int N;\n    Map m;\n    Set seen;\n    int color;\npublic:\n    Solution(AdjList& adj) : adj{ adj }, N{ int(adj.size()) } {\n    }\n    void init(int start) {\n        m.clear();\n        seen.clear();\n        color = start;\n    }\n    string topo_sort_bfs() {\n        init(1);  // 👉 color forward from 1..N\n        bfs();\n        return to_string();\n    }\n    string topo_sort_dfs() {\n        init(N);  // 👈 color reverse from N..1 (as the recursive stack unwinds)\n        for (auto [u, _]: adj)\n            dfs(u);\n        return to_string();\n    }\n    void bfs() {\n        Map degree;\n        for (auto [_, neighbors]: adj)\n            for (auto v: neighbors)\n                ++degree[v];\n        Queue q;\n        for (auto [u, _]: adj)\n            if (!degree[u] && seen.insert(u).second)\n                q.push(u);\n        while (q.size()) {\n            auto u = q.front(); q.pop();\n            m[u] = color++;\n            for (auto v: adj[u])\n                if (!--degree[v] && seen.insert(v).second)\n                    q.push(v);\n        }\n    }\n    void dfs(char start) {\n        fun go = [&](auto u) {\n            if (!seen.insert(u).second)\n                return;\n            for (auto v: adj[u])\n                go(v);\n            m[u] = color--;\n        };\n        go(start);\n    }\n    string to_string() {\n        ostringstream os;\n        for (auto [u, color]: m)\n            os << u << \": \" << color << endl;\n        return os.str();\n    }\n};\n\nint main() {\n    //\n    // graph from Quiz 8.3 on page 45 of Algorithms Illuminated: Part 2\n    //\n    AdjList adj{\n        { 's', { 'v', 'w' } },\n        { 'v', { 't' } },\n        { 'w', { 't' } },\n        { 't', {} }\n    };\n    Solution solution{ adj };\n\n    cout << \"BFS:\" << endl << solution.topo_sort_bfs() << endl\n         << \"DFS:\" << endl << solution.topo_sort_dfs() << endl;\n\n//    BFS:\n//    t: 4\n//    w: 3\n//    v: 2\n//    s: 1\n//\n//    DFS:\n//    s: 1\n//    w: 2\n//    v: 3\n//    t: 4\n\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Kosaraju\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Computing Strongly Connected Components (Part 1) (Section 8.6, Part 1)](https://www.youtube.com/watch?v=O98hLTYVN3c&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=9)\n* [Computing Strongly Connected Components (Part 2) (Section 8.6, Part 2)](https://www.youtube.com/watch?v=gbs3UNRJIYk&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=10)\n* [The Structure of the Web (Section 8.7)](https://www.youtube.com/watch?v=7YodysGShlo&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=11)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.util.Stack\nimport java.io.File\n\nclass RecursiveSolution(var adj: MutableMap<Int, MutableList<Int>>, var rev: MutableMap<Int, MutableList<Int>>) {\n    fun topo_sort(): MutableList<Int> {\n        var list = mutableListOf<Int>()\n        var seen = mutableSetOf<Int>()\n        fun go(u: Int) {\n            if (seen.contains(u))\n                return\n            seen.add(u)\n            for (v in rev[u]!!)\n                go(v)\n            list.add(0, u)\n        }\n        for ((u, _) in rev)\n            go(u)\n        return list\n    }\n    fun kosaraju(): MutableList<List<Int>> {\n        var lists = mutableListOf<List<Int>>()\n        var seen = mutableSetOf<Int>()\n        fun go(u: Int, list: MutableList<Int>) {\n            if (seen.contains(u))\n                return\n            list.add(u); seen.add(u)\n            for (v in adj[u]!!)\n                go(v, list)\n        }\n        for (u in topo_sort()) {\n            if (seen.contains(u))\n                continue\n            var list = mutableListOf<Int>()\n            go(u, list)\n            lists.add(list.toList())\n        }\n        return lists\n    }\n}\n\nclass IterativeSolution(var adj: MutableMap<Int, MutableList<Int>>, var rev: MutableMap<Int, MutableList<Int>>) {\n    fun topo_sort(): MutableList<Int> {\n        var list = mutableListOf<Int>()\n        var seen = mutableSetOf<Int>()\n        for ((u, _) in rev) {\n            if (seen.contains(u))\n                continue\n            var stack = Stack<Int>()\n            stack.push(u); seen.add(u)\n            while (!stack.empty()) {\n                var u = stack.last()\n                for (v in rev[u]!!) {\n                    if (!seen.contains(v)) {\n                        stack.push(v); seen.add(v)\n                    }\n                }\n                if (u == stack.last())\n                    list.add(0, stack.pop())\n            }\n        }\n        return list\n    }\n    fun kosaraju(): MutableList<List<Int>> {\n        var lists = mutableListOf<List<Int>>()\n        var seen = mutableSetOf<Int>()\n        for (u in topo_sort()) {\n            if (seen.contains(u))\n                continue\n            var list = mutableListOf<Int>()\n            var stack = Stack<Int>()\n            stack.push(u); seen.add(u)\n            while (!stack.empty()) {\n                var u = stack.last()\n                for (v in adj[u]!!) {\n                    if (!seen.contains(v)) {\n                        stack.push(v); seen.add(v)\n                    }\n                }\n                if (u == stack.last())\n                    list.add(stack.pop())\n            }\n            lists.add(list.toList())\n        }\n        return lists\n    }\n}\n\nfun run(filename: String) {\n    var adj = mutableMapOf<Int, MutableList<Int>>()\n    var rev = mutableMapOf<Int, MutableList<Int>>()\n    File(filename).forEachLine {\n        var (u, v) = it.trim().split(\" \").map{ it.toInt() }\n        if (!adj.contains(u)) adj[u] = mutableListOf(); if (!adj.contains(v)) adj[v] = mutableListOf()\n        if (!rev.contains(u)) rev[u] = mutableListOf(); if (!rev.contains(v)) rev[v] = mutableListOf()\n        adj[u]!!.add(v)\n        rev[v]!!.add(u)\n    }\n    // var solution = RecursiveSolution(adj, rev)\n    var solution = IterativeSolution(adj, rev)\n    var A = solution.kosaraju()\n    A.sortWith(Comparator{ a: List<Int>, b: List<Int> -> b.size - a.size })\n    println(filename + \": \" + A.map{ it.size }.slice(0 until Math.min(A.size, 5)).joinToString(\" \"))\n}\n\nfun main() {\n    run(\"section8.6.5page64.txt\");  // Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\n    run(\"problem8.10test1.txt\");    // Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\n    run(\"problem8.10test2.txt\");    // Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\n    run(\"problem8.10test3.txt\");    // Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\n    run(\"problem8.10test4.txt\");    // Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\n    run(\"problem8.10test5.txt\");    // Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\n    run(\"problem8.10.txt\");         // Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n//    section8.6.5page64.txt: 4 3 3 1\n//    problem8.10test1.txt: 3 3 3\n//    problem8.10test2.txt: 3 3 2\n//    problem8.10test3.txt: 3 3 1 1\n//    problem8.10test4.txt: 7 1\n//    problem8.10test5.txt: 6 3 2 1\n//    problem8.10.txt: 434821 968 459 313 211\n\n}\n```\n\n*Javascript*\n```javascript\nclass BaseSolution {\n    constructor(adj, rev) {\n        this.adj = adj;\n        this.rev = rev;\n    }\n}\n\nclass RecursiveSolution extends BaseSolution {\n    constructor(adj, rev) {\n        super(adj, rev);\n    }\n    topo_sort() {\n        let list = [];\n        let seen = new Set();\n        let go = u => {\n            if (seen.has(u))\n                return;\n            seen.add(u);\n            for (let v of [...this.rev.get(u)])\n                go(v);\n            list.unshift(u);\n        };\n        for (let [u, _] of [...this.rev])\n            go(u);\n        return list;\n    }\n    kosaraju() {\n        let lists = [];\n        let seen = new Set();\n        let go = (u, list) => {\n            if (seen.has(u))\n                return;\n            seen.add(u);\n            list.push(u);\n            for (let v of [...this.adj.get(u)])\n                go(v, list);\n        };\n        for (let u of this.topo_sort()) {\n            let list = [];\n            go(u, list);\n            lists.push([...list]);\n        }\n        lists.sort((a, b) => b.length - a.length);\n        return lists;\n    }\n}\n\nclass IterativeSolution extends BaseSolution {\n    constructor(adj, rev) {\n        super(adj, rev);\n    }\n    topo_sort() {\n        let list = [];\n        let seen = new Set();\n        for (let [u, _] of [...this.rev]) {\n            if (seen.has(u))\n                continue;\n            let stack = [ u ]; seen.add(u);\n            stack.back = () => stack[stack.length - 1];\n            while (stack.length) {\n                let u = stack.back();\n                for (let v of [...this.rev.get(u)])\n                    if (!seen.has(v))\n                        stack.push(v), seen.add(v);\n                if (u == stack.back())\n                    list.unshift(stack.pop());\n            }\n        }\n        return list;\n    }\n    kosaraju() {\n        let lists = [];\n        let seen = new Set();\n        for (let u of this.topo_sort()) {\n            if (seen.has(u))\n                continue;\n            let list = [];\n            let stack = [ u ]; seen.add(u);\n            stack.back = () => stack[stack.length - 1];\n            while (stack.length) {\n                let u = stack.back();\n                for (let v of [...this.adj.get(u)])\n                    if (!seen.has(v))\n                        stack.push(v), seen.add(v);\n                if (u == stack.back())\n                    list.push(stack.pop());\n            }\n            lists.push([...list]);\n        }\n        lists.sort((a, b) => b.length - a.length);\n        return lists;\n    }\n}\n\nlet run = filename => {\n    let adj = new Map(),\n        rev = new Map();\n    let LineByLine = require('n-readlines');\n    let input = new LineByLine(filename);\n    let line;\n    while (line = input.next()) {\n        let [u, v] = String.fromCharCode(...line).split(' ').map(Number);\n        if (!adj.has(u)) adj.set(u, []); if (!adj.has(v)) adj.set(v, []);\n        if (!rev.has(u)) rev.set(u, []); if (!rev.has(v)) rev.set(v, []);\n        adj.get(u).push(v);\n        rev.get(v).push(u);\n    }\n    // let A = new RecursiveSolution(adj, rev).kosaraju();\n    let A = new IterativeSolution(adj, rev).kosaraju();\n    console.log(`${filename}: ${A.slice(0, Math.min(A.length, 5)).map(scc => scc.length).join(' ')}`);\n};\n\nrun('section8.6.5page64.txt')  // Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\nrun('problem8.10test1.txt')    // Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\nrun('problem8.10test2.txt')    // Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\nrun('problem8.10test3.txt')    // Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\nrun('problem8.10test4.txt')    // Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\nrun('problem8.10test5.txt')    // Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\nrun('problem8.10.txt')         // Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n\n//    section8.6.5page64.txt: 4 3 3 1\n//    problem8.10test1.txt: 3 3 3\n//    problem8.10test2.txt: 3 3 2\n//    problem8.10test3.txt: 3 3 1 1\n//    problem8.10test4.txt: 7 1\n//    problem8.10test5.txt: 6 3 2 1\n//    problem8.10.txt: 434821 968 459 313 211\n```\n\n*Python3*\n```python\nfrom collections import deque\nfrom functools import cmp_to_key\n\nclass BaseSolution:\n    def __init__(self, adj, rev):\n        self.adj = adj\n        self.rev = rev\n\nclass RecursiveSolution(BaseSolution):\n    def topo_sort(self):\n        list = deque()\n        seen = set()\n        def go(u):\n            if u in seen:\n                return\n            seen.add(u)\n            for v in self.rev[u]:\n                go(v)\n            list.appendleft(u)\n        for u in self.rev.keys():\n            go(u)\n        return list\n\n    def kosaraju(self):\n        lists = []\n        seen = set()\n        def go(u, list):\n            if u in seen:\n                return\n            seen.add(u)\n            list.append(u)\n            for v in self.adj[u]:\n                go(v, list)\n        for u in self.topo_sort():\n            list = []\n            go(u, list)\n            lists.append(list.copy())\n        lists.sort(key = cmp_to_key(lambda a, b: len(b) - len(a)))\n        return lists\n\nclass IterativeSolution(BaseSolution):\n    def topo_sort(self):\n        list = deque()\n        seen = set()\n        for u in self.rev.keys():\n            if u in seen:\n                continue\n            stack = [ u ]; seen.add(u)\n            while len(stack):\n                u = stack[-1]\n                for v in self.rev[u]:\n                    if v not in seen:\n                        stack.append(v); seen.add(v)\n                if u == stack[-1]:\n                    list.appendleft(stack.pop())\n        return list\n\n    def kosaraju(self):\n        lists = []\n        seen = set()\n        for u in self.topo_sort():\n            if u in seen:\n                continue\n            list = deque()\n            stack = [ u ]; seen.add(u)\n            while len(stack):\n                u = stack[-1]\n                for v in self.adj[u]:\n                    if v not in seen:\n                        stack.append(v); seen.add(v)\n                if u == stack[-1]:\n                    list.appendleft(stack.pop())\n            lists.append(list.copy())\n        lists.sort(key = cmp_to_key(lambda a, b: len(b) - len(a)))\n        return lists\n\ndef run(filename):\n    adj, rev = {}, {}\n    with open(filename) as fin:\n        while True:\n            line = fin.readline().strip()\n            if not line:\n                break\n            u, v = [int(x) for x in line.split()]\n            if u not in adj: adj[u] = []\n            if v not in adj: adj[v] = []\n            if u not in rev: rev[u] = []\n            if v not in rev: rev[v] = []\n            adj[u].append(v)\n            rev[v].append(u)\n    # solution = RecursiveSolution(adj, rev)\n    solution = IterativeSolution(adj, rev)\n    A = solution.kosaraju()\n    print(filename + ': ' + ' '.join(str(len(scc)) for scc in A[:5]))\n\nrun('section8.6.5page64.txt')  # Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\nrun('problem8.10test1.txt')    # Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\nrun('problem8.10test2.txt')    # Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\nrun('problem8.10test3.txt')    # Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\nrun('problem8.10test4.txt')    # Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\nrun('problem8.10test5.txt')    # Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\nrun('problem8.10.txt')         # Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n#    section8.6.5page64.txt: 4 3 3 1\n#    problem8.10test1.txt: 3 3 3\n#    problem8.10test2.txt: 3 3 2\n#    problem8.10test3.txt: 3 3 1 1\n#    problem8.10test4.txt: 7 1\n#    problem8.10test5.txt: 6 3 2 1\n#    problem8.10.txt: 434821 968 459 313 211\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <unordered_map>\n#include <unordered_set>\n#include <queue>\n\nusing namespace std;\n\nusing List = deque<int>;\nusing Lists = deque<List>;\nusing AdjList = unordered_map<int, List>;\nusing Set = unordered_set<int>;\nusing Map = unordered_map<int, int>;\n\nnamespace Base {\n    class Solution {\n    protected:\n        AdjList adj, rev;\n    public:\n        Solution(AdjList& adj, AdjList& rev) : adj{ adj }, rev{ rev } {}\n    };\n}\nnamespace Recursive {\n    struct Solution : public Base::Solution {\n        Solution(AdjList& adj, AdjList& rev) : Base::Solution{ adj, rev } {}\n        Lists kosaraju() {\n            Lists lists;\n            Set seen;\n            using fun = function<void(int, List&)>;\n            fun go = [&](auto u, auto& list) {\n                if (!seen.insert(u).second)\n                    return;\n                list.push_back(u);\n                for (auto v: adj[u])\n                    go(v, list);\n            };\n            for (auto u: topo_sort()) {\n                List list;\n                go(u, list);\n                lists.emplace_back(list);\n            }\n            sort(lists.begin(), lists.end(), [](auto& a, auto& b) { return b.size() < a.size(); });\n            return lists;\n        }\n        List topo_sort() {\n            List list;\n            Set seen;\n            using fun = function<void(int)>;\n            fun go = [&](auto u) {\n                if (!seen.insert(u).second)\n                    return;\n                for (auto v: rev[u])\n                    go(v);\n                list.push_front(u);\n            };\n            for (auto [u, _]: rev)\n                go(u);\n            return list;\n        }\n    };\n}\nnamespace Iterative {\n    struct Solution : public Base::Solution {\n        Solution(AdjList& adj, AdjList& rev) : Base::Solution{ adj, rev } {}\n        Lists kosaraju() {\n            Lists lists;\n            Set seen;\n            for (auto u: topo_sort()) {\n                if (seen.find(u) != seen.end())\n                    continue;\n                List list;\n                List stack{ u }; seen.insert(u);\n                while (stack.size()) {\n                    auto u = stack.back();\n                    for (auto v: adj[u])\n                        if (seen.insert(v).second)\n                            stack.push_back(v);\n                    if (u == stack.back())\n                        list.push_back(u), stack.pop_back();\n                }\n                lists.emplace_back(list);\n            }\n            sort(lists.begin(), lists.end(), [](auto& a, auto& b) { return b.size() < a.size(); });\n            return lists;\n        }\n        List topo_sort() {\n            List list;\n            Set seen;\n            for (auto [u, _]: rev) {\n                if (seen.find(u) != seen.end())\n                    continue;\n                List stack{ u }; seen.insert(u);\n                while (stack.size()) {\n                    auto u = stack.back();\n                    for (auto v: rev[u])\n                        if (seen.insert(v).second)\n                            stack.push_back(v);\n                    if (u == stack.back())\n                        list.push_front(stack.back()), stack.pop_back();\n                }\n            }\n            return list;\n        }\n    };\n}\n\nvoid run(string filename) {\n    int u, v;\n    AdjList adj, rev;\n    fstream fin{ filename };\n    for (string line; fin >> u >> v;) {\n        adj[u].push_back(v);\n        rev[v].push_back(u);\n    }\n    auto A = Iterative::Solution{ adj, rev }.kosaraju();\n    A.resize(min(A.size(), size_t(5)));\n    cout << filename << \": \";\n    for (auto i{ 0 }; i < A.size(); cout << A[i++].size() << \" \");\n    cout << endl;\n}\n\nint main() {\n    run(\"section8.6.5page64.txt\");  // Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\n    run(\"problem8.10test1.txt\");    // Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\n    run(\"problem8.10test2.txt\");    // Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\n    run(\"problem8.10test3.txt\");    // Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\n    run(\"problem8.10test4.txt\");    // Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\n    run(\"problem8.10test5.txt\");    // Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\n    run(\"problem8.10.txt\");         // Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n//    section8.6.5page64.txt: 4 3 3 1\n//    problem8.10test1.txt: 3 3 3\n//    problem8.10test2.txt: 3 3 2\n//    problem8.10test3.txt: 3 3 1 1\n//    problem8.10test4.txt: 7 1\n//    problem8.10test5.txt: 6 3 2 1\n//    problem8.10.txt: 434821 968 459 313 211\n\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Dijkstra\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Shortest Paths and Dijkstra's Algorithm (Sections 9.1 and 9.2, Part 1)](https://www.youtube.com/watch?v=jRlNVmRjdRk&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=12)\n* [Dijkstra's Algorithm: Examples (Section 9.2, Part 2)](https://www.youtube.com/watch?v=ahYhIzLklYo&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=13)\n* [Correctness of Dijkstra's Algorithm (Section 9.3)](https://www.youtube.com/watch?v=sb7j3EW055M&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=14)\n* [Implementation and Running Time of Dijkstra's Algorithm (0:00-4:30) (Section 9.4)](https://www.youtube.com/watch?v=00LtSn_PQjc&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=15)\n* [Data Structures Overview (Section 10.1)](https://www.youtube.com/watch?v=cMrQxxrKg8I&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=16)\n* [Heaps: Operations and Applications (Sections 10.2 and 10.3)](https://www.youtube.com/watch?v=mNYHDv7SbDI&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=17)\n* [Speeding Up Dijkstra's Algorithm With Heaps (4:30-26:27) (Section 10.4)](https://www.youtube.com/watch?v=00LtSn_PQjc&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=15)\n* [Heaps: Implementation Details (Section 10.5)](https://www.youtube.com/watch?v=6VI5kJu8Mv4&list=PLEGCF-WLh2RJ5W-pt-KE9GUArTDzVwL1P&index=19&t=0s)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```java\nimport java.io.File\nimport java.util.PriorityQueue\n\nvar INF = (1e9 + 7).toInt()\n\ninterface BaseSolution {\n    fun run(filename: String, queries: Array<Int>): String\n}\n\nclass NaiveSolution : BaseSolution {\n    fun dijkstra(E: List<Triple<Int, Int, Int>>): MutableMap<Int, Int> {\n        var dist = mutableMapOf<Int, Int>()\n        var seen = mutableSetOf<Int>()\n        var start = 1\n        dist[start] = 0; seen.add(start)\n        var found: Boolean;\n        do {\n            found = false\n            var best_v = INF\n            var best_w = INF\n            for ((u, v, w) in E) {\n                if (!seen.contains(u) || seen.contains(v))\n                    continue\n                found = true\n                if (best_w > dist[u]!! + w) {\n                    best_v = v\n                    best_w = dist[u]!! + w\n                }\n            }\n            var v = best_v\n            var w = best_w\n            dist[v] = w; seen.add(v)\n        } while (found)\n        return dist\n    }\n    override fun run(filename: String, queries: Array<Int>): String {\n        var E = mutableListOf<Triple<Int, Int, Int>>()\n        File(filename).forEachLine {\n            var words = it.trim().split(\"\\t\")\n            var u = words[0].toInt()\n            for (i in 1 until words.size) {\n                var (v, w) = words[i].split(\",\").map{ it.toInt() }\n                E.add(Triple(u, v, w))\n            }\n        }\n        var dist = dijkstra(E.toList())\n        return queries.map{ dist[it] }.joinToString(\" \")\n    }\n}\n\nclass HeapSolution : BaseSolution {\n    fun dijkstra(adj: MutableMap<Int, MutableList<Pair<Int, Int>>>): MutableMap<Int, Int> {\n        var dist = mutableMapOf<Int, Int>()\n        var seen = mutableSetOf<Int>()\n        var start = 1\n        dist[start] = 0\n        var q = PriorityQueue<Pair<Int, Int>>(Comparator{ a: Pair<Int, Int>, b: Pair<Int, Int> -> a.first.compareTo(b.first) })\n        q.add(Pair(0, start))\n        while (0 < q.size) {\n            var (cost, u) = q.poll()\n            if (seen.contains(u))\n                continue\n            dist[u] = cost; seen.add(u)\n            for ((w, v) in adj[u]!!) {\n                if (seen.contains(v))\n                    continue\n                q.add(Pair(cost + w, v))\n            }\n        }\n        return dist\n    }\n    override fun run(filename: String, queries: Array<Int>): String {\n        var adj = mutableMapOf<Int, MutableList<Pair<Int, Int>>>()\n        File(filename).forEachLine {\n            var words = it.trim().split(\"\\t\")\n            var u = words[0].toInt()\n            if (!adj.contains(u))\n                adj[u] = mutableListOf()\n            for (i in 1 until words.size) {\n                var (v, w) = words[i].split(\",\").map{ it.toInt() }\n                adj[u]!!.add(Pair(w, v))\n            }\n        }\n        var dist = dijkstra(adj)\n        return queries.map{ dist[it] }.joinToString(\" \")\n    }\n}\n\nfun run(solution: BaseSolution) {\n    println(solution.run(\"problem9.8test.txt\", arrayOf(1, 2, 3, 4, 5, 6, 7, 8)))\n    println(solution.run(\"problem9.8.txt\", arrayOf(7, 37, 59, 82, 99, 115, 133, 165, 188, 197)))\n}\n\nfun main() {\n    run(NaiveSolution())\n    //    0 1 2 3 4 4 3 2\n    //    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n    run(HeapSolution())\n    //    0 1 2 3 4 4 3 2\n    //    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n}\n```\n\n*Javascript*\n```javascript\nlet LineByLine = require('n-readlines');\n\nlet INF = Number(1e9 + 7);\n\nclass NaiveSolution {\n    dijkstra(E) {\n        let dist = new Map();\n        let seen = new Set();\n        let start = 1;\n        dist[start] = 0; seen.add(start);\n        for (;;) {\n            let found = false;\n            let best_v = INF,\n                best_w = INF;\n            for (let [u, v, w] of E) {\n                if (!seen.has(u) || seen.has(v))\n                    continue;\n                found = true;\n                if (best_w > dist[u] + w)\n                    best_v = v,\n                    best_w = dist[u] + w;\n            }\n            if (!found)\n                break;\n            let [v, w] = [best_v, best_w];\n            dist[v] = w; seen.add(v);\n        }\n        return dist;\n    }\n    run(filename, queries) {\n        let E = [];\n        let input = new LineByLine(filename);\n        let line;\n        while (line = input.next()) {\n            let words = String.fromCharCode(...line).trim().split(/\\s+/);\n            let u = Number(words[0]);\n            for (let i = 1; i < words.length; ++i) {\n                let [v, w] = words[i].split(',').map(Number);\n                E.push([ u, v, w ]);\n            }\n        }\n        let dist = this.dijkstra(E);\n        return queries.map(x => dist[x]).join(' ');\n    }\n}\n\nlet heapkey = x => Array.isArray(x) ? x[0] : x;\nlet heappush = (A, x, f = Math.min) => {\n    let P = i => Math.floor((i - 1) / 2);  // parent\n    A.push(x);\n    let N = A.length,\n        i = N - 1;\n    while (0 < i && heapkey(A[i]) == f(heapkey(A[i]), heapkey(A[P(i)]))) {\n        [A[i], A[P(i)]] = [A[P(i)], A[i]];\n        i = P(i);\n    }\n};\nlet heappop = (A, f = Math.min) => {\n    let L = i => 2 * i + 1,  // children\n        R = i => 2 * i + 2;\n    let N = A.length,\n        i = 0;\n    let top = A[0];\n    [A[0], A[N - 1]] = [A[N - 1], A[0]], A.pop(), --N;\n    let ok = true;\n    do {\n        ok = true;\n        let left = f == Math.min ? Infinity : -Infinity,\n            right = left;\n        if (L(i) < N && heapkey(A[i]) != f(heapkey(A[i]), heapkey(A[L(i)]))) ok = false, left  = heapkey(A[L(i)]);\n        if (R(i) < N && heapkey(A[i]) != f(heapkey(A[i]), heapkey(A[R(i)]))) ok = false, right = heapkey(A[R(i)]);\n        if (!ok) {\n            let j = left == f(left, right) ? L(i) : R(i);\n            [A[i], A[j]] = [A[j], A[i]];\n            i = j;\n        }\n    } while (!ok);\n    return top;\n};\n\nclass HeapSolution {\n    dijkstra(adj) {\n        let dist = {};\n        let seen = new Set();\n        let start = 1;\n        let q = [[ 0, start ]];\n        while (q.length) {\n            let [cost, u] = heappop(q);\n            if (seen.has(u))\n                continue;\n            dist[u] = cost, seen.add(u);\n            for (let [w, v] of (adj[u] || []))\n                heappush(q, [ dist[u] + w, v ]);\n        }\n        return dist;\n    }\n    run(filename, queries) {\n        let adj = {};\n        let input = new LineByLine(filename);\n        let line;\n        while (line = input.next()) {\n            let words = String.fromCharCode(...line).trim().split('\\t');\n            let u = Number(words[0]);\n            if (!(u in adj))\n                adj[u] = [];\n            for (let i = 1; i < words.length; ++i) {\n                let [v, w] = words[i].split(',').map(Number);\n                adj[u].push([ w, v ]);\n            }\n        }\n        let dist = this.dijkstra(adj);\n        return queries.map(x => dist[x]).join(' ');\n    }\n}\n\nlet run = solution => {\n    console.log(solution.run('problem9.8test.txt', [1, 2, 3, 4, 5, 6, 7, 8]));\n    console.log(solution.run('problem9.8.txt', [7, 37, 59, 82, 99, 115, 133, 165, 188, 197]));\n};\n\nrun(new NaiveSolution());\n//    0 1 2 3 4 4 3 2\n//    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n\nrun(new HeapSolution());\n//    0 1 2 3 4 4 3 2\n//    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n```\n\n*Python3*\n```python\nfrom abc import ABC, abstractmethod\nfrom heapq import heappush, heappop\n\nINF = int(1e9 + 7)\n\nclass BaseSolution(ABC):\n    @abstractmethod\n    def run(self, filename, queries):\n        raise NotImplementedError\n\nclass NaiveSolution(BaseSolution):\n    def dijkstra(self, E):\n        dist = {}\n        seen = set()\n        start = 1\n        dist[start] = 0; seen.add(start)\n        while True:\n            found = False\n            best_v = INF\n            best_w = INF\n            for u, v, w in E:\n                if u not in seen or v in seen:\n                    continue\n                found = True\n                if best_w > dist[u] + w:\n                    best_v = v\n                    best_w = dist[u] + w\n            if not found:\n                break\n            v, w = best_v, best_w\n            dist[v] = w; seen.add(v)\n        return dist\n    def run(self, filename, queries):\n        E = []\n        with open(filename) as fin:\n            while True:\n                line = fin.readline()\n                if not line:\n                    break\n                words = line.split()\n                u = int(words[0])\n                for i in range(1, len(words)):\n                    v, w = map(int, words[i].split(','))\n                    E.append([ u, v, w ])\n        dist = self.dijkstra(E)\n        return ' '.join(str(dist[x]) for x in queries)\n\nclass HeapSolution(BaseSolution):\n    def dijkstra(self, adj, start = 1):\n        dist = {}\n        seen = set()\n        q = [[ 0, start ]]\n        while len(q):\n            cost, u = heappop(q)\n            if u in seen:\n                continue\n            dist[u] = cost; seen.add(u)\n            for w, v in adj[u]:\n                if v not in seen:\n                    heappush(q, [ dist[u] + w, v ])\n        return dist\n    def run(self, filename, queries):\n        adj = {}\n        with open(filename) as fin:\n            while True:\n                line = fin.readline()\n                if not line:\n                    break\n                words = line.split()\n                u = int(words[0])\n                if u not in adj:\n                    adj[u] = []\n                for i in range(1, len(words)):\n                    v, w = map(int, words[i].split(','))\n                    adj[u].append([ w, v ])\n        dist = self.dijkstra(adj)\n        return ' '.join(str(dist[x]) for x in queries)\n\ndef run(solution):\n    print(solution.run('problem9.8test.txt', [1, 2, 3, 4, 5, 6, 7, 8]))\n    print(solution.run('problem9.8.txt', [7, 37, 59, 82, 99, 115, 133, 165, 188, 197]))\n\nrun(NaiveSolution())\n#    0 1 2 3 4 4 3 2\n#    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n\nrun(HeapSolution())\n#    0 1 2 3 4 4 3 2\n#    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n#include <unordered_set>\n#include <queue>\n\nusing namespace std;\n\nusing Queries = vector<int>;\nusing Distance = unordered_map<int, int>;\nusing Set = unordered_set<int>;\n\nclass BaseSolution {\nprotected:\n    static constexpr auto INF = int(1e9 + 7);\npublic:\n    virtual string run(string filename, Queries&& queries) = 0;\n};\n\nclass NaiveSolution : public BaseSolution {\n    using Edge = tuple<int, int, int>;\n    using Edges = vector<Edge>;\npublic:\n    Distance dijkstra(Edges& E) {\n        Distance dist;\n        Set seen;\n        auto start{ 1 };\n        dist[start] = 0, seen.insert(start);\n        for (;;) {\n            auto found = false;\n            auto best_v = INF,\n                 best_w = INF;\n            for (auto [u, v, w]: E) {\n                if (seen.find(u) == seen.end() || seen.find(v) != seen.end())\n                    continue;\n                found = true;\n                if (best_w > dist[u] + w)\n                    best_v = v,\n                    best_w = dist[u] + w;\n            }\n            if (!found)\n                break;\n            auto [v, w] = tie(best_v, best_w);\n            dist[v] = w, seen.insert(v);\n        }\n        return dist;\n    }\n    string run(string filename, Queries&& queries) {\n        Edges E;\n        fstream fin{ filename };\n        string line;\n        int u, v, w;\n        char _;\n        while (getline(fin, line)) {\n            istringstream is{ line };\n            for (is >> u; is >> v >> _ >> w; E.push_back({ u, v, w }));\n        }\n        auto dist = dijkstra(E);\n        ostringstream os;\n        transform(queries.begin(), queries.end(), ostream_iterator<int>(os, \" \"), [&](auto x) { return dist[x]; });\n        return os.str();\n    }\n};\n\nclass HeapSolution : public BaseSolution {\n    using Pair = pair<int, int>;\n    using Pairs = vector<Pair>;\n    using AdjList = unordered_map<int, Pairs>;\n    priority_queue<Pair, Pairs, std::greater<Pair>> q;\npublic:\n    Distance dijkstra(AdjList& adj) {\n        Distance dist;\n        Set seen;\n        for (auto [u, _]: adj)\n            dist[u] = INF;\n        auto start{ 1 };\n        q.push({ 0, start });\n        while (q.size()) {\n            auto [cost, u] = q.top(); q.pop();\n            if (!seen.insert(u).second)\n                continue;\n            dist[u] = cost;\n            for (auto [w, v]: adj[u])\n                if (seen.find(v) == seen.end())\n                    q.push({ dist[u] + w, v });\n        }\n        return dist;\n    }\n    string run(string filename, Queries&& queries) {\n        AdjList adj;\n        fstream fin{ filename };\n        string line;\n        int u, v, w;\n        char _;\n        while (getline(fin, line)) {\n            istringstream is{ line };\n            for (is >> u; is >> v >> _ >> w; adj[u].push_back({ w, v }));\n        }\n        auto dist = dijkstra(adj);\n        ostringstream os;\n        transform(queries.begin(), queries.end(), ostream_iterator<int>(os, \" \"), [&](auto x) { return dist[x]; });\n        return os.str();\n    }\n};\n\nvoid run(BaseSolution&& solution) {\n    cout << \"problem9.8test.txt: \" << solution.run(\"problem9.8test.txt\", Queries{1, 2, 3, 4, 5, 6, 7, 8 }) << endl\n         << \"problem9.8.txt      \" << solution.run(\"problem9.8.txt\", Queries{7, 37, 59, 82, 99, 115, 133, 165, 188, 197 }) << endl;\n}\n\nint main() {\n    run(NaiveSolution());\n//    problem9.8test.txt: 0 1 2 3 4 4 3 2\n//    problem9.8.txt      2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n\n    run(HeapSolution());\n//    problem9.8test.txt: 0 1 2 3 4 4 3 2\n//    problem9.8.txt      2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n    return 0;\n}\n```\n\n</details>\n\n---\n\n# Part 3: Greedy Algorithms and Dynamic Programming\n\n<br/>\n<a href=\"https://www.amazon.com/dp/0999282948\" target=\"_blank\">\n    <img src=\"images/ai3large.jpg\" />\n</a>\n\n---\n\n### Greedy Scheduling\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Introduction to Greedy Algorithms (Section 13.1)](https://www.youtube.com/watch?v=NTFmxA3qgoo&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=4&t=0s)\n* [A Scheduling Problem (Section 13.2)](https://www.youtube.com/watch?v=jK3d_GLzKQA&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=5)\n* [Developing a Greedy Algorithm (Section 13.3)](https://www.youtube.com/watch?v=AJOTgHYjL6A&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=6)\n* [Scheduling: Correctness Proof (Part 1) (Section 13.4, Part 1)](https://www.youtube.com/watch?v=oyLxydVkQwo&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=7)\n* [Scheduling: Correctness Proof (Part 2) (Section 13.4, Part 2)](https://www.youtube.com/watch?v=fmXVPYxmFsU&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=8)\n* [Scheduling: Correctness Proof (Part 3) (Section 13.4, Part 3)](https://www.youtube.com/watch?v=aBFG5PghX68&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=9)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\n\ndata class Job(val weight: Long, val length: Long)\n\nclass Solution {\n    fun minSum(jobs: Array<Job>): Pair<Long, Long> {\n        class Diff: Comparator<Job> {\n            override fun compare(a: Job?, b: Job?): Int {\n                if (a == null || b == null)\n                    return 0\n                var first = a.weight - a.length\n                var second = b.weight - b.length\n                return if (first == second) b.weight.compareTo(a.weight) else second.compareTo(first) // sort by descending difference, break ties in favor of jobs with larger weights\n            }\n        }\n        class Ratio: Comparator<Job> {\n            override fun compare(a: Job?, b: Job?): Int {\n                if (a == null || b == null)\n                    return 0\n                var first = a.weight.toDouble() / a.length\n                var second = b.weight.toDouble() / b.length\n                return if (first == second) b.weight.compareTo(a.weight) else second.compareTo(first) // sort by descending difference, break ties in favor of jobs with larger weights\n            }\n        }\n        return Pair(calcSum(jobs, Diff()), calcSum(jobs, Ratio()))\n    }\n    private fun calcSum(jobs: Array<Job>, comp: Comparator<Job>): Long {\n        jobs.sortWith(comp)\n        var time: Long = 0\n        var total: Long = 0\n        jobs.forEach { job ->\n            time += job.length\n            total += job.weight * time\n        }\n        return total\n    }\n}\n\nfun run(filename: String) {\n    var jobs = mutableListOf<Job>()\n    var first = true\n    File(filename).forEachLine {\n        if (!first) {\n            var words = it.trim().split(\" \").map{ it.toLong() }\n            var (weight, length) = words\n            jobs.add(Job(weight, length))\n        } else {\n            first = false\n        }\n    }\n    var (diff, ratio) = Solution().minSum(jobs.toTypedArray())\n    println(\"$diff, $ratio\") // sub-optimal, optimal\n}\n\nfun main() {\n    run(\"problem13.4test1.txt\") // 23, 22\n    run(\"problem13.4test2.txt\") // 68615, 67247\n    run(\"problem13.4.txt\")      // 69119377652, 67311454237\n}\n```\n\n*Javascript*\n```javascript\nlet LineByLine = require('n-readlines');\n\nclass Job {\n    constructor(weight, length) {\n        this.weight = weight;\n        this.length = length;\n    }\n}\n\nclass Solution {\n    minSum(jobs) {\n        let diff = (a, b) => {\n            let first = a.weight - a.length,\n                second = b.weight - b.length;\n            return first == second ? b.weight - a.weight : second - first; // sort by descending difference, break ties in favor of jobs with larger weights\n        };\n        let ratio = (a, b) => {\n            let first = a.weight / a.length,\n                second = b.weight / b.length;\n            return first == second ? b.weight - a.weight : second - first; // sort by descending ratio, break ties in favor of jobs with larger weights\n        };\n        return [ this._calcSum(jobs, diff), this._calcSum(jobs, ratio) ];\n    }\n    _calcSum(jobs, comp, time = 0) {\n        jobs.sort((a, b) => comp(a, b));\n        return jobs.reduce((total, job) => total + job.weight * (time += job.length), 0);\n    }\n}\n\nlet run = filename => {\n    let jobs = [];\n    let input = new LineByLine(filename);\n    let line = input.next(); // N\n    while (line = input.next()) {\n        let words = String.fromCharCode(...line).trim().split(' ');\n        let [weight, length] = words.map(Number);\n        jobs.push(new Job(weight, length));\n    }\n    let [diff, ratio] = new Solution().minSum(jobs);\n    console.log(`${diff}, ${ratio}`); // sub-optimal, optimal\n};\n\nrun('problem13.4test1.txt'); // 23, 22\nrun('problem13.4test2.txt'); // 68615, 67247\nrun('problem13.4.txt');      // 69119377652, 67311454237\n```\n\n*Python3*\n```python\nfrom functools import cmp_to_key\n\nclass Job:\n    def __init__(self, weight, length):\n        self.weight = weight\n        self.length = length\n\nclass Solution:\n    def minSum(self, jobs):\n        def diff(a, b):\n            first = a.weight - a.length\n            second = b.weight - b.length\n            return b.weight - a.weight if first == second else second - first # sort by descending difference, break ties in favor of jobs with larger weights\n        def ratio(a, b):\n            first = a.weight / a.length\n            second = b.weight / b.length\n            return b.weight - a.weight if first == second else second - first # sort by descending difference, break ties in favor of jobs with larger weights\n        return [ self._calcSum(jobs, diff), self._calcSum(jobs, ratio) ]\n    def _calcSum(self, jobs, comp, time = 0, total = 0):\n        jobs.sort(key = cmp_to_key(lambda a, b: comp(a, b)))\n        for job in jobs:\n            time += job.length\n            total += job.weight * time\n        return total\n\ndef run(filename):\n    jobs = []\n    with open(filename) as fin:\n        line = fin.readline() # N\n        while True:\n            line = fin.readline().strip()\n            if not line:\n                break\n            words = line.split()\n            weight, length = [int(x) for x in words]\n            jobs.append(Job(weight, length))\n    diff, ratio = Solution().minSum(jobs)\n    print(f'{diff}, {ratio}') # sub-optimal, optimal\n\nrun('problem13.4test1.txt') # 23, 22\nrun('problem13.4test2.txt') # 68615, 67247\nrun('problem13.4.txt')      # 69119377652, 67311454237\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <numeric>\n\nusing namespace std;\n\nusing LL = long long;\nstruct Job {\n    LL weight, length;\n    Job(LL weight, LL length) : weight{ weight }, length{ length } {}\n};\nusing Jobs = vector<Job>;\n\nclass Solution {\npublic:\n    using Pair = pair<LL, LL>; // sub-optimal, optimal\n    Pair minSum(Jobs& jobs) {\n        auto diff = [](auto& a, auto& b) {\n            auto first = a.weight - a.length,\n                 second = b.weight - b.length;\n            return first == second ? b.weight < a.weight : second < first; // sort by descending difference, break ties in favor of jobs with larger weights\n        };\n        auto ratio = [](auto& a, auto& b) {\n            auto first = double(a.weight) / a.length,\n                 second = double(b.weight) / b.length;\n            return first == second ? b.weight < a.weight : second < first; // sort by descending ratio, break ties in favor of jobs with larger weights\n        };\n        return { calcSum(jobs, diff), calcSum(jobs, ratio) };\n    }\nprivate:\n    template<typename Comp>\n    LL calcSum(Jobs& jobs, Comp comp, LL time = 0LL) {\n        sort(jobs.begin(), jobs.end(), comp);\n        return accumulate(jobs.begin(), jobs.end(), 0LL, [&](LL total, auto& job) {\n            return total += job.weight * (time += job.length);\n        });\n    }\n};\n\nvoid run(const string& filename) {\n    Jobs jobs;\n    LL N, weight, length;\n    fstream fin{ filename };\n    for (fin >> N; fin >> weight >> length; jobs.emplace_back(Job{ weight, length }));\n    auto [diff, ratio] = Solution().minSum(jobs);\n    cout << diff << \", \" << ratio << endl;\n}\n\nint main() {\n    run(\"problem13.4test1.txt\"); // 23, 22\n    run(\"problem13.4test2.txt\"); // 68615, 67247\n    run(\"problem13.4.txt\");      // 69119377652, 67311454237\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Huffman Codes\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Codes (Section 14.1)](https://www.youtube.com/watch?v=K3WZhFZT6Y0&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=33)\n* [Codes as Trees (Section 14.2)](https://www.youtube.com/watch?v=HESrV5VDu8c&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=34)\n* [Huffman's Greedy Algorithm (Part 1) (Section 14.3, Part 1)](https://www.youtube.com/watch?v=NM6FZB7IfS8&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=35)\n* [Huffman's Greedy Algorithm (Part 2) (Section 14.3, Part 2)](https://www.youtube.com/watch?v=PPmn9osMDyI&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=36)\n* [Huffman's Algorithm: Correctness Proof (Part 1) (Section 14.4, Part 1)](https://www.youtube.com/watch?v=jibgSDjWxdI&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=37)\n* [Huffman's Algorithm: Correctness Proof (Part 2) (Section 14.4, Part 2)](https://www.youtube.com/watch?v=dAjCcqZKYf4&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=38)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\nimport java.util.PriorityQueue\nimport java.util.Queue\nimport java.util.LinkedList\n\nvar INF = (1e9 + 7).toInt()\n\ndata class Tree(val weight: Int, val left: Tree? = null, val right: Tree? = null)\n\n/*\nfun encode(A: List<Int>): Tree {\n    var q = PriorityQueue<Tree>(Comparator{ a: Tree, b: Tree -> a.weight.compareTo(b.weight) })\n    for (weight in A)\n        q.add(Tree(weight))\n    while (1 < q.size) {\n        var a = q.poll()\n        var b = q.poll()\n        var c = Tree(a.weight + b.weight, a, b)\n        q.add(c)\n    }\n    return q.poll()\n}\n*/\n\n/*\n * Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n * of a sorting subroutine, followed by a linear amount of additional work.\n */\nfun encode(A: MutableList<Int>): Tree {\n    A.sort()\n    var first: Queue<Tree> = LinkedList<Tree>(A.map{ weight -> Tree(weight) }.toList())\n    var second: Queue<Tree> = LinkedList<Tree>()\n    var next = mutableListOf<Tree>()\n    while (1 < first.size + second.size) {\n        next.clear()\n        do {\n            if (0 < first.size && 0 < second.size) {\n                if (first.peek().weight < second.peek().weight) next.add(first.poll()) else next.add(second.poll())\n            }\n            else if (0 < first.size) next.add(first.poll())\n            else if (0 < second.size) next.add(second.poll())\n        } while (next.size < 2)\n        var (a, b) = next\n        var c = Tree(a.weight + b.weight, a, b)\n        second.add(c)\n    }\n    return second.poll()\n}\n\nfun run(filename: String): Pair<Int, Int> {\n    var A = mutableListOf<Int>()\n    var first = true\n    File(filename).forEachLine {\n        if (!first) {\n            var weight = it.trim().toInt()\n            A.add(weight)\n        } else {\n            first = false\n        }\n    }\n    var tree = encode(A.toMutableList())\n    var lo = INF\n    var hi = -INF\n    fun go(root: Tree? = tree, depth: Int = 0) {\n        if (root == null)\n            return\n        var isLeaf = { node: Tree? -> node?.left == null && node?.right == null }\n        if (isLeaf(root)) {\n            lo = Math.min(lo, depth)\n            hi = Math.max(hi, depth)\n        } else {\n            go(root.left, depth + 1)\n            go(root.right, depth + 1)\n        }\n    }\n    go()\n    return Pair(lo, hi)\n}\n\nfun main() {\n    for (filename in listOf(\"problem14.6test1.txt\", \"problem14.6test2.txt\", \"problem14.6.txt\")) {\n        var (lo, hi) = run(filename)\n        println(\"$filename: $lo, $hi\") // min, max encoding length in the corresponding optimal prefix-free tree\n    }\n}\n\n//    problem14.6test1.txt: 2, 5\n//    problem14.6test2.txt: 3, 6\n//    problem14.6.txt: 9, 19\n```\n\n*Javascript*\n```javascript\nlet LineByLine = require('n-readlines');\n\nclass Tree {\n    constructor(weight, left = null, right = null) {\n        this.weight = weight;\n        this.left = left;\n        this.right = right;\n    }\n}\n\n/*\nlet key = x => Array.isArray(x) ? x[0] : x;\nlet heappush = (A, x, f = Math.min) => {\n    let P = i => Math.floor((i - 1) / 2);  // parent\n    A.push(x);\n    let N = A.length,\n        i = N - 1;\n    while (0 < i && key(A[i]) == f(key(A[i]), key(A[P(i)]))) {\n        [A[i], A[P(i)]] = [A[P(i)], A[i]];\n        i = P(i);\n    }\n};\nlet heappop = (A, f = Math.min) => {\n    let L = i => 2 * i + 1,  // children\n        R = i => 2 * i + 2;\n    let N = A.length,\n        i = 0;\n    let top = A[0];\n    [A[0], A[N - 1]] = [A[N - 1], A[0]], A.pop(), --N;\n    let ok;\n    do {\n        ok = true;\n        let left = f == Math.min ? Infinity : -Infinity,\n            right = left;\n        if (L(i) < N && key(A[i]) != f(key(A[i]), key(A[L(i)]))) ok = false, left  = key(A[L(i)]);\n        if (R(i) < N && key(A[i]) != f(key(A[i]), key(A[R(i)]))) ok = false, right = key(A[R(i)]);\n        if (!ok) {\n            let j = left == f(left, right) ? L(i) : R(i);\n            [A[i], A[j]] = [A[j], A[i]];\n            i = j;\n        }\n    } while (!ok);\n    return top;\n};\n\nlet encode = A => {\n    let T = [];\n    for (let weight of A)\n        heappush(T, [ weight, new Tree(weight) ]);\n    while (1 < T.length) {\n        let [ a, b ] = [ heappop(T), heappop(T) ];\n        let c = [ a[0] + b[0], new Tree(a[0] + b[0], a[1], b[1]) ];\n        heappush(T, c);\n    }\n    return T[0][1];\n};\n*/\n\n/*\n * Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n * of a sorting subroutine, followed by a linear amount of additional work.\n */\nlet encode = A => {\n    A.sort((a, b) => a - b)\n    let first = A.map(weight => new Tree(weight)),\n        second = [];\n    while (1 < first.length + second.length) {\n        let next = [];\n        while (next.length < 2) {\n            if (first.length && second.length) {\n                next.push(first[0].weight < second[0].weight ? first.shift() : second.shift());\n            }\n            else if (first.length) next.push(first.shift());\n            else if (second.length) next.push(second.shift());\n        }\n        let [a, b] = next;\n        let c = new Tree(a.weight + b.weight, a, b);\n        second.push(c);\n    }\n    return second.shift();\n};\n\nlet run = filename => {\n    let A = [];\n    let input = new LineByLine(filename);\n    let line;\n    line = input.next(); // N\n    while (line = input.next()) {\n        let weight = Number(String.fromCharCode(...line).trim());\n        A.push(weight);\n    }\n    let tree = encode(A);\n    let [lo, hi] = [Infinity, -Infinity];\n    let go = (root = tree, depth = 0) => {\n        if (!root)\n            return;\n        let isLeaf = root => !root.left && !root.right;\n        if (isLeaf(root))\n            lo = Math.min(lo, depth),\n            hi = Math.max(hi, depth);\n        else\n            go(root.left, depth + 1),\n            go(root.right, depth + 1);\n    };\n    go();\n    return [ lo, hi ];\n}\n\nfor (let filename of [ 'problem14.6test1.txt', 'problem14.6test2.txt', 'problem14.6.txt' ]) {\n    let [lo, hi] = run(filename);\n    console.log(`${filename}: ${lo}, ${hi}`); // min, max encoding length in the corresponding optimal prefix-free tree\n}\n\n//    problem14.6test1.txt: 2, 5\n//    problem14.6test2.txt: 3, 6\n//    problem14.6.txt: 9, 19\n```\n\n*Python3*\n```python\nclass Tree:\n    def __init__(self, weight, left = None, right = None):\n        self.weight = weight\n        self.left = left\n        self.right = right\n    def __lt__(self, other):\n        return self.weight < other.weight\n\n#\n# priority queue\n#\n\n# from heapq import heappush\n# from heapq import heappop\n# def encode(A):\n#     T = []\n#     for weight in A:\n#         heappush(T, Tree(weight))\n#     while 1 < len(T):\n#         a, b = heappop(T), heappop(T)\n#         c = Tree(a.weight + b.weight, a, b)\n#         heappush(T, c)\n#     return heappop(T)\n\n#\n# Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n# of a sorting subroutine, followed by a linear amount of additional work.\n#\nfrom collections import deque\ndef encode(A):\n    A.sort()\n    first, second = deque([Tree(weight) for weight in A]), deque()\n    while 1 < len(first) + len(second):\n        next = []\n        while len(next) < 2:\n            if len(first) and len(second):\n                next.append(first.popleft() if first[0].weight < second[0].weight else second.popleft())\n            elif len(first): next.append(first.popleft())\n            elif len(second): next.append(second.popleft())\n        a, b = next\n        c = Tree(a.weight + b.weight, a, b)\n        second.append(c)\n    return second.popleft()\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        N = int(fin.readline())\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            weight = int(line.strip())\n            A.append(weight)\n    tree = encode(A)\n    lo, hi = float('inf'), float('-inf')\n    def go(root = tree, depth = 0):\n        nonlocal lo, hi\n        if not root:\n            return\n        isLeaf = lambda root: not root.left and not root.right\n        if isLeaf(root):\n            lo = min(lo, depth)\n            hi = max(hi, depth)\n        else:\n            go(root.left, depth + 1)\n            go(root.right, depth + 1)\n    go()\n    return [ lo, hi ]\n\nfor filename in [ 'problem14.6test1.txt', 'problem14.6test2.txt', 'problem14.6.txt' ]:\n    lo, hi = run(filename)\n    print(f'{filename}: {lo}, {hi}') # min, max encoding length in the corresponding optimal prefix-free tree\n\n#    problem14.6test1.txt: 2, 5\n#    problem14.6test2.txt: 3, 6\n#    problem14.6.txt: 9, 19\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <queue>\n#include <list>\n\n#define PRIORITY_QUEUE    // O(N * logN)\n#ifndef PRIORITY_QUEUE\n#define TWO_QUEUES        // O(N)\n#endif\n\nusing namespace std;\nusing LL = long long;\nusing Weight = LL;\nusing Weights = vector<Weight>;\n\nstruct Tree;\nusing TreePtr = shared_ptr<Tree>;\nstruct Tree {\n    Weight weight;\n    TreePtr left, right;\n    Tree(Weight weight, TreePtr left = nullptr, TreePtr right = nullptr) :\n            weight{ weight }, left{ left }, right{ right } {}\n};\nusing TreePtrs = vector<TreePtr>;\n\n#ifdef PRIORITY_QUEUE\nstruct Comp {\n    size_t operator()(const TreePtr& a, const TreePtr& b) const {\n        return b->weight < a->weight;\n    }\n};\nusing Queue = priority_queue<TreePtr, TreePtrs, Comp>;\nTreePtr encode(const Weights& A, Queue q = {}) {\n    for (auto weight: A)\n        q.emplace(make_shared<Tree>(weight));\n    while (1 < q.size()) {\n        auto a = q.top(); q.pop();\n        auto b = q.top(); q.pop();\n        auto c = make_shared<Tree>(a->weight + b->weight, a, b);\n        q.emplace(c);\n    }\n    return q.top();\n}\n#else // TWO_QUEUES\n/*\n * Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n * of a sorting subroutine, followed by a linear amount of additional work.\n */\nusing Queue = queue<TreePtr>;\nTreePtr encode(Weights& A, Queue first = {}, Queue second = {}) {\n    sort(A.begin(), A.end());\n    for (auto weight: A)\n        first.push(make_shared<Tree>(weight));\n    TreePtrs next;\n    auto takeFirst = [&]() { next.push_back(first.front()), first.pop(); };\n    auto takeSecond = [&]() { next.push_back(second.front()), second.pop(); };\n    while (1 < first.size() + second.size()) {\n        next.clear();\n        do {\n            if (first.size() && second.size()) {\n                if (first.front()->weight < second.front()->weight) takeFirst(); else takeSecond();\n            }\n            else if (first.size()) takeFirst();\n            else if (second.size()) takeSecond();\n        } while (next.size() < 2);\n        auto [a, b] = tie(next[0], next[1]);\n        auto c = make_shared<Tree>(a->weight + b->weight, a, b);\n        second.emplace(c);\n    }\n    return second.front();\n}\n#endif\n\nusing MinMax = pair<LL, LL>;\nconstexpr auto Min = numeric_limits<LL>::min();\nconstexpr auto Max = numeric_limits<LL>::max();\nMinMax run(const string& filename) {\n    Weights A; // weight of each symbol\n    fstream fin{ filename };\n    LL N, weight;\n    for (fin >> N; fin >> weight; A.push_back(weight));\n    auto tree = encode(A);\n    LL lo = Max,\n       hi = Min;\n    using fun = function<void(TreePtr, int)>;\n    fun go = [&](auto root, LL depth) {\n        if (!root)\n            return;\n        auto isLeaf = [](auto root) { return !root->left && !root->right; };\n        if (isLeaf(root))\n            lo = min(lo, depth),\n            hi = max(hi, depth);\n        else\n            go(root->left, depth + 1),\n            go(root->right, depth + 1);\n    };\n    go(tree, 0);\n    return make_pair(lo, hi);\n}\n\nint main() {\n    for (auto& filename: { \"problem14.6test1.txt\", \"problem14.6test2.txt\", \"problem14.6.txt\" }) {\n        auto [lo, hi] = run(filename);\n        cout << filename << \": \" << lo << \", \" << hi << endl; // min, max encoding length in the corresponding optimal prefix-free tree\n    }\n//    problem14.6test1.txt: 2, 5\n//    problem14.6test2.txt: 3, 6\n//    problem14.6.txt: 9, 19\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Prim's MST\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Minimum Spanning Trees: Problem Definition (Section 15.1)](https://www.youtube.com/watch?v=tDj9BkaQDO8&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=10)\n* [Prim's MST Algorithm (Section 15.2)](https://www.youtube.com/watch?v=jsvOPssDVJA&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=11)\n* [Speeding Up Prim's Algorithm via Heaps (Part 1) (Section 15.3, Part 1)](https://www.youtube.com/watch?v=cDtQnXMZGtg&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=15)\n* [Speeding Up Prim's Algorithm via Heaps (Part 2) (Section 15.3, Part 2)](https://www.youtube.com/watch?v=jGR_LAwGLGk&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=16)\n* [Prim's Algorithm: Correctness Proof (Part 1) (Section 15.4, Part 1) [Note: this video provides an alternative treatment to that in the book.]](https://www.youtube.com/watch?v=pGUzn3S7bp4&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=12)\n* [Prim's Algorithm: Correctness Proof (Part 2) (Section 15.4, Part 2) [Note: this video provides an alternative treatment to that in the book.]](https://www.youtube.com/watch?v=199ItGt4mE8&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=13)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\nimport java.util.PriorityQueue\nimport java.util.Random\n\nfun prim(N: Int, adj: MutableMap<Int, MutableList<Pair<Int, Int>>>): Int {\n    var total: Int = 0\n    var start = Random().nextInt(N) + 1\n    var q = PriorityQueue<Pair<Int, Int>>(Comparator{ a: Pair<Int, Int>, b: Pair<Int, Int> -> a.first.compareTo(b.first) })\n    var seen = mutableSetOf<Int>(start)\n    for ((w, v) in adj[start]!!)\n        q.add(Pair(w, v))\n    while (0 < q.size) {\n        var (cost, u) = q.poll()\n        if (seen.contains(u))\n            continue\n        total += cost; seen.add(u)\n        for ((w, v) in adj[u]!!)\n            if (!seen.contains(v))\n                q.add(Pair(w, v))\n    }\n    return total\n}\n\nfun run(filename: String) {\n    var N: Int = 0\n    var adj = mutableMapOf<Int, MutableList<Pair<Int, Int>>>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (u, v, w) = line.split(\" \").map{ it.toInt() }\n            if (!adj.contains(u)) adj[u] = mutableListOf<Pair<Int, Int>>()\n            if (!adj.contains(v)) adj[v] = mutableListOf<Pair<Int, Int>>()\n            adj[u]!!.add(Pair(w, v))\n            adj[v]!!.add(Pair(w, u))\n        } else {\n            var (numVertex, _) = line.split(\" \").map{ it.toInt() }\n            N = numVertex\n            first = false\n        }\n    }\n    var cost = prim(N, adj)\n    println(\"$filename: $cost\")\n}\n\nfun main() {\n    run(\"problem15.9test.txt\") // problem15.9test.txt: 14\n    run(\"problem15.9.txt\")     // problem15.9.txt: -3612829\n}\n```\n\n*Javascript*\n```javascript\nlet LineByLine = require('n-readlines');\n\nlet key = x => Array.isArray(x) ? x[0] : x;\nlet heappush = (A, x, f = Math.min) => {\n    let P = i => Math.floor((i - 1) / 2);  // parent\n    A.push(x);\n    let N = A.length,\n        i = N - 1;\n    while (0 < i && key(A[i]) == f(key(A[i]), key(A[P(i)]))) {\n        [A[i], A[P(i)]] = [A[P(i)], A[i]];\n        i = P(i);\n    }\n};\nlet heappop = (A, f = Math.min) => {\n    let L = i => 2 * i + 1,  // children\n        R = i => 2 * i + 2;\n    let N = A.length,\n        i = 0;\n    let top = A[0];\n    [A[0], A[N - 1]] = [A[N - 1], A[0]], A.pop(), --N;\n    let ok;\n    do {\n        ok = true;\n        let left = f == Math.min ? Infinity : -Infinity,\n            right = left;\n        if (L(i) < N && key(A[i]) != f(key(A[i]), key(A[L(i)]))) ok = false, left  = key(A[L(i)]);\n        if (R(i) < N && key(A[i]) != f(key(A[i]), key(A[R(i)]))) ok = false, right = key(A[R(i)]);\n        if (!ok) {\n            let j = left == f(left, right) ? L(i) : R(i);\n            [A[i], A[j]] = [A[j], A[i]];\n            i = j;\n        }\n    } while (!ok);\n    return top;\n};\n\nlet prim = (N, adj, q = [], seen = new Set(), total = 0) => {\n    let start = Math.ceil(N * Math.random());\n    seen.add(start);\n    for (let [w, v] of adj.get(start))\n        heappush(q, [w, v]);\n    while (q.length) {\n        let [cost, u] = heappop(q);\n        if (seen.has(u))\n            continue;\n        total += cost; seen.add(u);\n        for (let [w, v] of adj.get(u))\n            if (!seen.has(v))\n                heappush(q, [w, v]);\n    }\n    return total;\n};\n\nlet run = filename => {\n    let adj = new Map();\n    let input = new LineByLine(filename);\n    let line = input.next();\n    let [N, M] = String.fromCharCode(...line).trim().split(' ').map(Number);\n    while (line = input.next()) {\n        let [u, v, w] = String.fromCharCode(...line).trim().split(' ').map(Number);\n        if (!adj.has(u)) adj.set(u, []);\n        if (!adj.has(v)) adj.set(v, []);\n        adj.get(u).push([w, v]);\n        adj.get(v).push([w, u]);\n    }\n    let cost = prim(N, adj);\n    console.log(`${filename}: ${cost}`);\n}\n\nrun('problem15.9test.txt') // problem15.9test.txt: 14\nrun('problem15.9.txt')     // problem15.9.txt: -3612829\n```\n\n*Python3*\n```python\nfrom random import randint\nfrom heapq import heappush, heappop\n\ndef prim(N, adj, total = 0):\n    q = []\n    seen = set()\n    start = randint(1, N); seen.add(start)\n    for w, v in adj[start]:\n        heappush(q, [w, v])\n    while q:\n        cost, u = heappop(q)\n        if u in seen:\n            continue\n        total += cost; seen.add(u)\n        for w, v in adj[u]:\n            if v not in seen:\n                heappush(q, [w, v])\n    return total\n\ndef run(filename):\n    adj = {}\n    first = True\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            words = line.split()\n            if not first:\n                u, v, w = [int(x) for x in words]\n                if u not in adj: adj[u] = []\n                if v not in adj: adj[v] = []\n                adj[u].append([w, v])\n                adj[v].append([w, u])\n            else:\n                N, M = [int(x) for x in words]\n                first = False\n    cost = prim(N, adj)\n    print(f'{filename}: {cost}')\n\nrun('problem15.9test.txt') # problem15.9test.txt: 14\nrun('problem15.9.txt')     # problem15.9.txt: -3612829\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <unordered_set>\n#include <unordered_map>\n#include <queue>\n#include <random>\n\nusing namespace std;\nusing Pair = pair<int, int>;\nusing Pairs = vector<Pair>;\nusing AdjList = unordered_map<int, Pairs>;\nusing Queue = priority_queue<Pair, Pairs, std::greater<Pair>>;\nusing Set = unordered_set<int>;\n\nconstexpr auto INF = int(1e9 + 7);\n\nint getRandom(int N) {\n    default_random_engine generator;\n    uniform_int_distribution<int> distribution(1, N);\n    return distribution(generator);\n}\n\nint prim(int N, AdjList& adj, Queue q = {}, Set seen = {}, int total = 0) {\n    auto start = getRandom(N);\n    seen.insert(start);\n    for (auto [w, v]: adj[start])\n        q.push({ w, v });\n    while (q.size()) {\n        auto [cost, u] = q.top(); q.pop();\n        if (!seen.insert(u).second)\n            continue;\n        total += cost;\n        for (auto [w, v]: adj[u])\n            if (seen.find(v) == seen.end())\n                q.push({ w, v });\n    }\n    return total;\n}\n\nvoid run(const string& filename) {\n    AdjList adj;\n    fstream fin{ filename };\n    int N, M; fin >> N >> M; // N vertices and M edges\n    int u, v, w;             // edge u -> v of weight w\n    while (fin >> u >> v >> w) {\n        adj[u].emplace_back(w, v);\n        adj[v].emplace_back(w, u);\n    }\n    auto cost = prim(N, adj);\n    cout << filename << \": \" << cost << endl;\n}\n\nint main() {\n    run(\"problem15.9test.txt\"); // problem15.9test.txt: 14\n    run(\"problem15.9.txt\");     // problem15.9.txt: -3612829\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Kruskal's MST\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Minimum Spanning Trees: Problem Definition (Section 15.1)](https://www.youtube.com/watch?v=tDj9BkaQDO8&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=10)\n* [Kruskal's MST Algorithm (Section 15.5)](https://www.youtube.com/watch?v=SZuCspj5AJc&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=17)\n* [Speeding Up Kruskal's Algorithm via Union-Find (Part 1) (Section 15.6, Part 1)](https://www.youtube.com/watch?v=fItEZEVyJKE&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=19)\n* [Speeding Up Kruskal's Algorithm via Union-Find (Part 2) (Section 15.6, Part 2) [Note: this video provides an alternative treatment to that in the book.]](https://www.youtube.com/watch?v=jY-vY6d18W4&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=20)\n* [Lazy Unions (Section 15.6, Part 3) [Note: this video is closer to the union-find implementation in the book.]](https://www.youtube.com/watch?v=bRwTSPIEI9k&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=24)\n* [Kruskal's Algorithm: Correctness Proof (Section 15.7) [Note: this video provides an alternative treatment to that in the book.]](https://www.youtube.com/watch?v=AjLjL0Rp10g&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=18)\n* [Application: Single-Link Clustering (Section 15.8)](https://www.youtube.com/watch?v=MSSzOs1X4K8&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=22)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\n\nfun kruskal(E: MutableList<Triple<Int, Int, Int>>): Int {\n    var total: Int = 0\n    var M = E.size\n    var P = IntArray(M) { it } // 🙂 parent representatives of 1..M disjoint sets\n    fun find(x: Int): Int {\n        P[x] = if (P[x] == x) x else find(P[x])\n        return P[x]\n    }\n    fun union(a: Int, b: Int): Boolean {\n        var x = find(a)\n        var y = find(b)\n        if (x == y)\n            return false\n        P[x] = y // 🎲 arbitrary choice\n        return true\n    }\n    E.sortWith(Comparator{ a, b -> a.third.compareTo(b.third) }) // sort edges by nondecreasing weight\n    for ((u, v, w) in E)\n        if (union(u, v))\n            total += w\n    return total\n}\n\nfun run(filename: String) {\n    var E = mutableListOf<Triple<Int, Int, Int>>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (u, v, w) = line.trim().split(\" \").map{ it.toInt() }\n            E.add(Triple(u, v, w))\n        } else {\n            first = false // ignore first line with N vertices and M edges\n        }\n    }\n    var cost = kruskal(E)\n    println(\"$filename: $cost\")\n}\n\nfun main() {\n    run(\"problem15.9test.txt\") // problem15.9test.txt: 14\n    run(\"problem15.9.txt\")     // problem15.9.txt: -3612829\n}\n```\n\n*Javascipt*\n```javascript\nlet LineByLine = require('n-readlines');\n\nlet kruskal = E => {\n    let total = 0;\n    let M = E.length;\n    let P = [...Array(M).keys()]; // 🙂 parent representatives of 1..M disjoint sets\n    let find = x => P[x] = P[x] == x ? x : find(P[x]);\n    let union = (a, b) => {\n        a = find(a);\n        b = find(b);\n        if (a == b)\n            return false;\n        P[a] = b; // 🎲 arbitrary choice\n        return true;\n    };\n    E.sort((first, second) => { // sort edges by nondecreasing weight\n        let [u1, v1, w1] = first,\n            [u2, v2, w2] = second;\n        return w1 - w2;\n    });\n    for (let [u, v, w] of E)\n        if (union(u, v))\n            total += w;\n    return total;\n};\n\nlet run = filename => {\n    let E = [];\n    let input = new LineByLine(filename);\n    let line = input.next(); // ignore first line with N vertices and M edges\n    while (line = input.next()) {\n        let [u, v, w] = String.fromCharCode(...line).trim().split(' ').map(Number);\n        E.push([ u, v, w ]);\n    }\n    let cost = kruskal(E);\n    console.log(`${filename}: ${cost}`);\n};\n\nrun('problem15.9test.txt'); // problem15.9test.txt: 14\nrun('problem15.9.txt');     // problem15.9.txt: -3612829\n```\n\n*Python3*\n```python\nfrom functools import cmp_to_key\n\ndef kruskal(E, total = 0):\n    M = len(E)\n    P = [i for i in range(M)] # 🙂 parent representatives of 1..M disjoint sets\n    def find(x):\n        P[x] = P[x] if P[x] == x else find(P[x])\n        return P[x]\n    def union(a, b):\n        a = find(a)\n        b = find(b)\n        if a == b:\n            return False\n        P[a] = b # 🎲 arbitary choice\n        return True\n    E.sort(key = cmp_to_key(lambda first, second: first[2] - second[2])) # sort edges by nondecreasing weight\n    for u, v, w in E:\n        if union(u, v):\n            total += w\n    return total\n\ndef run(filename):\n    E = []\n    first = True\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            values = [int(x) for x in line.strip().split()]\n            if not first:\n                u, v, w = values # edge u -> v of weight w\n                E.append([ u, v, w ])\n            else:\n                first = False # ignore first line with N vertices and M edges\n    cost = kruskal(E)\n    print(f'{filename}: {cost}')\n\nrun('problem15.9test.txt') # problem15.9test.txt: 14\nrun('problem15.9.txt')     # problem15.9.txt: -3612829\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <unordered_map>\n#include <numeric>\n\nusing namespace std;\nusing Edge = tuple<int, int, int>;\nusing Edges = vector<Edge>;\nusing Parents = vector<int>;\nusing fun = function<int(int)>;\n\nint kruskal(Edges& E, int total = 0) {\n    auto M = E.size();\n    Parents P(M); iota(P.begin(), P.end(), 0); // 🙂 parent representatives of 1..M disjoint sets\n    fun find = [&](auto x) {\n         return P[x] = P[x] == x ? x : find(P[x]);\n    };\n    auto join = [&](auto a, auto b) {\n        a = find(a);\n        b = find(b);\n        if (a == b)\n            return false;\n        P[a] = b; // 🎲 arbitrary choice\n        return true;\n    };\n    sort(E.begin(), E.end(), [](auto& first, auto& second) { // sort edges by nondecreasing weight\n        auto [u1, v1, w1] = first;\n        auto [u2, v2, w2] = second;\n        return w1 < w2;\n    });\n    for (auto [u, v, w]: E)\n        if (join(u, v))\n            total += w;\n    return total;\n}\n\nvoid run(const string& filename, Edges E = {}) {\n    fstream fin{ filename };\n    int N, M; fin >> N >> M; // ignore first line with N vertices and M edges\n    int u, v, w;             // edge u -> v of weight w\n    while (fin >> u >> v >> w)\n        E.emplace_back(u, v, w);\n    auto cost = kruskal(E);\n    cout << filename << \": \" << cost << endl;\n}\n\nint main() {\n    run(\"problem15.9test.txt\"); // problem15.9test.txt: 14\n    run(\"problem15.9.txt\");     // problem15.9.txt: -3612829\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Weighted Independent Set\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [The Weighted Independent Set Problem (Section 16.1)](https://www.youtube.com/watch?v=0awkct8SkxA&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=39)\n* [A Linear-Time Algorithm for WIS in Path Graphs (Part 1) (Section 16.2, Part 1)](https://www.youtube.com/watch?v=pLOkbHGRsv0&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=40)\n* [A Linear-Time Algorithm for WIS in Path Graphs (Part 2) (Section 16.2, Part 2)](https://www.youtube.com/watch?v=Im_zjFkZDCY&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=41)\n* [A Reconstruction Algorithm (Section 16.3)](https://www.youtube.com/watch?v=W2ncNfksRqo&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=42)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\n\nfun topDown(A: MutableList<Long>): Long {\n    var N = A.size\n    var m = mutableMapOf<Int, Long>()\n    fun go(i: Int = N - 1): Long {\n        if (m.contains(i))                    // 🤔 memo\n            return m[i]!!\n        if (i < 0) {                          // 🛑 empty set\n            m[i] = 0\n            return 0\n        }\n        if (i == 0) {                         // 🛑 single set\n            m[i] = A[0]\n            return A[0]\n        }\n        var include = go(i - 2) + A[i]        // ✅ include A[i]\n        var exclude = go(i - 1)               // 🚫 exclude A[i]\n        m[i] = Math.max(include, exclude)     // 🎯 best\n        return m[i]!!\n    }\n    return go()\n}\n\nfun bottomUp(A: MutableList<Long>): Long {\n    var N = A.size\n    var dp = LongArray(N + 1)                 // 🤔 memo\n    dp[0] = 0                                 // 🛑 empty set\n    dp[1] = A[0]                              // 🛑 single set\n    for (i in 2..N) {\n        var include = dp[i - 2] + A[i - 1]    // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        var exclude = dp[i - 1]               // 🚫 exclude A[i]\n        dp[i] = Math.max(include, exclude)    // 🎯 best\n    }\n    return dp[N]\n}\n\nfun bottomUpMemOpt(A: MutableList<Long>): Long {\n    var N = A.size\n    var a: Long = 0                     // 🤔 memo + 🛑 empty set\n    var b: Long = A[0]                  // 🤔 memo + 🛑 single set\n    var c: Long = -1\n    for (i in 2..N) {\n        var include = a + A[i - 1]      // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        var exclude = b                 // 🚫 exclude A[i]\n        c = Math.max(include, exclude)  // 🎯 best\n        a = b; b = c                    // 👈 slide window\n    }\n    return c\n}\n\nfun run(filename: String) {\n    var A = mutableListOf<Long>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            A.add(line.toLong())\n        } else {\n            first = false\n        }\n    }\n    var a = topDown(A)\n    var b = bottomUp(A)\n    var c = bottomUpMemOpt(A)\n    assert(a == b && b == c) // 💩 sanity check\n    println(\"$filename: $a\")\n}\n\nfun main() {\n    run(\"problem16.6test.txt\")  // problem16.6test.txt: 2617\n    run(\"problem16.6.txt\")      // problem16.6.txt: 2955353732\n}\n```\n\n*Javascript*\n```javascript\nconst assert = require('assert');\nconst LineByLine = require('n-readlines');\n\nlet top_down = (A, m = {}) => {\n    let N = A.length;\n    let go = (i = N - 1) => {\n        if (m[i])                                     // 🤔 memo\n            return m[i];\n        if (i < 0) return m[i] = 0;                   // 🛑 empty set\n        if (!i) return m[i] = A[0];                   // 🛑 single set\n        let include = go(i - 2) + A[i],               // ✅ include A[i]\n            exclude = go(i - 1);                      // 🚫 exclude A[i]\n        return m[i] = Math.max(include, exclude);     // 🎯 best\n    };\n    return go();\n};\n\nlet bottom_up = A => {\n    let N = A.length;\n    let dp = Array(N + 1);                    // 🤔 memo\n    dp[0] = 0;                                // 🛑 empty set\n    dp[1] = A[0];                             // 🛑 single set\n    for (let i = 2; i <= N; ++i) {\n        let include = dp[i - 2] + A[i - 1],   // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n            exclude = dp[i - 1];              // 🚫 exclude A[i]\n        dp[i] = Math.max(include, exclude);   // 🎯 best\n    }\n    return dp[N];\n};\n\nlet bottom_up_memopt = A => {\n    let N = A.length;\n    let a = 0,                           // 🤔 memo + 🛑 empty set\n        b = A[0],                        // 🤔 memo + 🛑 single set\n        c = -1;\n    for (let i = 2; i <= N; ++i) {\n        let include = a + A[i - 1],      // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n            exclude = b;                 // 🚫 exclude A[i]\n        c = Math.max(include, exclude);  // 🎯 best\n        a = b, b = c;                    // 👈 slide window\n    }\n    return c;\n};\n\nlet run = filename => {\n    let A = [];\n    let input = new LineByLine(filename);\n    let line;\n    let first = true;\n    while (line = input.next()) {\n        if (!first) {\n            A.push(Number(line.toString('ascii')));\n        } else {\n            first = false;\n        }\n    }\n    let a = top_down(A),\n        b = bottom_up(A),\n        c = bottom_up_memopt(A);\n    assert(a == b && b == c); // 💩 sanity check\n    console.log(`${filename}: ${a}`);\n};\n\nrun('problem16.6test.txt');  // problem16.6test.txt: 2617\nrun('problem16.6.txt');      // problem16.6.txt: 2955353732\n```\n\n*Python3*\n```python\nfrom functools import lru_cache\n\ndef top_down(A):\n    N = len(A)\n    @lru_cache                        # 🤔 memo\n    def go(i = N - 1):\n        if i < 0: return 0            # 🛑 empty set\n        if i == 0: return A[0]        # 🛑 single set\n        include = go(i - 2) + A[i]    # ✅ include A[i]\n        exclude = go(i - 1)           # 🚫 exclude A[i]\n        return max(include, exclude)  # 🎯 best\n    return go()\n\ndef bottom_up(A):\n    N = len(A)\n    dp = [0] * (N + 1)                  # 🤔 memo\n    dp[0] = 0                           # 🛑 empty set\n    dp[1] = A[0]                        # 🛑 single set\n    for i in range(2, N + 1):\n        include = dp[i - 2] + A[i - 1]  # ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        exclude = dp[i - 1]             # 🚫 exclude A[i]\n        dp[i] = max(include, exclude)   # 🎯 best\n    return dp[N]\n\ndef bottom_up_memopt(A):\n    N = len(A)\n    a = 0                          # 🤔 memo + 🛑 empty set\n    b = A[0]                       # 🤔 memo + 🛑 single set\n    c = -1\n    for i in range(2, N + 1):\n        include = a + A[i - 1]     # ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        exclude = b                # 🚫 exclude A[i]\n        c = max(include, exclude)  # 🎯 best\n        a = b; b = c               # 👈 slide window\n    return c\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        first = True\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            x = int(line)\n            if not first:\n                A.append(x)\n            else:\n                first = False\n                N = x\n    a = top_down(A)\n    b = bottom_up(A)\n    c = bottom_up_memopt(A)\n    assert(a == b and b == c) # 💩 sanity check\n    print(f'{filename}: {a}')\n\nrun('problem16.6test.txt')     # problem16.6test.txt: 2617\nrun('problem16.6.txt')         # problem16.6.txt: 2955353732\n```\n\n*C++*\n```cpp\n#include <cassert>\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <unordered_map>\n\nusing namespace std;\nusing LL = long long;\nusing List = vector<LL>;\nusing Map = unordered_map<int, LL>;\n\nnamespace TopDown {\n    LL best(List& A, Map m = {}) {\n        int N = A.size();\n        using fun = function<LL(int)>;\n        fun go = [&](auto i) {\n            if (m[i]) return m[i];                // 🤔 memo\n            if (i < 0) return m[i] = 0LL;         // 🛑 empty set\n            if (!i) return m[i] = A[0];           // 🛑 single set\n            auto include = go(i - 2) + A[i],      // ✅ include A[i]\n                 exclude = go(i - 1);             // 🚫 exclude A[i]\n            return m[i] = max(include, exclude);  // 🎯 best\n        };\n        return go(N - 1);\n    }\n}\nnamespace BottomUp {\n    LL best(List& A, Map m = {}) {\n        int N = A.size();\n        List dp(N + 1);                           // 🤔 memo\n        dp[0] = 0LL;                              // 🛑 empty set\n        dp[1] = A[0];                             // 🛑 single set\n        for (auto i{ 2 }; i <= N; ++i) {\n            auto include = dp[i - 2] + A[i - 1],  // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n                 exclude = dp[i - 1];             // 🚫 exclude A[i]\n            dp[i] = max(include, exclude);        // 🎯 best\n        }\n        return dp[N];\n    }\n}\n\nnamespace BottomUpMemOpt {\n    LL best(List& A) {\n        int N = A.size();\n        LL a = 0LL,                       // 🤔 memo + 🛑 empty set\n           b = A[0],                      // 🤔 memo + 🛑 single set\n           c = -1;\n        for (auto i{ 2 }; i <= N; ++i) {\n            auto include = a + A[i - 1],  // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n                 exclude = b;             // 🚫 exclude A[i]\n            c = max(include, exclude);    // 🎯 best\n            a = b, b = c;                 // 👈 slide window\n        }\n        return c;\n    }\n}\n\nvoid run(const string& filename) {\n    List A;\n    fstream fin{ filename };\n    int N; fin >> N;\n    copy_n(istream_iterator<LL>(fin), N, back_inserter(A));\n    auto a = TopDown::best(A),\n         b = BottomUp::best(A),\n         c = BottomUpMemOpt::best(A);\n    assert(a == b && b == c); // 💩 sanity check\n    cout << filename << \": \" << a << endl;\n}\n\nint main() {\n    run(\"problem16.6test.txt\");  // problem16.6test.txt: 2617\n    run(\"problem16.6.txt\");      // problem16.6.txt: 2955353732\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Knapsack\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Principles of Dynamic Programming (Section 16.4)](https://www.youtube.com/watch?v=27nK8C-GCPM&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=43)\n* [The Knapsack Problem (Part 1) (Section 16.5, Part 1)](https://www.youtube.com/watch?v=jlHIBaUizOU&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=44)\n* [The Knapsack Problem (Part 2) (Section 16.5, Part 2)](https://www.youtube.com/watch?v=KX_6OF8X6HQ&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=45)\n* [The Knapsack Problem (Part 3) (Section 16.5, Part 3)](https://www.youtube.com/watch?v=1dRUOZKcvYs&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=46)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\n\nvar INF = (1e9 + 7).toInt()\n\nfun top_down(A: List<Pair<Int, Int>>, K: Int): Int {\n    var N = A.size\n    var m = mutableMapOf<String, Int>()\n    fun go(i: Int = 0, k: Int = K): Int {\n        if (i == N)                                                                 // 🛑 empty set\n            return 0\n        var key = \"$i,$k\"\n        if (m.contains(key))                                                        // 🤔 memo\n            return m[key]!!\n        var (value, weight) = A[i]\n        var include = if (0 <= k - weight) go(i + 1, k - weight) + value else -INF  // ✅ include A[i]\n        var exclude = go(i + 1, k)                                                  // 🚫 exclude A[i]\n        m[key] = Math.max(include, exclude)                                         // 🎯 best\n        return m[key]!!\n    }\n    return go()\n}\n\nfun bottom_up(A: List<Pair<Int, Int>>, K: Int): Int {\n    var N = A.size\n    var dp = Array(N + 1){ Array(K + 1){ -INF } }                                       // 🤔 memo\n    for (k in 0..K)                                                                     // 🛑 empty set\n        dp[0][k] = 0\n    for (i in 1..N) {\n        for (k in 0..K) {\n            var (value, weight) = A[i - 1]\n            var include = if (0 <= k - weight) dp[i - 1][k - weight] + value else -INF  // ✅ include A[i]\n            var exclude = dp[i - 1][k]                                                  // 🚫 exclude A[i]\n            dp[i][k] = Math.max(include, exclude)                                       // 🎯 best\n        }\n    }\n    return dp[N][K]\n}\n\nfun bottom_up_memopt(A: List<Pair<Int, Int>>, K: Int): Int {\n    var N = A.size\n    var pre = Array(K + 1) { 0 }                                                  // 🤔 memo + 🛑 empty set\n    for (i in 1..N) {\n        var cur = Array(K + 1) { -INF }\n        for (k in 0..K) {\n            var (value, weight) = A[i - 1]\n            var include = if (0 <= k - weight) pre[k - weight] + value else -INF  // ✅ include A[i]\n            var exclude = pre[k]                                                  // 🚫 exclude A[i]\n            cur[k] = Math.max(include, exclude)                                   // 🎯 best\n        }\n        pre = cur.also { cur = pre }\n    }\n    return pre[K]\n}\n\nfun run(filename: String) {\n    var A = mutableListOf<Pair<Int, Int>>()\n    var K = 0\n    var N = 0\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (value, weight) = line.trim().split(\" \").map{ it -> it.toInt() }\n            A.add(Pair(value, weight))\n        } else {\n            var (a, b) = line.trim().split(\" \").map{ it -> it.toInt() }\n            K = a\n            N = b\n            first = false\n        }\n    }\n    var a = top_down(A, K)\n    var b = bottom_up(A, K)\n    var c = bottom_up_memopt(A, K)\n    assert(a == b && b == c) // 💩 sanity check\n    println(\"$filename: $a\")\n}\n\nfun main() {\n    run(\"problem16.7test.txt\")  // problem16.7test.txt: 2493893\n}\n```\n\n*Javascript*\n```javascript\nconst assert = require('assert');\nconst LineByLine = require('n-readlines');\n\nlet top_down = (A, K, m = new Map()) => {\n    let N = A.length;\n    let go = (i = 0, k = K) => {\n        if (i == N)                                                                 // 🛑 empty set\n            return 0;\n        let key = `${i},${k}`;\n        if (m.has(key))                                                             // 🤔 memo\n            return m.get(key);\n        let [value, weight] = A[i];\n        let include = 0 <= k - weight ? go(i + 1, k - weight) + value : -Infinity,  // ✅ include A[i]\n            exclude = go(i + 1, k);                                                 // 🚫 exclude A[i]\n        return m.set(key, Math.max(include, exclude))                               // 🎯 best\n                .get(key);\n    };\n    return go();\n};\n\nlet bottom_up = (A, K) => {\n    let N = A.length;\n    let dp = [...Array(N + 1)].map(_ => Array(K + 1).fill(-Infinity));                  // 🤔 memo\n    for (let k = 0; k < K; dp[0][k++] = 0);                                             // 🛑 empty set\n    for (let i = 1; i <= N; ++i) {\n        for (let k = 0; k <= K; ++k) {\n            let [value, weight] = A[i - 1];\n            let include = 0 <= k - weight ? dp[i - 1][k - weight] + value : -Infinity,  // ✅ include A[i]\n                exclude = dp[i - 1][k];                                                 // 🚫 exclude A[i]\n            dp[i][k] = Math.max(include, exclude);                                      // 🎯 best\n        }\n    }\n    return dp[N][K];\n};\n\nlet bottom_up_memopt = (A, K) => {\n    let N = A.length;\n    let pre = Array(K + 1).fill(0);                                               // 🤔 memo + 🛑 empty set\n    for (let i = 1; i <= N; ++i) {\n        let cur = Array(K + 1).fill(-Infinity);\n        for (let k = 0; k <= K; ++k) {\n            let [value, weight] = A[i - 1];\n            let include = 0 <= k - weight ? pre[k - weight] + value : -Infinity,  // ✅ include A[i]\n                exclude = pre[k];                                                 // 🚫 exclude A[i]\n            cur[k] = Math.max(include, exclude);                                  // 🎯 best\n        }\n        [pre, cur] = [cur, pre];\n    }\n    return pre[K];\n};\n\nlet run = filename => {\n    let A = [];\n    const input = new LineByLine(filename)\n    let [K, N] = input.next().toString().split(' ').map(Number);  // K capacity, N items\n    let line;\n    while (line = input.next()) {\n        let [value, weight] = line.toString().split(' ').map(Number);\n        A.push([value, weight]);\n    }\n    let a = top_down(A, K),\n        b = bottom_up(A, K),\n        c = bottom_up_memopt(A, K);\n    assert(a == b && b == c); // 💩 sanity check\n    console.log(`${filename}: ${a}`);\n};\n\nrun('problem16.7test.txt')  // problem16.7test.txt: 2493893\n```\n\n*Python3*\n```python\nfrom functools import lru_cache\n\ndef top_down(A, K):\n    N = len(A)\n    total = [0] * N\n    @lru_cache(maxsize = None)                                                          # 🤔 memo\n    def go(i = 0, k = K):\n        if i == N:                                                                      # 🛑 empty set\n            return 0\n        value, weight = A[i]\n        include = go(i + 1, k - weight) + value if 0 <= k - weight else float('-inf')  # ✅ include A[i]\n        exclude = go(i + 1, k)                                                         # 🚫 exclude A[i]\n        return max(include, exclude)                                                   # 🎯 best\n    return go()\n\ndef bottom_up(A, K):\n    N = len(A)\n    dp = [[float('-inf')] * (K + 1) for _ in range(N + 1)]                                 # 🤔 memo\n    for j in range(K):                                                                     # 🛑 empty set\n        dp[0][j] = 0\n    for i in range(1, N + 1):\n        for k in range(1, K + 1):\n            value, weight = A[i - 1]\n            include = dp[i - 1][k - weight] + value if 0 <= k - weight else float('-inf')  # ✅ include A[i]\n            exclude = dp[i - 1][k]                                                         # 🚫 exclude A[i]\n            dp[i][k] = max(include, exclude)                                               # 🎯 best\n    return dp[N][K]\n\ndef bottom_up_memopt(A, K):\n    N = len(A)\n    pre = [0] * (K + 1)                                                              # 🤔 memo + 🛑 empty set\n    for i in range(1, N + 1):\n        cur = [float('-inf')] * (K + 1)\n        for k in range(1, K + 1):\n            value, weight = A[i - 1]\n            include = pre[k - weight] + value if 0 <= k - weight else float('-inf')  # ✅ include A[i]\n            exclude = pre[k]                                                         # 🚫 exclude A[i]\n            cur[k] = max(include, exclude)                                           # 🎯 best\n        pre, cur = cur, pre\n    return pre[K]\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        line = fin.readline()\n        [K, N] = [int(word) for word in line.split()]  # K capacity, N items\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            value, weight = [int(word) for word in line.split()]\n            A.append([value, weight])\n    a = top_down(A, K)\n    b = bottom_up(A, K)\n    c = bottom_up_memopt(A, K)\n    assert(a == b and b == c) # 💩 sanity check\n    print(f'{filename}: {a}')\n\nrun('problem16.7test.txt')  # problem16.7test.txt: 2493893\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n\nusing namespace std;\nusing Pair = pair<int, int>;  // value, weight\nusing Pairs = vector<Pair>;\nusing fun = function<int(int, int)>;\nusing Map = unordered_map<string, int>;\n\nint INF = 1e9 + 7;\n\nint top_down(Pairs& A, int K, Map m = {}) {\n    auto N = A.size();\n    fun go = [&](auto i, auto k) {\n        if (i == N)                                                             // 🛑 empty set\n            return 0;\n        stringstream key; key << i << \",\" << k;\n        if (m.find(key.str()) != m.end())                                       // 🤔 memo\n            return m[key.str()];\n        auto [value, weight] = A[i];\n        auto include = 0 <= k - weight ? go(i + 1, k - weight) + value : -INF,  // ✅ include A[i]\n             exclude = go(i + 1, k);                                            // 🚫 exclude A[i]\n        return m[key.str()] = max(include, exclude);                            // 🎯 best\n    };\n    return go(0, K);\n}\n\nint bottom_up(Pairs& A, int K) {\n    auto N = A.size();\n    using VI = vector<int>;\n    using VVI = vector<VI>;\n    VVI dp(N + 1, VI(K + 1, -INF));                                                // 🤔 memo\n    for (auto k{ 0 }; k < K; dp[0][k++] = 0);                                      // 🛑 empty set\n    for (auto i{ 1 }; i <= N; ++i) {\n        for (auto k{ 0 }; k <= K; ++k) {\n            auto [value, weight] = A[i - 1];\n            auto include = 0 <= k - weight ? dp[i - 1][k - weight] +value : -INF,  // ✅ include A[i]\n                 exclude = dp[i - 1][k];                                           // 🚫 exclude A[i]\n            dp[i][k] = max(include, exclude);                                      // 🎯 best\n        }\n    }\n    return dp[N][K];\n}\n\nint bottom_up_memopt(Pairs& A, int K) {\n    auto N = A.size();\n    using VI = vector<int>;\n    VI pre(K + 1, 0);                                                        // 🤔 memo + 🛑 empty set\n    for (auto i{ 1 }; i <= N; ++i) {\n        VI cur(K + 1, -INF);\n        for (auto k{ 0 }; k <= K; ++k) {\n            auto [value, weight] = A[i - 1];\n            auto include = 0 <= k - weight ? pre[k - weight] +value : -INF,  // ✅ include A[i]\n            exclude = pre[k];                                                // 🚫 exclude A[i]\n            cur[k] = max(include, exclude);                                  // 🎯 best\n        }\n        swap(pre, cur);\n    }\n    return pre[K];\n}\n\nvoid run(const string& filename) {\n    Pairs A;\n    fstream fin{ filename };\n    int K, N;                // K capacity, N items\n    fin >> K >> N;\n    for (int value, weight; fin >> value >> weight; A.emplace_back(value, weight));\n    auto a = top_down(A, K),\n         b = bottom_up(A, K),\n         c = bottom_up_memopt(A, K);\n    assert(a == b && b == c); // 💩 sanity check\n    cout << filename << \": \" << a << endl;\n}\n\nint main() {\n    run(\"problem16.7test.txt\");  // problem16.7test.txt: 2493893\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Bellman-Ford\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Shortest Paths with Negative Edge Lengths (Section 18.1)](https://www.youtube.com/watch?v=oyHoqtxHiOs&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=54)\n* [The Bellman-Ford Algorithm (Part 1) (Section 18.2, Part 1)](https://www.youtube.com/watch?v=06OK99Aak60&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=55)\n* [The Bellman-Ford Algorithm (Part 2) (Section 18.2, Part 2)](https://www.youtube.com/watch?v=d1TWZa20Mkw&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=56)\n* [The Bellman-Ford Algorithm (Part 3) (Section 18.2, Part 3)](https://www.youtube.com/watch?v=HaXTsC8eOfo&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=57)\n* [The Bellman-Ford Algorithm (Part 4) (Section 18.2, Part 4)](https://www.youtube.com/watch?v=Otn0kbliRUQ&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=58)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\nimport java.util.LinkedList\nimport java.util.Queue\n\n// bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\nfun bell(E: Array<Triple<Int, Int, Int>>, N: Int, start: Int = 1, INF: Int = (1e6).toInt()): IntArray {\n    var dist = IntArray(N) { INF }\n    dist[start] = 0\n    var K = N - 1\n    while (0 < K--)\n        E.forEach{ (u, v, w) -> dist[v] = Math.min(dist[v], dist[u] + w)}\n    return dist\n}\n\n// shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\nfun spfa(E: Array<Triple<Int, Int, Int>>, N: Int, start: Int = 1, INF: Int = (1e6).toInt()): IntArray {\n    var dist = IntArray(N) { INF }\n    dist[start] = 0\n    var adj = Array<MutableList<Pair<Int, Int>>>(N) { mutableListOf<Pair<Int, Int>>() }\n    for ((u, v, w) in E)\n        adj[u].add(Pair(v, w))\n    var q: Queue<Int> = LinkedList<Int>(listOf(start))\n    while (0 < q.size) {\n        var u = q.poll()\n        for ((v, w) in adj[u]) {\n            if (dist[v] > dist[u] + w) {\n                dist[v] = dist[u] + w; q.add(v)\n            }\n        }\n    }\n    return dist\n}\n\nfun run(filename: String): IntArray {\n    var N = 0\n    var E = mutableListOf<Triple<Int, Int, Int>>()\n    File(filename).forEachLine {\n        var A = ArrayDeque(it.trim().split(\"\\t\"))\n        var u = A.removeFirst().toInt()\n        for ((v, w) in A.map{ it.split(\",\").map{ it.toInt() } })\n            E.add(Triple(u, v, w))\n        ++N;\n    }\n    var A = E.toTypedArray()\n    var a = bell(A, N + 1)  // +1 for 1-based indexing\n    var b = spfa(A, N + 1)\n    assert(a == b)          // 💩 sanity check: single source shortest paths are the same\n    return b\n}\n\nfun main() {\n    var dist = run(\"test.txt\")\n    println(listOf(7, 37, 59, 82, 99, 115, 133, 165, 188, 197).map{ dist[it] }.joinToString(\",\"))  // 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068\n}\n```\n\n*Javascript*\n```javascript\nconst assert = require('assert');\nconst zip = require('lodash/zip');\nconst LineByLine = require('n-readlines');\n\n// bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\nlet bell = (E, N, start = 1, INF = Number(1e6)) => {\n    let dist = Array(N).fill(INF);\n    dist[start] = 0;\n    let K = N - 1;\n    while (K--)\n        E.forEach(([u, v, w]) => dist[v] = Math.min(dist[v], dist[u] + w));\n    return dist;\n};\n\n// shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\nlet spfa = (E, N, start = 1, INF = Number(1e6)) => {\n    let dist = Array(N).fill(INF);\n    dist[start] = 0;\n    let adj = [...Array(N)].map(_ => []);\n    E.forEach(([u, v, w]) => adj[u].push([v, w]));\n    let q = [start];\n    while (q.length) {\n        let u = q.shift();\n        for (let [v, w] of adj[u])\n            if (dist[v] > dist[u] + w)\n                dist[v] = dist[u] + w, q.push(v);\n    }\n    return dist;\n};\n\nlet run = filename => {\n    let N = 0;\n    let E = [];\n    let input = new LineByLine(filename);\n    let line;\n    while (line = input.next()) {\n        let A = line.toString('ascii').split('\\t').filter(it => it.length);\n        let u = Number(A.shift());\n        A.map(pair => pair.split(',').map(Number)).forEach(([v, w]) => E.push([u, v, w]));\n        ++N;\n    }\n    let a = bell(E, N + 1),  // +1 for 1-based indexing\n        b = spfa(E, N + 1);\n    zip(a, b).forEach(([x, y]) => assert(x == y));  // 💩 sanity check: single source shortest paths are the same\n    return a;\n};\n\nlet dist = run('test.txt');\nconsole.log([7, 37, 59, 82, 99, 115, 133, 165, 188, 197].map(x => dist[x]).join(','));  // 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068\n```\n\n*Python3*\n```python\nfrom collections import deque\n\n# bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\ndef bell(E, N, start = 1, INF = int(1e6)):\n    dist = [INF] * N\n    dist[start] = 0\n    k = N - 1\n    while k:\n        for u, v, w in E:\n            dist[v] = min(dist[v], dist[u] + w)\n        k -= 1\n    return dist\n\n# shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\ndef spfa(E, N, start = 1, INF = int(1e6)):\n    dist = [INF] * N\n    dist[start] = 0\n    adj = {i: [] for i in range(N)}\n    for u, v, w in E:\n        adj[u].append([v, w])\n    q = deque([start])\n    while q:\n        u = q.popleft()\n        for v, w in adj[u]:\n            if dist[v] > dist[u] + w:\n                dist[v] = dist[u] + w; q.append(v)\n    return dist\n\ndef run(filename):\n    E = []\n    N = 0\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            line = line.strip()\n            A = [word for word in line.split('\\t') if len(word)]\n            u = int(A[0])\n            for i in range(1, len(A)):\n                v, w = [int(x) for x in A[i].split(',')]\n                E.append([u, v, w])\n            N += 1\n    a = bell(E, N + 1)  # +1 for 1-based indexing\n    b = spfa(E, N + 1)\n    assert(a == b)\n    return b\n\ndist = run('test.txt')\nprint(','.join(str(dist[x]) for x in [7, 37, 59, 82, 99, 115, 133, 165, 188, 197]))  # 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n#include <queue>\n\nusing namespace std;\nusing VI = vector<int>;\nusing VS = vector<string>;\nusing Edge = tuple<int, int, int>;\nusing Edges = vector<Edge>;\nusing Pair = pair<int, int>;\nusing Pairs = vector<Pair>;\nusing AdjList = unordered_map<int, Pairs>;\nusing Queue = queue<int>;\n\n// bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\nVI bell(Edges& E, int N, int start = 1, int INF = 1e6) {\n    VI dist(N, INF);\n    dist[start] = 0;\n    auto K = N - 1;\n    while (K--)\n        for (auto [u, v, w]: E)\n            dist[v] = min(dist[v], dist[u] + w);\n    return dist;\n}\n\n// shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\nVI spfa(Edges& E, int N, int start = 1, int INF = 1e6, AdjList adj = {}) {\n    VI dist(N, INF);\n    dist[start] = 0;\n    for (auto [u, v, w]: E)\n        adj[u].emplace_back(v, w);\n    Queue q{{ start }};\n    while (q.size()) {\n        auto u = q.front(); q.pop();\n        for (auto [v, w]: adj[u])\n            if (dist[v] > dist[u] + w)\n                dist[v] = dist[u] + w, q.push(v);\n    }\n    return dist;\n}\n\nVI run(const string& filename) {\n    auto N = 0;\n    Edges E;\n    fstream fin{ filename };\n    VS A;\n    for (string line; getline(fin, line); A.emplace_back(line));\n    for (auto& s: A) {\n        transform(s.begin(), s.end(), s.begin(), [](auto c) { return c == ',' ? ' ' : c; });\n        stringstream ss{ s };\n        auto [u, v, w] = make_tuple(0, 0, 0);\n        ss >> u;\n        while (ss >> v >> w)\n            E.emplace_back(u, v, w);\n        ++N;\n    }\n    auto a = bell(E, N + 1),  // +1 for 1-based indexing\n         b = spfa(E, N + 1);\n    assert(a == b);\n    return b;\n}\n\nint main() {\n    auto dist = run(\"test.txt\");\n    VI A{ 7, 37, 59, 82, 99, 115, 133, 165, 188, 197 };\n    transform(A.begin(), A.end(), A.begin(), [&](auto x) { return dist[x]; });\n    copy(A.begin(), A.end(), ostream_iterator<int>(cout, \",\"));  // 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068,\n    return 0;\n}\n```\n\n</details>\n\n---\n\n### Floyd-Warshall\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [The All-Pairs Shortest Path Problem (Section 18.3)](https://www.youtube.com/watch?v=TENbWZPz3Ho&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=62)\n* [The Floyd-Warshall Algorithm (Part 1) (Section 18.4, Part 1)](https://www.youtube.com/watch?v=ogcvCr02gqM&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=63)\n* [The Floyd-Warshall Algorithm (Part 2) (Section 18.4, Part 2)](https://www.youtube.com/watch?v=3cBHwPjDZxg&list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6&index=64)\n\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\n\nvar key = { i: Int, j: Int -> \"$i,$j\" }\nvar INF = (1e9 + 7).toInt()\n\nfun floyd_warshall(E: MutableMap<String, Int>, N: Int): Array<IntArray> {\n    var dp = Array(N + 1) { Array(N + 1) { IntArray(N + 1) { INF } } }\n    for (i in 0..N)\n        for (j in 0..N)\n            if (i == j)\n                dp[0][i][j] = 0\n            else\n            if (E.contains(key(i, j)))\n                dp[0][i][j] = E[key(i, j)]!!\n    for (k in 1..N)\n        for (i in 1..N)\n            for (j in 1..N)\n                dp[k][i][j] = Math.min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j])\n    return dp[N]\n}\n\nfun floyd_warshall_memopt(E: MutableMap<String, Int>, N: Int): Array<IntArray> {\n    var pre = Array(N + 1) { IntArray(N + 1) { INF } }\n    for (i in 0..N)\n        for (j in 0..N)\n            if (i == j)\n                pre[i][j] = 0\n            else\n            if (E.contains(key(i, j)))\n                pre[i][j] = E[key(i, j)]!!\n    for (k in 1..N) {\n        var cur = Array(N + 1) { IntArray(N + 1) { INF } }\n        for (i in 1..N)\n            for (j in 1..N)\n                cur[i][j] = Math.min(pre[i][j], pre[i][k] + pre[k][j])\n        pre = cur.also{ cur = pre }\n    }\n    return pre\n}\n\nfun run(filename: String) {\n    var N = 0\n    var E = mutableMapOf<String, Int>()\n    var first = true\n    File(filename).forEachLine {\n        if (!first) {\n            var (u, v, w) = it.trim().split(\" \").map{ it.toInt() }\n            E[key(u, v)] = w\n        } else {\n            N = it.trim().split(\" \").map{ it.toInt() }[0]\n            first = false\n        }\n    }\n    var a = floyd_warshall_memopt(E, N)\n    var b = floyd_warshall(E, N)\n    for (i in 1..N)\n        for (j in 1..N)\n            assert(a[i][j] == b[i][j])  // 💩 sanity check\n    var cycle = false\n    for (i in 1..N)\n        if (a[i][i] < 0)\n            cycle = true\n    if (cycle) {\n        println(\"$filename: contains a negative cycle\")\n        return\n    }\n    var best = INF\n    for (i in 1..N)\n        for (j in 1..N)\n            best = Math.min(best, a[i][j])\n    println(\"$filename: $best\")\n}\n\nfun main() {\n    run(\"problem18.8test1.txt\");  // problem18.8test1.txt: -2\n    run(\"problem18.8test2.txt\");  // problem18.8test2.txt: contains a negative cycle\n    run(\"problem18.8file1.txt\");  // problem18.8file1.txt: contains a negative cycle\n    run(\"problem18.8file2.txt\");  // problem18.8file2.txt: contains a negative cycle\n    run(\"problem18.8file3.txt\");  // problem18.8file3.txt: -19\n    // run(\"problem18.8file4.txt\");\n}\n```\n\n*Javascript*\n```javascript\nconst LineByLine = require('n-readlines');\nconst assert = require('assert');\n\nlet key = (i, j) => `${i},${j}`;\n\nlet floyd_warshall = (E, N) => {\n    let dp = [...Array(N + 1)].map(_ => [...Array(N + 1)].map(_ => Array(N + 1).fill(Infinity)));\n    for (let i = 1; i <= N; ++i)\n        for (let j = 1; j <= N; ++j)\n            if (i == j)\n                dp[0][i][j] = 0;\n            else\n            if (E.has(key(i, j)))\n                dp[0][i][j] = E.get(key(i, j));\n    for (let k = 1; k <= N; ++k)\n        for (let i = 1; i <= N; ++i)\n            for (let j = 1; j <= N; ++j)\n                dp[k][i][j] = Math.min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j]);\n    return dp[N];\n};\n\nlet floyd_warshall_memopt = (E, N) => {\n    let pre = [...Array(N + 1)].map(_ => Array(N + 1).fill(Infinity));\n    for (let i = 1; i <= N; ++i)\n        for (let j = 1; j <= N; ++j)\n            if (i == j)\n                pre[i][j] = 0;\n            else\n            if (E.has(key(i, j)))\n                pre[i][j] = E.get(key(i, j));\n    for (let k = 1; k <= N; ++k) {\n        let cur = [...Array(N + 1)].map(_ => Array(N + 1).fill(Infinity));\n        for (let i = 1; i <= N; ++i)\n            for (let j = 1; j <= N; ++j)\n                cur[i][j] = Math.min(pre[i][j], pre[i][k] + pre[k][j]);\n        [pre, cur] = [cur, pre];\n    }\n    return pre;\n};\n\nlet run = filename => {\n    let E = new Map();\n    let input = new LineByLine(filename);\n    let [N, _] = input.next().toString('ascii').split(' ').map(Number);\n    let line;\n    while (line = input.next()) {\n        let [u, v, w] = line.toString('ascii').split(' ').map(Number);\n        E.set(key(u, v), w);\n    }\n    let a = floyd_warshall_memopt(E, N),\n        b = floyd_warshall(E, N);\n    for (let i = 1; i <= N; ++i)\n        for (let j = 1; j <= N; ++j)\n            assert(a[i][j] == b[i][j]);\n    let cycle = false;\n    for (let i = 1; i <= N; ++i)\n        if (a[i][i] < 0)\n            cycle = true;\n    if (cycle) {\n        console.log(`${filename}: contains a negative cycle`);\n        return;\n    }\n    var best = Infinity;\n    for (row of a)\n        best = Math.min(best, ...row);\n    console.log(`${filename}: ${best}`);\n};\n\nrun('problem18.8test1.txt');  // problem18.8test1.txt: -2\nrun('problem18.8test2.txt');  // problem18.8test2.txt: contains a negative cycle\nrun('problem18.8file1.txt');  // problem18.8file1.txt: contains a negative cycle\nrun('problem18.8file2.txt');  // problem18.8file2.txt: contains a negative cycle\nrun('problem18.8file3.txt');  // problem18.8file3.txt: -19\n// run('problem18.8file4.txt');\n```\n\n*Python3*\n```python\nkey = lambda i, j: f'{i},{j}'\n\ndef floyd_warshall(E, N):\n    dp = [[[float('inf')] * (N + 1) for _ in range(N + 1)] for _ in range(N + 1)]\n    for i in range(1, N + 1):\n        for j in range(1, N + 1):\n            if i == j:\n                dp[0][i][j] = 0\n            elif key(i, j) in E:\n                dp[0][i][j] = E[key(i, j)]\n    for k in range(1, N + 1):\n        for i in range(1, N + 1):\n            for j in range(1, N + 1):\n                dp[k][i][j] = min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j])\n    return dp[N]\n\ndef floyd_warshall_memopt(E, N):\n    pre = [[float('inf')] * (N + 1) for _ in range(N + 1)]\n    for i in range(1, N + 1):\n        for j in range(1, N + 1):\n            if i == j:\n                pre[i][j] = 0\n            elif key(i, j) in E:\n                pre[i][j] = E[key(i, j)]\n    for k in range(1, N + 1):\n        cur = [[float('inf')] * (N + 1) for _ in range(N + 1)]\n        for i in range(1, N + 1):\n            for j in range(1, N + 1):\n                cur[i][j] = min(pre[i][j], pre[i][k] + pre[k][j])\n        pre, cur = cur, pre\n    return pre\n\ndef run(filename):\n    E = {}\n    N = 0\n    first = True\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            if not first:\n                u, v, w = [int(x) for x in line.strip().split(' ')]\n                E[key(u, v)] = w\n            else:\n                N = [int(x) for x in line.strip().split(' ')][0]\n                first = False\n    a = floyd_warshall_memopt(E, N)\n    b = floyd_warshall(E, N)\n    for i in range(1, N + 1):\n        for j in range(1, N + 1):\n            assert(a[i][j] == b[i][j])  # 💩 sanity check\n    cycle = False\n    for i in range(1, N + 1):\n        if a[i][i] < 0:\n            cycle = True\n    if cycle:\n        print(f'{filename}: contains a negative cycle')\n        return\n    best = float('inf')\n    for row in a:\n        best = min(best, *row)\n    print(f'{filename}: {best}')\n\nrun('problem18.8test1.txt')  # problem18.8test1.txt: -2\nrun('problem18.8test2.txt')  # problem18.8test2.txt: contains a negative cycle\nrun('problem18.8file1.txt')  # problem18.8file1.txt: contains a negative cycle\nrun('problem18.8file2.txt')  # problem18.8file2.txt: contains a negative cycle\nrun('problem18.8file3.txt')  # problem18.8file3.txt: -19\n# run('problem18.8file4.txt')\n```\n\n*C++*\n```cpp\n#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n\n#define PERF_TEST\n\nusing namespace std;\n\nusing LL = long long;\nusing VL = vector<LL>;\nusing VVL = vector<VL>;\nusing VVVL = vector<VVL>;\nusing Edges = unordered_map<string, LL>;\n\nLL INF = 1e9 + 7;\n\nstring key(int i, int j) {\n    stringstream ss; ss << i << \",\" << j;\n    return ss.str();\n}\n\nVVL floyd_warshall(Edges& E, int N) {\n    VVVL dp(N + 1, VVL(N + 1, VL(N + 1, INF)));\n    for (auto i{ 1 }; i <= N; ++i)\n        for (auto j{ 1 }; j <= N; ++j)\n            if (i == j)\n                dp[0][i][j] = 0;\n            else\n            if (E.find(key(i, j)) != E.end())\n                dp[0][i][j] = E[key(i, j)];\n    for (auto k{ 1 }; k <= N; ++k)\n        for (auto i{ 1 }; i <= N; ++i)\n            for (auto j{ 1 }; j <= N; ++j)\n                dp[k][i][j] = min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j]);\n    return dp[N];\n}\n\nVVL floyd_warshall_memopt(Edges& E, int N) {\n    VVL pre(N + 1, VL(N + 1, INF));\n    for (auto i{ 1 }; i <= N; ++i)\n        for (auto j{ 1 }; j <= N; ++j)\n            if (i == j)\n                pre[i][j] = 0;\n            else\n            if (E.find(key(i, j)) != E.end())\n                pre[i][j] = E[key(i, j)];\n    for (auto k{ 1 }; k <= N; ++k) {\n        VVL cur(N + 1, VL(N + 1, INF));\n        for (auto i{ 1 }; i <= N; ++i)\n            for (auto j{ 1 }; j <= N; ++j)\n                cur[i][j] = min(pre[i][j], pre[i][k] + pre[k][j]);\n        swap(pre, cur);\n    }\n    return pre;\n}\n\nvoid run(const string& filename) {\n    Edges E;\n    fstream fin{ filename };\n    int N, M; fin >> N >> M;\n    for (int u, v, w; fin >> u >> v >> w; E[key(u, v)] = w);\n#ifdef PERF_TEST\n    auto a = floyd_warshall_memopt(E, N);\n#else\n    auto a = floyd_warshall_memopt(E, N),\n         b = floyd_warshall(E, N);\n    assert(a == b);  // 💩 sanity check\n#endif\n    auto cycle = false;\n    for (auto i{ 1 }; i <= N && !cycle; ++i)\n        cycle = a[i][i] < 0;\n    if (cycle) {\n        cout << filename << \": contains a negative cycle\" << endl;\n        return;\n    }\n    auto best = INF;\n    for (auto& row: a)\n        best = min(best, *min_element(row.begin(), row.end()));\n    cout << filename << \": \" << best << endl;\n}\n\nint main() {\n    run(\"problem18.8test1.txt\");  // problem18.8test1.txt: -2\n    run(\"problem18.8test2.txt\");  // problem18.8test2.txt: contains a negative cycle\n    run(\"problem18.8file1.txt\");  // problem18.8file1.txt: contains a negative cycle\n    run(\"problem18.8file2.txt\");  // problem18.8file2.txt: contains a negative cycle\n    run(\"problem18.8file3.txt\");  // problem18.8file3.txt: -19\n//    run(\"problem18.8file4.txt\");\n    return 0;\n}\n```\n\n</details>\n\n---\n\n# Part 4: Algorithms for NP-Hard Problems\n\n<br/>\n<a href=\"https://www.amazon.com/dp/0999282964\" target=\"_blank\">\n    <img src=\"images/ai4large.jpg\" />\n</a>\n\n---\n\n### Traveling Salesman\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Overview and Prerequisites (Section 19.0)](https://www.youtube.com/watch?v=qOFLAjxqoK0&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=1)\n* [MST vs. TSP: An Algorithmic Mystery (Section 19.1)](https://www.youtube.com/watch?v=9uImnCfKMlA&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=2)\n* [Possible Levels of Expertise (Section 19.2)](https://www.youtube.com/watch?v=TQ_f5PqmtYo&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=3)\n* [Easy and Hard Problems (Section 19.3)](https://www.youtube.com/watch?v=PEyRWZA3ESE&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=4)\n* [Algorithmic Strategies for NP-Hard Problems (Section 19.4)](https://www.youtube.com/watch?v=K4HZKRZ3v-M&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=5)\n* [Proving NP-Hardness: A Simple Recipe (Section 19.5)](https://www.youtube.com/watch?v=ZqDT-tlIAyY&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=6)\n* [Rookie Mistakes (Section 19.6)](https://www.youtube.com/watch?v=SBsCjEeSoeQ&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=7)\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*Kotlin*\n```kotlin\nimport java.io.File\n\nclass Solution() {\n    private var best = (1e9 + 7).toInt()\n    private var best_path = listOf<Int>()\n    private var start = 0\n    private var M = 0\n    private var N = 0\n    private var adj = mutableMapOf<Int, MutableSet<Int>>()\n    private var cost = mutableMapOf<String, Int>()\n    private var key = { u: Int, v: Int -> \"$u,$v\" }\n    private fun init(input_file: String) {\n        best = (1e9 + 7).toInt()\n        best_path = mutableListOf<Int>()\n        adj = mutableMapOf<Int, MutableSet<Int>>()\n        cost = mutableMapOf<String, Int>()\n        var i = 0\n        File(input_file).forEachLine { line ->\n            var A = line.trim().split(\" \").map{ it.toInt() }\n            if (0 < i++) {\n                var (u, v, w) = A\n                if (!adj.contains(u)) adj[u] = mutableSetOf<Int>()\n                if (!adj.contains(v)) adj[v] = mutableSetOf<Int>()\n                adj[u]!!.add(v); cost[key(u, v)] = w\n                adj[v]!!.add(u); cost[key(v, u)] = w\n            } else {\n                N = A[0]\n                M = A[1]\n            }\n        }\n    }\n    fun run(input_file: String): Pair<Int, List<Int>> {\n        init(input_file)\n        start = 1\n        go(start, mutableListOf<Int>(start), mutableSetOf<Int>(start))\n        return Pair<Int, List<Int>>(best, best_path)\n    }\n    fun go(u: Int, path: MutableList<Int>, seen: MutableSet<Int>, t_: Int = 0) {\n        if (seen.size == N) {\n            var t = t_ + (cost[key(u, start)] ?: 0)\n            if (adj[u]!!.contains(start) && t < best) {\n                best = t; best_path = path.toList()\n            }\n            return\n        }\n        for (v in adj[u]!!) {\n            if (seen.contains(v))\n                continue\n            path.add(v); seen.add(v)\n            go(v, path, seen, t_ + cost[key(u, v)]!!)\n            path.removeLast(); seen.remove(v)\n        }\n    }\n}\n\nfun main() {\n    var s = Solution()\n    for (input_file in listOf(\"quiz19.2.txt\", \"quiz20.7.txt\")) {\n        var (best, path) = s.run(input_file)\n        println(\"$input_file  best: $best  path: ${path.joinToString()}\")\n    }\n}\n// quiz19.2.txt  best: 13  path: 1, 2, 4, 3\n// quiz20.7.txt  best: 23  path: 1, 3, 2, 5, 4\n```\n\n*Javascript*\n```javascript\nlet LineByLine = require('n-readlines');\n\nclass Solution {\n    key = (u, v) => `${u},${v}`;\n    init(input_file) {\n        this.best = Number(1e9 + 7);\n        this.best_path = [];\n        this.M = 0;\n        this.N = 0;\n        this.adj = new Map();\n        this.cost = new Map();\n        let [A, line, i] = [[], '', 0];\n        let input = new LineByLine(input_file);\n        while (line = input.next()) {\n            let A = String.fromCharCode(...line).trim().split(' ').map(Number);\n            if (0 < i++) {\n                let [u, v, w] = A;\n                if (!this.adj.has(u)) this.adj.set(u, new Set());\n                if (!this.adj.has(v)) this.adj.set(v, new Set());\n                this.adj.get(u).add(v), this.cost.set(this.key(u, v), w);\n                this.adj.get(v).add(u), this.cost.set(this.key(v, u), w);\n            } else {\n                [this.N, this.M] = A;\n            }\n        }\n    }\n    run(input_file) {\n        this.init(input_file);\n        this.start = 1;\n        this.go(this.start, [this.start], new Set([this.start]));\n        return [this.best, this.best_path];\n    }\n    go(u, path, seen, t = 0) {\n        if (seen.size == this.N) {\n            t += this.cost.get(this.key(u, this.start)) || 0;\n            if (this.adj.get(u).has(this.start) && t < this.best)\n                this.best = t, this.best_path = [...path];\n            return;\n        }\n        for (let v of this.adj.get(u)) {\n            if (seen.has(v))\n                continue;\n            path.push(v), seen.add(v);\n            this.go(v, path, seen, t + this.cost.get(this.key(u, v)));\n            path.pop(), seen.delete(v);\n        }\n    }\n}\n\nlet s = new Solution();\nfor (let input_file of ['quiz19.2.txt', 'quiz20.7.txt']) {\n    let [best, path] = s.run(input_file);\n    console.log(`${input_file}  best: ${best}  path: ${path}`);\n}\n// quiz19.2.txt  best: 13  path: 1,2,4,3\n// quiz20.7.txt  best: 23  path: 1,3,2,5,4\n```\n\n*Python3*\n```python\nfrom random import randint\nfrom collections import defaultdict\n\nclass Solution():\n    def init(self, input_file):\n        self.best = int(1e9 + 7)\n        self.best_path = []\n        self.M = 0\n        self.N = 0\n        self.adj = defaultdict(set)\n        self.cost = defaultdict(int)\n        with open(input_file) as input:\n            for i, line in enumerate(input):\n                A = [int(x) for x in line.strip().split(' ')]\n                if 0 < i:\n                    u, v, w = A\n                    self.adj[u].add(v); self.cost[(u, v)] = w\n                    self.adj[v].add(u); self.cost[(v, u)] = w\n                else:\n                    self.N, self.M = A\n    def run(self, input_file):\n        self.init(input_file)\n        self.start = 1\n        self.go(self.start, [self.start], set([self.start]))\n        return self.best, self.best_path\n\n    def go(self, u, path, seen, t = 0):\n        if len(seen) == self.N:\n            t += self.cost[(u, self.start)] # connect ultimate edge of tour\n            if self.start in self.adj[u] and t < self.best:\n                self.best = t\n                self.best_path = path[:]\n            return\n        for v in self.adj[u]:\n            if v not in seen:\n                path.append(v); seen.add(v)\n                self.go(v, path, seen, t + self.cost[(u, v)])\n                path.pop(); seen.remove(v)\n\ns = Solution()\nfor input_file in ['quiz19.2.txt', 'quiz20.7.txt']:\n    best, path = s.run(input_file)\n    print(f'{input_file}  best: {best}  path: {path}')\n# quiz19.2.txt  best: 13  path: [1, 2, 4, 3]\n# quiz20.7.txt  best: 23  path: [1, 3, 2, 5, 4]\n```\n\n*C++*\n```cpp\n#include <fstream>\n#include <iostream>\n#include <iterator>\n#include <sstream>\n#include <unordered_map>\n#include <unordered_set>\n#include <vector>\n\nusing namespace std;\nusing VI = vector<int>;\nusing Pair = pair<int, VI>;\nusing Set = unordered_set<int>;\nusing Adj = unordered_map<int, Set>;\nusing Cost = unordered_map<string, int>;\n\nclass Solution {\n    int best, start, M, N;\n    VI best_path;\n    Adj adj;\n    Cost cost;\n    string key(int u, int v) {\n        stringstream ss;\n        ss << u << \",\" << v;\n        return ss.str();\n    }\n    void init(const string& input_file, string line = {}) {\n        best = 1e9 + 7; start = M = N = 0;\n        best_path.clear();\n        adj.clear();\n        cost.clear();\n        auto i = 0;\n        fstream fin{ input_file };\n        while (getline(fin, line)) {\n            VI A;\n            istringstream is{ line };\n            copy(istream_iterator<int>(is), istream_iterator<int>(), back_inserter(A));\n            if (0 < i++) {\n                auto [u, v, w] = tie(A[0], A[1], A[2]);\n                adj[u].insert(v); cost[key(u, v)] = w;\n                adj[v].insert(u); cost[key(v, u)] = w;\n            } else {\n                N = A[0];\n                M = A[1];\n            }\n        }\n    }\n    void go(int u, VI&& path, Set&& seen, int t = 0) {\n        if (seen.size() == N) {\n            t += cost[key(u, start)]; // connect ultimate edge of tour\n            if (adj[u].find(start) != adj[u].end() && t < best)\n                best = t, best_path = path;\n            return;\n        }\n        for (auto v: adj[u]) {\n            if (seen.find(v) != seen.end())\n                continue;\n            path.push_back(v), seen.insert(v);\n            go(v, move(path), move(seen), t + cost[key(u, v)]);\n            path.pop_back(), seen.erase(v);\n        }\n    }\npublic:\n    Pair run(const string& input_file) {\n        init(input_file);\n        start = 1;\n        go(start, {start}, {start});\n        return {best, best_path};\n    }\n};\n\nint main() {\n    auto s = Solution();\n    for (auto& input_file: {\"quiz19.2.txt\", \"quiz20.7.txt\"}) {\n        auto [best, path] = s.run(input_file);\n        cout << input_file << \"  best: \" << best << \"  path: \";\n        copy(path.begin(), path.end(), ostream_iterator<int>(cout, \" \"));\n        cout << endl;\n    }\n    // quiz19.2.txt  best: 13  path: 1 3 4 2\n    // quiz20.7.txt  best: 23  path: 1 4 5 2 3\n    return 0;\n}\n```\n\n</details>\n\n### Traveling Salesman (Heuristic)\n\n<details><summary>📚 Lectures</summary>\n<br/>\n\n* [Makespan Minimization (Part 1) (Section 20.1, Part 1)](https://www.youtube.com/watch?v=fn5HNoiMwHM&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=8)\n* [Makespan Minimization (Part 2) (Section 20.1, Part 2)](https://www.youtube.com/watch?v=CcdYLcLymV4&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=9)\n* [Maximum Coverage (Part 1) (Section 20.2, Part 1)](https://www.youtube.com/watch?v=GcJy8uzSUbA&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=10)\n* [Maximum Coverage (Part 2) (Section 20.2, Part 2)](https://www.youtube.com/watch?v=fHldsoBMFKI&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=11)\n* [Influence Maximization (Part 1) (Section 20.3, Part 1)](https://www.youtube.com/watch?v=GqKbx3LCQqE&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=12)\n* [Influence Maximization (Part 2) (Section 20.3, Part 2)](https://www.youtube.com/watch?v=_1-Vv5Vid9Q&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=13)\n* [2-OPT Heuristic for the TSP (Part 1) (Section 20.4, Part 1)](https://www.youtube.com/watch?v=dYEWqrp-mho&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=14)\n* [2-OPT Heuristic for the TSP (Part 2) (Section 20.4, Part 2)](https://www.youtube.com/watch?v=8vbKIfpDPJI&list=PLEGCF-WLh2RK6lq3iSsiU84rWVee3A-hz&index=15)\n</details>\n\n<details><summary>🎯 Solutions</summary>\n<br/>\n\n*TSP Nearest Neighbor Heuristic (Python3)*\n```python\nfrom collections import defaultdict\n\nN, M = -1, -1\nadj = defaultdict(list)\ncost, key = {}, lambda u, v: f'{u},{v}'\nwith open('input.txt') as input:\n    for line in input:\n        A = [int(x) for x in line.strip().split(' ')]\n        if len(A) == 3:\n            u, v, w = A\n            adj[u].append(v); cost[key(u, v)] = w\n            adj[v].append(u); cost[key(v, u)] = w\n        elif len(A) == 2:\n            N, M = A\n\nstart = 1\nu, seen, path = start, set([start]), [start]\nwhile len(seen) < N:\n    best, best_v = float('inf'), -1\n    for v in adj[u]:\n        if v not in seen:\n            cand = cost[key(u, v)]\n            if best > cand:\n                best = cand; best_v = v\n    u = best_v; seen.add(best_v); path.append(best_v)\npath.append(start) # add last edge to complete the tour\nt = sum(cost[key(path[i - 1], path[i])] for i in range(1, len(path)))\nprint(f'total: {t}  path: {path}')\n# total: 29  path: [1, 2, 3, 4, 5, 1]\n```\n\n</details>"
  },
  {
    "path": "_challenge_problems/index_equal_element.py",
    "content": "# You are given a sorted (from smallest to largest) array A of N distinct integers which can be positive, negative, or zero.  Design the fastest algorithm you can for deciding whether there is an index i such that A[i] = i.\n\n# use case: if the value is less-than the index, search right half\n\n#    -3 -2 -1  0  4\n#     0  1  2  3  4\n#                 ^\n\n# use case: if the value is greater than the index, search left half\n\n#     0  2  3  4  5\n#     0  1  2  3  4\n#     ^\n\ndef same(A):\n    i, j = 0, len(A) - 1\n    while i < j:\n        k = (i + j) // 2\n        if A[k] < k:\n            i = k + 1\n        else:\n            j = k\n    return A[i] == i\n\ndef run(A, ok=False):\n    assert(same(A) == ok)\n\nrun([0, 2, 3, 4, 5], True)\nrun([-3, -2, -1, 0, 4], True)\n"
  },
  {
    "path": "_challenge_problems/unimodal_array.py",
    "content": "\n# Problem: You are given a unimodal array of n distinct elemnts, meaning that its entries are in increasing order up until its maximum element, after which its elemnets are in decreasing order.  Give an algorithm to compute the maximum element of a unimodal array that runs in O(logN) time.\n\ndef best(A):\n    i, j = 0, len(A) - 1\n    while i < j:\n        k = (i + j) // 2\n        if A[k] < A[k + 1]:\n            i = k + 1\n        else:\n            j = k\n    return A[i]\n\ndef run(A):\n    error = f'NOT ({best(A)} == {max(A)})'\n    assert best(A) == max(A), error\n\n# small inputs to test edge cases\nrun([0, 1, 0])\nrun([1, 3, 1])\nrun([2, 5, 4])\n\n# mediuim inputs\nrun([0, 2, 4, 6, 8, 6, 4, 2])\nrun([1, 4, 7, 9, 8, 3])\nrun([3, 5, 9, 12, 10, 6, 2])\n\n# peak near beginning/end\nrun([1, 5, 4, 3, 2])\nrun([0, 2, 4, 6, 5])\n\n# larger inputs\nrun([0, 1, 3, 6, 10, 15, 21, 18, 14, 9, 5, 2])\nrun([2, 4, 6, 8, 11, 14, 17, 16, 13, 9, 5, 1])\nrun([1, 5, 10, 20, 35, 50, 49, 30, 15, 7, 2])\nrun([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0])\nrun([0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 34, 21, 13, 8, 5, 3, 2, 1, 0])\n\nimport random\ndef random_unimodal(seed=0):\n    A = []\n    random.seed(seed)\n    while len(A) < int(1e4):\n        A.append(random.randint(0, int(1e9)))\n    A.sort()\n    L = A[:len(A) // 2]\n    R = A[len(A) // 2:]\n    return L + list(reversed(R))\n\nfor _ in range(10):\n    run(random_unimodal())\n"
  },
  {
    "path": "bellman_ford/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(bellman_ford)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(bellman_ford main.cpp)"
  },
  {
    "path": "bellman_ford/main.cpp",
    "content": "#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n#include <queue>\n\nusing namespace std;\nusing VI = vector<int>;\nusing VS = vector<string>;\nusing Edge = tuple<int, int, int>;\nusing Edges = vector<Edge>;\nusing Pair = pair<int, int>;\nusing Pairs = vector<Pair>;\nusing AdjList = unordered_map<int, Pairs>;\nusing Queue = queue<int>;\n\n// bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\nVI bell(Edges& E, int N, int start = 1, int INF = 1e6) {\n    VI dist(N, INF);\n    dist[start] = 0;\n    auto K = N - 1;\n    while (K--)\n        for (auto [u, v, w]: E)\n            dist[v] = min(dist[v], dist[u] + w);\n    return dist;\n}\n\n// shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\nVI spfa(Edges& E, int N, int start = 1, int INF = 1e6, AdjList adj = {}) {\n    VI dist(N, INF);\n    dist[start] = 0;\n    for (auto [u, v, w]: E)\n        adj[u].emplace_back(v, w);\n    Queue q{{ start }};\n    while (q.size()) {\n        auto u = q.front(); q.pop();\n        for (auto [v, w]: adj[u])\n            if (dist[v] > dist[u] + w)\n                dist[v] = dist[u] + w, q.push(v);\n    }\n    return dist;\n}\n\nVI run(const string& filename) {\n    auto N = 0;\n    Edges E;\n    fstream fin{ filename };\n    VS A;\n    for (string line; getline(fin, line); A.emplace_back(line));\n    for (auto& s: A) {\n        transform(s.begin(), s.end(), s.begin(), [](auto c) { return c == ',' ? ' ' : c; });\n        stringstream ss{ s };\n        auto [u, v, w] = make_tuple(0, 0, 0);\n        ss >> u;\n        while (ss >> v >> w)\n            E.emplace_back(u, v, w);\n        ++N;\n    }\n    auto a = bell(E, N + 1),  // +1 for 1-based indexing\n         b = spfa(E, N + 1);\n    assert(a == b);\n    return b;\n}\n\nint main() {\n    auto dist = run(\"test.txt\");\n    VI A{ 7, 37, 59, 82, 99, 115, 133, 165, 188, 197 };\n    transform(A.begin(), A.end(), A.begin(), [&](auto x) { return dist[x]; });\n    copy(A.begin(), A.end(), ostream_iterator<int>(cout, \",\"));  // 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068,\n    return 0;\n}\n"
  },
  {
    "path": "bellman_ford/main.js",
    "content": "const assert = require('assert');\nconst zip = require('lodash/zip');\nconst LineByLine = require('n-readlines');\n\n// bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\nlet bell = (E, N, start = 1, INF = Number(1e6)) => {\n    let dist = Array(N).fill(INF);\n    dist[start] = 0;\n    let K = N - 1;\n    while (K--)\n        E.forEach(([u, v, w]) => dist[v] = Math.min(dist[v], dist[u] + w));\n    return dist;\n};\n\n// shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\nlet spfa = (E, N, start = 1, INF = Number(1e6)) => {\n    let dist = Array(N).fill(INF);\n    dist[start] = 0;\n    let adj = [...Array(N)].map(_ => []);\n    E.forEach(([u, v, w]) => adj[u].push([v, w]));\n    let q = [start];\n    while (q.length) {\n        let u = q.shift();\n        for (let [v, w] of adj[u])\n            if (dist[v] > dist[u] + w)\n                dist[v] = dist[u] + w, q.push(v);\n    }\n    return dist;\n};\n\nlet run = filename => {\n    let N = 0;\n    let E = [];\n    let input = new LineByLine(filename);\n    let line;\n    while (line = input.next()) {\n        let A = line.toString('ascii').split('\\t').filter(it => it.length);\n        let u = Number(A.shift());\n        A.map(pair => pair.split(',').map(Number)).forEach(([v, w]) => E.push([u, v, w]));\n        ++N;\n    }\n    let a = bell(E, N + 1),  // +1 for 1-based indexing\n        b = spfa(E, N + 1);\n    zip(a, b).forEach(([x, y]) => assert(x == y));  // 💩 sanity check: single source shortest paths are the same\n    return a;\n};\n\nlet dist = run('test.txt');\nconsole.log([7, 37, 59, 82, 99, 115, 133, 165, 188, 197].map(x => dist[x]).join(','));  // 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068\n"
  },
  {
    "path": "bellman_ford/main.kt",
    "content": "import java.io.File\nimport java.util.LinkedList\nimport java.util.Queue\n\n// bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\nfun bell(E: Array<Triple<Int, Int, Int>>, N: Int, start: Int = 1, INF: Int = (1e6).toInt()): IntArray {\n    var dist = IntArray(N) { INF }\n    dist[start] = 0\n    var K = N - 1\n    while (0 < K--)\n        E.forEach{ (u, v, w) -> dist[v] = Math.min(dist[v], dist[u] + w)}\n    return dist\n}\n\n// shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\nfun spfa(E: Array<Triple<Int, Int, Int>>, N: Int, start: Int = 1, INF: Int = (1e6).toInt()): IntArray {\n    var dist = IntArray(N) { INF }\n    dist[start] = 0\n    var adj = Array<MutableList<Pair<Int, Int>>>(N) { mutableListOf<Pair<Int, Int>>() }\n    for ((u, v, w) in E)\n        adj[u].add(Pair(v, w))\n    var q: Queue<Int> = LinkedList<Int>(listOf(start))\n    while (0 < q.size) {\n        var u = q.poll()\n        for ((v, w) in adj[u]) {\n            if (dist[v] > dist[u] + w) {\n                dist[v] = dist[u] + w; q.add(v)\n            }\n        }\n    }\n    return dist\n}\n\nfun run(filename: String): IntArray {\n    var N = 0\n    var E = mutableListOf<Triple<Int, Int, Int>>()\n    File(filename).forEachLine {\n        var A = ArrayDeque(it.trim().split(\"\\t\"))\n        var u = A.removeFirst().toInt()\n        for ((v, w) in A.map{ it.split(\",\").map{ it.toInt() } })\n            E.add(Triple(u, v, w))\n        ++N;\n    }\n    var A = E.toTypedArray()\n    var a = bell(A, N + 1)  // +1 for 1-based indexing\n    var b = spfa(A, N + 1)\n    assert(a == b)          // 💩 sanity check: single source shortest paths are the same\n    return b\n}\n\nfun main() {\n    var dist = run(\"test.txt\")\n    println(listOf(7, 37, 59, 82, 99, 115, 133, 165, 188, 197).map{ dist[it] }.joinToString(\",\"))  // 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068\n}\n"
  },
  {
    "path": "bellman_ford/main.py",
    "content": "from collections import deque\n\n# bellman-ford: N - 1 edge relaxations (u -> v of cost w) [ie. attempting to relax M edges N - 1 times] given N vertices\ndef bell(E, N, start = 1, INF = int(1e6)):\n    dist = [INF] * N\n    dist[start] = 0\n    k = N - 1\n    while k:\n        for u, v, w in E:\n            dist[v] = min(dist[v], dist[u] + w)\n        k -= 1\n    return dist\n\n# shortest-paths faster algorithm: only attempt to relax candidate edges (note: adjacency list needed)\ndef spfa(E, N, start = 1, INF = int(1e6)):\n    dist = [INF] * N\n    dist[start] = 0\n    adj = {i: [] for i in range(N)}\n    for u, v, w in E:\n        adj[u].append([v, w])\n    q = deque([start])\n    while q:\n        u = q.popleft()\n        for v, w in adj[u]:\n            if dist[v] > dist[u] + w:\n                dist[v] = dist[u] + w; q.append(v)\n    return dist\n\ndef run(filename):\n    E = []\n    N = 0\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            line = line.strip()\n            A = [word for word in line.split('\\t') if len(word)]\n            u = int(A[0])\n            for i in range(1, len(A)):\n                v, w = [int(x) for x in A[i].split(',')]\n                E.append([u, v, w])\n            N += 1\n    a = bell(E, N + 1)  # +1 for 1-based indexing\n    b = spfa(E, N + 1)\n    assert(a == b)\n    return b\n\ndist = run('test.txt')\nprint(','.join(str(dist[x]) for x in [7, 37, 59, 82, 99, 115, 133, 165, 188, 197]))  # 2599,2610,2947,2052,2367,2399,2029,2442,2505,3068\n"
  },
  {
    "path": "bellman_ford/package.json",
    "content": "{\n  \"name\": \"bellman_ford\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"clayton wong\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"assert\": \"^2.0.0\",\n    \"lodash\": \"^4.17.21\",\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "bellman_ford/test.txt",
    "content": "1\t80,982\t163,8164\t170,2620\t145,648\t200,8021\t173,2069\t92,647\t26,4122\t140,546\t11,1913\t160,6461\t27,7905\t40,9047\t150,2183\t61,9146\t159,7420\t198,1724\t114,508\t104,6647\t30,4612\t99,2367\t138,7896\t169,8700\t49,2437\t125,2909\t117,2597\t55,6399\n2\t42,1689\t127,9365\t5,8026\t170,9342\t131,7005\t172,1438\t34,315\t30,2455\t26,2328\t6,8847\t11,1873\t17,5409\t157,8643\t159,1397\t142,7731\t182,7908\t93,8177\n3\t57,1239\t101,3381\t43,7313\t41,7212\t91,2483\t31,3031\t167,3877\t106,6521\t76,7729\t122,9640\t144,285\t44,2165\t6,9006\t177,7097\t119,7711\n4\t162,3924\t70,5285\t195,2490\t72,6508\t126,2625\t121,7639\t31,399\t118,3626\t90,9446\t127,6808\t135,7582\t159,6133\t106,4769\t52,9267\t190,7536\t78,8058\t75,7044\t116,6771\t49,619\t107,4383\t89,6363\t54,313\n5\t200,4009\t112,1522\t25,3496\t23,9432\t64,7836\t56,8262\t120,1862\t2,8026\t90,8919\t142,1195\t81,2469\t182,8806\t17,2514\t83,8407\t146,5308\t147,1087\t51,22\n6\t141,8200\t98,5594\t66,6627\t159,9500\t143,3110\t129,8525\t118,8547\t88,2039\t83,4949\t165,6473\t162,6897\t184,8021\t123,13\t176,3512\t195,2233\t42,7265\t47,274\t132,1514\t2,8847\t171,3722\t3,9006\n7\t156,7027\t187,9522\t87,4976\t121,8739\t56,6616\t10,2904\t71,8206\t53,179\t146,4823\t165,6019\t125,5670\t27,4888\t63,9920\t150,9031\t84,4061\n8\t152,1257\t189,2780\t58,4708\t26,8342\t199,1918\t31,3987\t35,3160\t71,5829\t27,3483\t69,8815\t130,55\t168,2076\t122,5338\t73,4528\t28,9996\t17,3535\t40,3193\t72,7308\t24,8434\t87,2833\t25,3949\t175,1022\t177,8508\n9\t152,1087\t115,7827\t17,7002\t72,794\t150,4539\t190,3613\t95,9480\t36,5284\t166,8702\t63,1753\t199,70\t131,700\t76,9340\t70,2\t139,8701\t140,4163\t180,5995\n10\t57,9988\t78,3771\t62,4816\t137,5273\t7,2904\t187,4786\t184,3207\t96,807\t31,1184\t88,2539\t135,4650\t168,9495\t164,3866\t11,8988\t116,1493\t51,5578\t171,2029\n11\t1,1913\t185,2045\t77,815\t22,8425\t181,8448\t47,8727\t81,7299\t150,4802\t178,1696\t28,2275\t183,594\t131,833\t157,8497\t25,5057\t59,3203\t10,8988\t2,1873\t134,294\t83,4211\t124,6180\n12\t78,5753\t17,4602\t62,5676\t16,8068\t60,5933\t67,371\t71,6734\t53,7001\t72,3626\t34,6690\t59,761\t18,1520\t128,7542\t38,6699\t57,9416\n13\t144,9987\t59,9801\t97,7026\t50,758\t43,5400\t163,3870\t178,4194\t151,9629\t45,1794\t105,6821\t29,2784\t172,2070\t57,6850\t77,8638\t135,861\n14\t149,4352\t187,4874\t26,3841\t128,9662\t155,4446\t118,373\t123,2733\t106,7912\t169,4333\t53,9197\t161,4275\t126,9602\t73,4106\t160,7860\t131,358\t141,4477\t119,960\t43,3199\t47,7898\t175,6718\t177,6741\t60,2464\t127,5682\t31,1945\t143,5848\t94,3551\t82,3283\n15\t42,1789\t22,3571\t25,7019\t163,818\t56,2334\t100,809\t143,1041\t107,4589\t190,6854\t169,7485\t94,9606\t34,7961\t54,8983\t157,2136\t24,8040\n16\t200,2848\t198,2223\t92,2896\t18,8663\t27,8673\t75,4116\t150,1680\t36,1555\t41,2747\t90,4558\t68,5894\t12,8068\t42,2596\t185,6280\t171,3482\t109,1469\t127,9807\t178,1714\t35,839\t56,9828\t134,5203\t55,6680\t110,4252\n17\t26,1275\t45,5114\t142,8016\t83,4615\t140,6440\t8,3535\t69,3610\t153,8545\t9,7002\t12,4602\t173,7312\t114,8915\t108,1942\t54,3115\t66,6176\t190,7000\t70,3899\t5,2514\t178,7464\t166,4762\t2,5409\t146,5362\t117,6266\n18\t57,4216\t80,5252\t86,7517\t62,1926\t120,44\t173,7256\t133,2702\t148,589\t167,7625\t16,8663\t170,4989\t118,6388\t142,332\t95,6122\t99,5717\t154,453\t150,5150\t149,2664\t146,9000\t171,4403\t111,785\t12,1520\n19\t33,6938\t77,7013\t187,107\t109,8397\t88,2002\t95,8691\t132,3157\t195,5038\t154,4320\t23,8560\t152,9751\t185,5896\t119,7406\t160,3997\t80,62\n20\t66,2667\t173,2676\t43,8105\t135,6434\t33,6387\t74,6183\t106,8785\t75,2484\t130,9048\t56,7194\t50,9507\t88,3014\t124,392\t61,2580\t90,7372\t92,1704\t87,2639\t154,2398\t41,4203\t85,1435\t169,5990\t166,6086\t28,2234\t145,8099\n21\t23,5183\t40,2199\t31,2556\t71,4986\t165,2151\t193,494\t154,1845\t111,3060\t85,2880\t101,2775\t182,2447\t80,9884\t87,2681\t102,6643\t131,3748\n22\t92,5592\t64,4257\t11,8425\t24,594\t15,3571\t42,3783\t41,1374\t114,9960\t144,9362\t146,3620\t71,3243\t143,8603\t131,6075\t192,4606\t108,9656\t168,4356\t177,8713\t132,1560\n23\t143,7543\t161,6863\t45,8074\t165,208\t21,5183\t118,5079\t40,8336\t27,9054\t112,3201\t135,4560\t167,2133\t188,4236\t166,8077\t195,3179\t48,4485\t137,7591\t99,6485\t5,9432\t71,3316\t96,2431\t125,922\t19,8560\n24\t141,6862\t197,9337\t66,5879\t59,6941\t70,4670\t55,4106\t103,8083\t61,7906\t48,7959\t151,784\t177,393\t102,8731\t199,2838\t73,3509\t8,8434\t187,9327\t22,594\t150,5669\t164,7312\t157,9540\t15,8040\n25\t115,9233\t197,3875\t185,3573\t72,2332\t104,4899\t137,5378\t8,3949\t5,3496\t77,2729\t136,9251\t143,108\t83,9569\t15,7019\t48,3214\t155,3242\t153,2477\t129,3005\t132,219\t11,5057\t37,1591\t68,4188\n26\t14,3841\t8,8342\t1,4122\t147,5759\t113,5553\t157,7\t65,9434\t116,4221\t66,2747\t138,7027\t145,6697\t130,5706\t60,701\t127,9896\t136,7200\t17,1275\t120,5788\t175,6165\t70,9252\t95,36\t106,6940\t2,2328\t96,425\t51,9329\t183,4842\t196,6754\n27\t23,9054\t78,3066\t8,3483\t1,7905\t152,2124\t108,9929\t63,3896\t151,5915\t111,3101\t34,8912\t182,6234\t133,7749\t16,8673\t192,5344\t114,714\t168,1578\t175,210\t138,5918\t7,4888\t122,84\n28\t8,9996\t188,3816\t116,2638\t132,5604\t20,2234\t178,3642\t76,3705\t122,9165\t184,4164\t198,366\t161,9217\t160,9059\t56,5375\t120,8874\t11,2275\t111,4495\t193,9441\t157,6880\t48,2803\n29\t78,8190\t144,6452\t114,9478\t156,5083\t62,9692\t121,4537\t184,9797\t109,6873\t153,5446\t67,3449\t172,5830\t111,1005\t100,1642\t148,3252\t13,2784\n30\t78,5469\t119,7372\t144,1616\t130,1356\t59,4458\t40,9818\t79,503\t43,6233\t148,4760\t42,263\t1,4612\t57,5668\t185,3846\t101,6979\t94,6976\t106,7819\t2,2455\t71,9294\n31\t4,399\t8,3987\t50,2598\t75,7688\t47,7840\t99,8583\t190,5055\t112,5231\t114,7617\t118,6949\t180,3598\t21,2556\t199,5564\t14,1945\t3,3031\t35,9855\t10,1184\t146,2837\t51,3739\t83,6588\t46,5964\n32\t136,3823\t77,1689\t92,3395\t121,1615\t85,7494\t173,9631\t177,6902\t88,8129\t36,7329\t116,6065\t61,3332\t68,7352\t119,1914\t82,8571\t70,9909\n33\t144,4841\t173,5949\t170,3648\t113,652\t110,1986\t82,3577\t61,1837\t97,5671\t55,1252\t19,6938\t48,914\t74,3642\t125,67\t89,3089\t176,3258\t20,6387\t138,6960\t153,6574\t171,3913\n34\t86,6435\t156,8641\t72,2540\t181,5267\t27,8912\t58,8824\t179,8528\t62,9864\t70,2348\t57,5471\t53,236\t168,3923\t101,3383\t142,7791\t55,7174\t2,315\t147,9758\t15,7961\t199,8196\t12,6690\n35\t57,3693\t8,3160\t144,3087\t114,490\t65,8910\t178,5774\t172,992\t16,839\t118,8640\t41,6749\t31,9855\t39,853\t64,6071\t166,2816\t184,7437\t49,3098\t182,7369\t110,4985\t93,8775\n36\t80,2032\t130,7589\t123,6226\t16,1555\t150,116\t88,7759\t100,8612\t9,5284\t198,6280\t49,953\t143,5111\t42,4917\t134,979\t159,6043\t32,7329\t67,2380\t148,9550\t48,7266\n37\t197,9188\t119,9313\t187,4105\t191,3573\t109,2135\t75,751\t200,7541\t139,8208\t155,609\t142,6433\t25,1591\t132,821\t156,7714\t107,1144\t99,7757\n38\t91,7087\t88,502\t132,6092\t126,5441\t147,8391\t12,6699\t130,5227\t146,4400\t108,8712\t100,1369\t134,4730\t87,2975\t99,6169\t183,5213\t109,4945\n39\t200,4319\t98,3993\t130,2414\t40,2489\t196,9267\t133,8145\t82,3528\t44,9175\t42,5464\t127,6103\t93,6132\t180,9506\t192,7454\t119,1376\t115,983\t81,7400\t35,853\n40\t23,8336\t1,9047\t120,7760\t101,2885\t21,2199\t144,7772\t96,5739\t136,4658\t184,4306\t189,4263\t30,9818\t39,2489\t108,8883\t8,3193\t80,9657\t181,2338\t162,3056\t71,2826\t68,5800\n41\t200,2622\t78,63\t66,4654\t198,7215\t59,284\t75,7333\t22,1374\t181,5235\t16,2747\t154,901\t150,7278\t3,7212\t103,7917\t163,5256\t20,4203\t91,7776\t35,6749\t147,1858\t165,3741\t107,8116\n42\t160,2382\t156,6539\t6,7265\t15,1789\t61,8096\t164,347\t194,6498\t172,5383\t104,2726\t124,3496\t161,4792\t159,5951\t117,7074\t2,1689\t186,9391\t62,3249\t79,9404\t39,5464\t187,3075\t22,3783\t30,263\t16,2596\t137,4572\t163,1278\t60,6663\t70,9396\t36,4917\t73,9154\n43\t200,8943\t159,9621\t97,3906\t20,8105\t164,6849\t13,5400\t3,7313\t133,8488\t108,8964\t30,6233\t79,5052\t131,8231\t167,8120\t14,3199\t130,2685\t138,7965\t177,9544\t143,1171\t65,5805\t118,8008\t140,4482\t93,8479\n44\t197,4900\t144,2276\t198,2619\t39,9175\t87,7875\t191,8130\t166,6953\t170,6940\t163,18\t79,9988\t145,2888\t173,5518\t57,9979\t82,3134\t54,4113\t3,2165\n45\t57,4630\t23,8074\t112,9496\t130,4994\t86,8207\t17,5114\t120,5279\t169,662\t162,3436\t170,8060\t118,5918\t124,3290\t110,8317\t13,1794\t167,1163\n46\t57,2413\t152,9550\t86,7512\t123,132\t138,2860\t195,8206\t176,9923\t119,2687\t54,9328\t196,9632\t73,5109\t31,5964\t173,2969\t193,199\t80,7968\t194,2429\n47\t57,9584\t114,9480\t145,9483\t190,5892\t182,8382\t31,7840\t129,9533\t142,5297\t58,1229\t146,2959\t6,274\t14,7898\t189,5939\t11,8727\t76,2138\t70,2236\n48\t152,5835\t23,4485\t33,914\t24,7959\t25,3214\t135,8869\t53,3578\t162,201\t28,2803\t141,7941\t36,7266\t85,2792\t86,3588\t124,2593\t130,7921\n49\t160,8648\t154,2962\t109,7520\t36,953\t178,9747\t192,3113\t112,2935\t35,3098\t71,3441\t4,619\t96,9901\t171,9736\t163,4688\t1,2437\t133,5167\t117,2896\t105,9278\n50\t152,5767\t112,6454\t185,3968\t77,5220\t20,9507\t165,2667\t98,990\t187,2485\t198,3798\t13,758\t128,2987\t189,7031\t52,9931\t127,3622\t31,2598\t179,2502\t191,5026\t153,4905\n51\t80,7589\t72,4882\t137,1096\t138,8755\t109,662\t67,4225\t181,158\t132,6107\t189,8899\t159,3017\t5,22\t10,5578\t31,3739\t120,5675\t26,9329\t176,1625\n52\t4,9267\t115,4973\t159,7816\t185,8925\t188,7805\t97,9063\t50,9931\t137,9846\t91,424\t150,634\t56,2416\t107,3647\t68,7601\t168,1134\t179,3504\n53\t14,9197\t114,7352\t156,4662\t62,153\t85,1227\t177,9852\t34,236\t7,179\t12,7001\t48,3578\t71,9285\t86,7353\t150,662\t183,5304\t125,8054\t54,8361\n54\t197,2223\t66,2906\t136,1794\t188,4883\t17,3115\t109,7832\t44,4113\t182,438\t15,8983\t200,4899\t112,2279\t169,2296\t4,313\t53,8361\t138,6261\t46,9328\n55\t33,1252\t188,5181\t101,6050\t24,4106\t169,7795\t149,3088\t34,7174\t193,8583\t1,6399\t145,3342\t105,8477\t166,3686\t121,44\t16,6680\t82,3547\n56\t101,3516\t20,7194\t179,5284\t127,3031\t5,8262\t161,9811\t16,9828\t15,2334\t52,2416\t7,6616\t77,7923\t182,7267\t88,3375\t61,1315\t117,1934\t28,5375\t124,552\t100,361\n57\t18,4216\t94,558\t186,8815\t3,1239\t8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8208\n140\t1,546\t17,6440\t97,6527\t158,4029\t151,5289\t68,9624\t138,5446\t43,4482\t169,2230\t9,4163\t155,5001\t188,6223\t102,6370\t166,9829\t65,5376\n141\t154,3188\t68,3540\t106,674\t79,7918\t104,8162\t24,6862\t63,5607\t6,8200\t75,9237\t150,2634\t124,168\t14,4477\t112,130\t164,6499\t198,2621\t114,6388\t185,6820\t59,9126\t64,158\t137,7872\t81,4032\t76,1969\t48,7941\n142\t66,777\t17,8016\t104,6236\t18,332\t47,5297\t81,424\t91,9164\t150,2598\t5,1195\t34,7791\t155,6613\t169,7506\t86,1663\t100,2994\t190,8070\t2,7731\t71,6038\t145,5378\t37,6433\n143\t23,7543\t6,3110\t22,8603\t108,972\t25,108\t81,9810\t43,1171\t186,8430\t14,5848\t129,8021\t101,4042\t76,1079\t98,4300\t155,2442\t177,3884\t36,5111\t153,9940\t96,9274\t15,1041\t176,5062\n144\t115,3825\t173,8693\t29,6452\t98,7198\t68,2277\t195,652\t102,7884\t30,1616\t111,5456\t33,4841\t13,9987\t44,2276\t86,8808\t148,3617\t35,3087\t40,7772\t101,3619\t22,9362\t184,5222\t135,6396\t90,6223\t3,285\t100,6605\n145\t200,2753\t1,648\t136,1769\t26,6697\t64,2685\t174,7252\t47,9483\t108,521\t44,2888\t123,8804\t71,6127\t142,5378\t20,8099\t78,7244\t110,6099\t100,5512\t55,3342\n146\t115,9828\t22,3620\t47,2959\t60,2317\t5,5308\t127,8151\t7,4823\t134,9556\t18,9000\t31,2837\t17,5362\t68,3895\t72,4264\t188,5715\t167,52\t107,7862\t38,4400\n147\t26,5759\t59,2651\t163,7221\t95,1278\t132,2847\t124,9014\t5,1087\t34,9758\t96,6736\t38,8391\t41,1858\t167,5546\t130,9251\t149,6379\t58,2267\t93,7807\n148\t160,3995\t144,3617\t185,2814\t64,6419\t18,589\t30,4760\t173,6725\t179,6374\t70,7231\t155,6603\t122,3230\t192,4834\t36,9550\t121,8115\t29,3252\n149\t14,4352\t59,2405\t188,1003\t163,9897\t70,2366\t83,6823\t187,9580\t174,2824\t73,5233\t112,8736\t55,3088\t18,2664\t176,2255\t190,3755\t180,3407\t147,6379\n150\t141,2634\t1,2183\t16,1680\t41,7278\t36,116\t135,9732\t11,4802\t98,2093\t58,4857\t142,2598\t73,8061\t9,4539\t18,5150\t24,5669\t52,634\t190,5243\t88,6770\t53,662\t7,9031\t93,9213\n151\t80,6728\t156,6169\t24,784\t27,5915\t174,1846\t168,9216\t99,4990\t88,2295\t178,5979\t96,5643\t83,162\t13,9629\t140,5289\t189,9732\t163,3624\n152\t161,6939\t58,5877\t48,5835\t9,1087\t8,1257\t46,9550\t189,8140\t199,2697\t109,2743\t65,3595\t186,2075\t115,4383\t50,5767\t193,5444\t90,4427\t80,9606\t114,9627\t62,7404\t79,6519\t27,2124\t111,1940\t19,9751\t93,6543\n153\t17,8545\t99,4560\t70,6532\t164,8748\t29,5446\t25,2477\t72,541\t143,9940\t173,7613\t77,4483\t50,4905\t165,897\t133,8437\t33,6574\t67,6204\t100,9522\n154\t141,3188\t119,741\t198,5078\t156,8062\t62,3238\t20,2398\t18,453\t49,2962\t187,1808\t168,6317\t200,229\t185,1448\t93,4073\t78,8423\t84,5421\t41,901\t60,6667\t170,5971\t19,4320\t21,1845\t199,5786\n155\t57,893\t14,4446\t98,5515\t112,7915\t123,3251\t120,6822\t25,3242\t139,2100\t143,2442\t65,5533\t142,6613\t96,1251\t137,5736\t148,6603\t61,5301\t126,307\t37,609\t140,5001\t194,6768\n156\t66,2965\t42,6539\t82,4691\t53,4662\t151,6169\t7,7027\t85,6669\t29,5083\t154,8062\t130,2264\t108,7039\t34,8641\t121,195\t175,2205\t69,9959\t70,4830\t127,6372\t37,7714\n157\t119,9158\t26,7\t86,4447\t101,1393\t187,7184\t137,5286\t99,6818\t11,8497\t2,8643\t158,1881\t128,6815\t175,1597\t72,604\t24,9540\t28,6880\t15,2136\n158\t78,6367\t187,6714\t91,5553\t139,3451\t169,1709\t135,8348\t63,5709\t195,4912\t140,4029\t157,1881\t124,1870\t181,969\t112,383\t87,4081\t134,119\n159\t4,6133\t160,4243\t61,49\t180,5757\t6,9500\t194,9391\t43,9621\t100,6567\t126,2980\t73,4969\t131,4355\t124,6580\t1,7420\t52,7816\t74,8960\t198,8330\t42,5951\t120,5811\t87,19\t36,6043\t84,8763\t129,6895\t2,1397\t51,3017\t193,3786\n160\t14,7860\t138,9902\t127,7534\t49,8648\t85,3613\t189,1530\t57,2058\t159,4243\t183,9293\t148,3995\t87,8712\t180,624\t179,2542\t91,383\t42,2382\t1,6461\t77,105\t28,9059\t111,9702\t19,3997\n161\t152,6939\t14,4275\t23,6863\t78,6310\t136,3866\t42,4792\t62,4144\t79,8395\t127,6643\t69,6171\t126,4512\t56,9811\t196,9729\t102,8230\t88,1726\t28,9217\n162\t4,3924\t98,6139\t6,6897\t59,391\t194,1483\t122,3518\t57,6483\t121,1977\t179,9718\t139,4510\t199,7749\t40,3056\t111,8771\t96,3737\t45,3436\t186,6114\t48,201\n163\t1,8164\t101,6033\t41,5256\t173,5799\t15,818\t13,3870\t149,9897\t131,8625\t181,5593\t119,5189\t61,448\t42,1278\t68,4920\t100,9709\t147,7221\t44,18\t49,4688\t192,2762\t151,3624\t89,4055\n164\t141,6499\t112,1492\t42,347\t120,5926\t43,6849\t87,3629\t184,9774\t170,328\t153,8748\t10,3866\t172,9550\t74,8627\t195,9730\t105,4661\t24,7312\t183,615\t176,8681\n165\t23,208\t6,6473\t79,3768\t187,1291\t50,2667\t153,897\t166,4221\t74,2602\t21,2151\t121,7147\t124,9797\t83,1555\t65,3705\t7,6019\t41,3741\t110,4097\n166\t23,8077\t98,2364\t79,8726\t173,6917\t44,6953\t167,7080\t118,3979\t165,4221\t168,4399\t17,4762\t9,8702\t122,6712\t20,6086\t169,5530\t115,3001\t35,2816\t55,3686\t140,9829\n167\t23,2133\t188,6549\t187,9538\t43,8120\t18,7625\t127,3756\t180,6183\t87,1022\t79,820\t83,8200\t3,3877\t129,5370\t85,8110\t193,8116\t166,7080\t131,6269\t146,52\t147,5546\t45,1163\t199,2001\t93,5670\n168\t119,1890\t8,2076\t136,9519\t87,9716\t154,6317\t121,7186\t133,899\t122,1574\t85,6193\t173,3859\t59,4170\t27,1578\t69,2357\t151,9216\t22,4356\t70,1295\t34,3923\t166,4399\t10,9495\t52,1134\n169\t14,4333\t175,9164\t177,2274\t45,662\t20,5990\t63,5160\t119,3511\t104,3712\t187,9225\t192,8603\t109,382\t158,1709\t55,7795\t1,8700\t138,7498\t142,7506\t166,5530\t107,668\t15,7485\t54,2296\t140,2230\n170\t119,275\t1,2620\t198,8089\t136,1529\t33,3648\t18,4989\t177,2774\t44,6940\t84,2436\t2,9342\t154,5971\t164,328\t45,8060\t71,1539\t94,9318\n171\t188,6981\t101,4083\t16,3482\t67,1394\t61,6888\t49,9736\t182,4704\t94,9959\t10,2029\t33,3913\t185,5113\t71,6702\t6,3722\t18,4403\t72,8573\n172\t200,6888\t42,5383\t72,3153\t104,561\t174,3433\t102,6572\t175,5353\t35,992\t73,2239\t164,9550\t29,5830\t80,7715\t77,4771\t2,1438\t60,2781\t125,8515\t13,2070\n173\t112,7338\t1,2069\t144,8693\t33,5949\t17,7312\t20,2676\t18,7256\t121,2976\t168,3859\t32,9631\t148,6725\t82,591\t163,5799\t192,2550\t166,6917\t179,4234\t138,8555\t44,5518\t95,4092\t153,7613\t135,5664\t61,4803\t125,2615\t193,4808\t46,2969\n174\t130,4481\t89,858\t73,2581\t135,6977\t68,7082\t136,5711\t91,3418\t125,9048\t122,8205\t145,7252\t72,2019\t151,1846\t172,3433\t108,5669\t99,5675\t179,1886\t149,2824\t90,6914\n175\t156,2205\t187,2864\t27,210\t199,3779\t67,5048\t121,8821\t169,9164\t134,4489\t65,7920\t26,6165\t172,5353\t197,5909\t8,1022\t129,7121\t14,6718\t184,9107\t70,3256\t58,3675\t157,1597\n176\t200,1709\t115,8236\t6,3512\t33,3258\t187,1128\t191,3352\t139,8186\t149,2255\t116,4512\t46,9923\t143,5062\t51,1625\t164,8681\t107,6806\t74,8129\n177\t86,7010\t92,3182\t24,393\t64,7660\t102,4462\t43,9544\t22,8713\t190,1332\t14,6741\t8,8508\t170,2774\t82,7882\t169,2274\t32,6902\t53,9852\t60,5345\t143,3884\t178,7547\t118,8279\t3,7097\n178\t130,615\t72,5128\t70,3394\t13,4194\t120,8906\t11,1696\t151,5979\t16,1714\t138,6589\t102,1334\t17,7464\t49,9747\t177,7547\t35,5774\t136,2752\t28,3642\t76,8433\n179\t80,7729\t160,2542\t136,6711\t120,3327\t56,5284\t50,2502\t186,9993\t180,664\t104,8827\t90,3149\t74,1223\t148,6374\t174,1886\t126,7436\t173,4234\t162,9718\t116,8099\t34,8528\t52,3504\t122,7377\n180\t160,624\t159,5757\t114,8490\t59,2435\t86,4604\t39,9506\t85,5525\t179,664\t191,6312\t31,3598\t149,3407\t167,6183\t89,6612\t9,5995\t126,7176\t105,341\n181\t112,2524\t187,7956\t41,5235\t118,8129\t185,9712\t139,5456\t76,3275\t40,2338\t11,8448\t34,5267\t102,3585\t126,8920\t106,5332\t93,4071\t91,5060\t191,4844\t163,5593\t158,969\t51,158\n182\t27,6234\t47,8382\t99,2897\t139,2354\t5,8806\t133,8241\t132,6433\t56,7267\t74,1873\t35,7369\t64,4701\t107,8313\t54,438\t171,4704\t2,7908\t21,2447\n183\t160,9293\t112,9037\t102,9634\t99,3577\t81,3061\t88,5547\t11,594\t96,5939\t53,5304\t105,7722\t26,4842\t57,9093\t70,5332\t125,9920\t164,615\t38,5213\n184\t6,8021\t130,8488\t188,198\t40,4306\t123,2832\t101,9591\t113,4999\t129,5623\t144,5222\t175,9107\t136,6682\t164,9774\t86,801\t57,7592\t29,9797\t81,4485\t35,7437\t135,7629\t28,4164\t10,3207\t128,6339\n185\t57,9772\t105,1033\t90,7284\t52,8925\t83,9306\t97,7065\t148,2814\t25,3573\t197,3140\t50,3968\t11,2045\t141,6820\t76,3674\t108,8699\t60,6670\t188,700\t120,556\t181,9712\t154,1448\t30,3846\t16,6280\t109,6644\t171,5113\t19,5896\t196,1339\n186\t57,8815\t152,2075\t197,1324\t42,9391\t188,5027\t92,7980\t179,9993\t191,8255\t58,8993\t143,8430\t116,8639\t162,6114\t71,7143\t189,8128\t195,2099\t68,2528\t103,9654\n187\t14,4874\t200,6767\t176,1128\t37,4105\t7,9522\t175,2864\t19,107\t107,2610\t167,9538\t157,7184\t24,9327\t181,7956\t42,3075\t158,6714\t165,1291\t50,2485\t154,1808\t113,6332\t169,9225\t149,9580\t10,4786\n188\t23,4236\t198,9114\t137,9117\t184,198\t101,8531\t167,6549\t54,4883\t149,1003\t28,3816\t196,88\t52,7805\t55,5181\t185,700\t186,5027\t171,6981\t97,4695\t138,892\t125,230\t146,5715\t140,6223\n189\t152,8140\t160,1530\t8,2780\t114,3102\t86,1115\t40,4263\t77,5702\t50,7031\t47,5939\t85,1147\t60,4415\t69,5215\t186,8128\t198,9430\t122,2017\t51,8899\t151,9732\t193,2375\n190\t4,7536\t200,5999\t47,5892\t113,697\t130,3429\t135,1431\t150,5243\t61,9775\t69,8022\t133,9958\t128,2968\t100,6674\t17,7000\t106,3305\t9,3613\t177,1332\t31,5055\t149,3755\t142,8070\t15,6854\t105,2518\n191\t77,5135\t126,3989\t176,3352\t94,8318\t186,8255\t121,8606\t87,6921\t44,8130\t103,9683\t75,1403\t181,4844\t50,5026\t180,6312\t111,5723\t37,3573\t133,4296\n192\t114,6813\t97,6411\t77,561\t39,7454\t22,4606\t104,4219\t27,5344\t85,544\t173,2550\t91,6625\t169,8603\t116,5906\t49,3113\t163,2762\t122,1494\t148,4834\n193\t152,5444\t167,8116\t114,4000\t55,8583\t58,6166\t189,2375\t159,3786\t96,8831\t79,7737\t21,494\t28,9441\t62,6610\t123,7460\t99,4566\t173,4808\t46,199\n194\t200,2915\t159,9391\t136,2496\t130,9429\t42,6498\t92,426\t139,6966\t162,1483\t73,8521\t99,5832\t155,6768\t114,949\t46,2429\t79,5784\t135,5726\n195\t23,3179\t4,2490\t197,5337\t144,652\t136,4279\t6,2233\t158,4912\t186,2099\t200,8114\t61,8928\t46,8206\t164,9730\t119,617\t19,5038\t67,5737\n196\t188,88\t39,9267\t139,3988\t95,231\t61,5577\t161,9729\t125,4519\t117,3366\t103,696\t46,9632\t26,6754\t112,5663\t128,1760\t119,2824\t185,1339\n197\t54,2223\t186,1324\t121,6502\t134,6225\t68,8223\t24,9337\t25,3875\t139,1386\t81,5540\t44,4900\t195,5337\t37,9188\t111,4083\t86,9714\t110,751\t136,9068\t185,3140\t104,4174\t175,5909\n198\t141,2621\t170,8089\t44,2619\t188,9114\t41,7215\t1,1724\t154,5078\t84,5999\t16,2223\t117,3936\t123,3493\t159,8330\t69,6284\t132,2393\t134,4071\t77,5081\t50,3798\t65,3575\t36,6280\t28,366\t128,1860\t189,9430\n199\t152,2697\t8,1918\t136,7783\t59,8958\t24,2838\t175,3779\t31,5564\t162,7749\t65,11\t76,6878\t9,70\t89,2446\t34,8196\t167,2001\t154,5786\n200\t108,9976\t103,6851\t145,2753\t41,2622\t187,6767\t190,5999\t16,2848\t194,2915\t5,4009\t172,6888\t39,4319\t176,1709\t60,3269\t138,678\t43,8943\t98,2690\t1,8021\t104,7083\t154,229\t91,1988\t67,475\t76,4623\t195,8114\t37,7541\t54,4899"
  },
  {
    "path": "closest_pair/naive.py",
    "content": "P = [(1, 8), (2, 5), (4, 7), (6, 3)]\nN = len(P)\nINF = 1234567890  # arbitary choice for infinity\n\ndef dist(i, j):\n    x1, y1 = P[i]\n    x2, y2 = P[j]\n    return (x1 - x2) ** 2 \\\n         + (y1 - y2) ** 2\n\nbest_dist = INF\nbest_pair = None\n\nD = [[INF] * N for _ in range(N)]\nfor i in range(N):\n    for j in range(N):\n        D[i][j] = dist(i, j)\n        if i != j:  # candidates for best pair cannot be the same point\n            if best_dist >= D[i][j]:\n                best_dist = D[i][j]\n                best_pair = (i, j)\n\ni, j = best_pair\nprint(f'best pair: {P[i]}, {P[j]}')\n\n# ➜  closest_pair git:(main) ✗ python3 ./naive.py\n# best pair: (4, 7), (2, 5)\n"
  },
  {
    "path": "closest_pair/recursive.py",
    "content": "INF = 1234567890  # arbitary choice for infinity\n\ndef distance(a, b):\n    x1, y1 = a\n    x2, y2 = b\n    return (x1 - x2) ** 2 \\\n         + (y1 - y2) ** 2\n\ndef split(Px, Py, d):\n    # median x-coordinate\n    median = Px[len(Px) // 2][0]\n\n    # identify points near left/right boundary\n    Sy = [(x, y) for x, y in Py if median - d <= x <= median + d]\n\n    # return the best split pair (if it exists)\n    best_dist, best_pairs = INF, set()\n    for i in range(len(Sy) - 1):\n        for j in range(i + 1, min(i + 1 + 7, len(Sy))):\n            cand = distance(Sy[i], Sy[j])\n            if best_dist > cand:\n                best_dist = cand\n                best_pairs = set()\n            if best_dist == cand:\n                best_pairs.add((Sy[i], Sy[j]))\n    return best_dist, best_pairs\n\ndef best(P):\n    best_dist, best_pairs = INF, set()\n    for i in range(len(P)):\n        for j in range(i + 1, len(P)):\n            cand = distance(P[i], P[j]) if P[i] != P[j] else INF\n            if best_dist > cand:\n                best_dist = cand\n                best_pairs = set()\n            if best_dist == cand:\n                best_pairs.add((P[i], P[j]))\n    return best_dist, best_pairs\n\ndef go(Px, Py):\n    if len(Px) <= 3:  # Base case\n        return best(Px)\n\n    Lx, Rx = Px[:len(Px) // 2], Px[len(Px) // 2:]\n    Ly, Ry = [], []\n    for x, y in Py:\n        if x <= Lx[-1][0]:\n            Ly.append((x, y))\n        else:\n            Ry.append((x, y))\n\n    dist_left, best_left = go(Lx, Ly)\n    dist_right, best_right = go(Rx, Ry)\n    dist_split, best_split = split(Px, Py, min(dist_left, dist_right))\n\n    cands = sorted([(dist_left, best_left), (dist_right, best_right), (dist_split, best_split)], key=lambda it: it[0])\n    best_dist, best_pairs = cands[0][0], set()\n    for dist, pairs in cands:\n        if dist == best_dist:\n            for a, b in pairs:\n                best_pairs.add((a, b) if a < b else (b, a))\n    return best_dist, best_pairs\n\ndef run(points, expected_best_pair):\n    Px = sorted(points, key=lambda it: it[0])\n    Py = sorted(points, key=lambda it: it[1])\n    _, best_pair = go(Px, Py)\n    print(f'points: {points}')\n    print(f'actual: {sorted(best_pair)}')\n    print(f'expect: {sorted(expected_best_pair)}')\n    print()\n    assert(sorted(best_pair) == sorted(expected_best_pair))\n\n# initial example\nrun(points=[(1, 8), (2, 5), (4, 7), (6, 3)], expected_best_pair=set([((2, 5), (4, 7))]))\n\n# simple, obvious nearest neighbors\nrun(points=[(0, 0), (3, 4), (7, 1), (10, 6)], expected_best_pair=set([((0, 0), (3, 4)), ((3, 4), (7, 1))]))\n\n# closest pair not adjacent in sorted-by-x\nrun(points=[(1, 1), (4, 10), (7, 4), (9, 8)], expected_best_pair=set([((7, 4), (9, 8))]))\n\n# tight cluster inside larger spread\nrun(points=[(2, 9), (5, 3), (6, 5), (11, 1)], expected_best_pair=set([((5, 3), (6, 5))]))\n\n# stress: diagonal-ish\nrun(points=[(1, 10), (4, 7), (8, 3), (13, 6)], expected_best_pair=set([((1, 10), (4, 7))]))\n\n# larger input: 10 points\nrun(points=[(1, 17), (3, 4), (6, 14), (8, 9), (11, 2), (14, 7), (17, 12), (19, 5), (22, 15), (25, 1)], expected_best_pair=set([((6, 14), (8, 9)), ((14, 7), (19, 5))]))\n\n# larger input: 12 points more spread out\nrun(points=[(2, 21), (4, 6), (7, 15), (9, 2), (12, 18), (14, 9), (16, 4), (19, 13), (21, 7), (24, 16), (27, 1), (30, 11)], expected_best_pair=set([((14, 9), (16, 4))]))\n\n# same x-coordinate (vertical stack)\nrun(points=[(5, 1), (5, 4), (5, 9), (8, 20), (12, 30)], expected_best_pair=set([((5, 1), (5, 4))]))\n\n# same y-coordinate (horizontal line)\nrun(points=[(1, 7), (4, 7), (9, 7), (20, 2), (25, 11)], expected_best_pair=set([((1, 7), (4, 7))]))\n\n# redundant x-coordinate to test split pairs\nrun(points=[(10, 1), (10, 4), (10, 8), (10, 13), (11, 7), (20, 50)], expected_best_pair=set([((10, 8), (11, 7))]))\n\n# redundant x-coordinate to test split pairs\nrun(points=[(0, 0), (0, 1000), (0, 2000), (0, 3000), (0, 4000), (0, 5000), (0, 6000), (0, 7000), (5, 1), (5, 7002)], expected_best_pair=set([((0, 0), (5, 1))]))\n\n# tie for best\nrun(points=[(0, 0), (0, 1), (1, 0)], expected_best_pair=set([((0, 0), (0, 1)), ((0, 0), (1, 0))]))\n\n# ➜  closest_pair git:(main) ✗ python3 recursive.py\n# points: [(1, 8), (2, 5), (4, 7), (6, 3)]\n# actual: [((2, 5), (4, 7))]\n# expect: [((2, 5), (4, 7))]\n\n# points: [(0, 0), (3, 4), (7, 1), (10, 6)]\n# actual: [((0, 0), (3, 4)), ((3, 4), (7, 1))]\n# expect: [((0, 0), (3, 4)), ((3, 4), (7, 1))]\n\n# points: [(1, 1), (4, 10), (7, 4), (9, 8)]\n# actual: [((7, 4), (9, 8))]\n# expect: [((7, 4), (9, 8))]\n\n# points: [(2, 9), (5, 3), (6, 5), (11, 1)]\n# actual: [((5, 3), (6, 5))]\n# expect: [((5, 3), (6, 5))]\n\n# points: [(1, 10), (4, 7), (8, 3), (13, 6)]\n# actual: [((1, 10), (4, 7))]\n# expect: [((1, 10), (4, 7))]\n\n# points: [(1, 17), (3, 4), (6, 14), (8, 9), (11, 2), (14, 7), (17, 12), (19, 5), (22, 15), (25, 1)]\n# actual: [((6, 14), (8, 9)), ((14, 7), (19, 5))]\n# expect: [((6, 14), (8, 9)), ((14, 7), (19, 5))]\n\n# points: [(2, 21), (4, 6), (7, 15), (9, 2), (12, 18), (14, 9), (16, 4), (19, 13), (21, 7), (24, 16), (27, 1), (30, 11)]\n# actual: [((14, 9), (16, 4))]\n# expect: [((14, 9), (16, 4))]\n\n# points: [(5, 1), (5, 4), (5, 9), (8, 20), (12, 30)]\n# actual: [((5, 1), (5, 4))]\n# expect: [((5, 1), (5, 4))]\n\n# points: [(1, 7), (4, 7), (9, 7), (20, 2), (25, 11)]\n# actual: [((1, 7), (4, 7))]\n# expect: [((1, 7), (4, 7))]\n\n# points: [(10, 1), (10, 4), (10, 8), (10, 13), (11, 7), (20, 50)]\n# actual: [((10, 8), (11, 7))]\n# expect: [((10, 8), (11, 7))]\n\n# points: [(0, 0), (0, 1000), (0, 2000), (0, 3000), (0, 4000), (0, 5000), (0, 6000), (0, 7000), (5, 1), (5, 7002)]\n# actual: [((0, 0), (5, 1))]\n# expect: [((0, 0), (5, 1))]\n\n# points: [(0, 0), (0, 1), (1, 0)]\n# actual: [((0, 0), (0, 1)), ((0, 0), (1, 0))]\n# expect: [((0, 0), (0, 1)), ((0, 0), (1, 0))]\n"
  },
  {
    "path": "dijkstra/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(dijkstra)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(dijkstra main.cpp)"
  },
  {
    "path": "dijkstra/main.cpp",
    "content": "#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n#include <unordered_set>\n#include <queue>\n\nusing namespace std;\n\nusing Queries = vector<int>;\nusing Distance = unordered_map<int, int>;\nusing Set = unordered_set<int>;\n\nclass BaseSolution {\nprotected:\n    static constexpr auto INF = int(1e9 + 7);\npublic:\n    virtual string run(string filename, Queries&& queries) = 0;\n};\n\nclass NaiveSolution : public BaseSolution {\n    using Edge = tuple<int, int, int>;\n    using Edges = vector<Edge>;\npublic:\n    Distance dijkstra(Edges& E) {\n        Distance dist;\n        Set seen;\n        auto start{ 1 };\n        dist[start] = 0, seen.insert(start);\n        for (;;) {\n            auto found = false;\n            auto best_v = INF,\n                 best_w = INF;\n            for (auto [u, v, w]: E) {\n                if (seen.find(u) == seen.end() || seen.find(v) != seen.end())\n                    continue;\n                found = true;\n                if (best_w > dist[u] + w)\n                    best_v = v,\n                    best_w = dist[u] + w;\n            }\n            if (!found)\n                break;\n            auto [v, w] = tie(best_v, best_w);\n            dist[v] = w, seen.insert(v);\n        }\n        return dist;\n    }\n    string run(string filename, Queries&& queries) {\n        Edges E;\n        fstream fin{ filename };\n        string line;\n        int u, v, w;\n        char _;\n        while (getline(fin, line)) {\n            istringstream is{ line };\n            for (is >> u; is >> v >> _ >> w; E.push_back({ u, v, w }));\n        }\n        auto dist = dijkstra(E);\n        ostringstream os;\n        transform(queries.begin(), queries.end(), ostream_iterator<int>(os, \" \"), [&](auto x) { return dist[x]; });\n        return os.str();\n    }\n};\n\nclass HeapSolution : public BaseSolution {\n    using Pair = pair<int, int>;\n    using Pairs = vector<Pair>;\n    using AdjList = unordered_map<int, Pairs>;\n    priority_queue<Pair, Pairs, std::greater<Pair>> q;\npublic:\n    Distance dijkstra(AdjList& adj) {\n        Distance dist;\n        Set seen;\n        for (auto [u, _]: adj)\n            dist[u] = INF;\n        auto start{ 1 };\n        q.push({ 0, start });\n        while (q.size()) {\n            auto [cost, u] = q.top(); q.pop();\n            if (!seen.insert(u).second)\n                continue;\n            dist[u] = cost;\n            for (auto [w, v]: adj[u])\n                if (seen.find(v) == seen.end())\n                    q.push({ dist[u] + w, v });\n        }\n        return dist;\n    }\n    string run(string filename, Queries&& queries) {\n        AdjList adj;\n        fstream fin{ filename };\n        string line;\n        int u, v, w;\n        char _;\n        while (getline(fin, line)) {\n            istringstream is{ line };\n            for (is >> u; is >> v >> _ >> w; adj[u].push_back({ w, v }));\n        }\n        auto dist = dijkstra(adj);\n        ostringstream os;\n        transform(queries.begin(), queries.end(), ostream_iterator<int>(os, \" \"), [&](auto x) { return dist[x]; });\n        return os.str();\n    }\n};\n\nvoid run(BaseSolution&& solution) {\n    cout << \"problem9.8test.txt: \" << solution.run(\"problem9.8test.txt\", Queries{1, 2, 3, 4, 5, 6, 7, 8 }) << endl\n         << \"problem9.8.txt      \" << solution.run(\"problem9.8.txt\", Queries{7, 37, 59, 82, 99, 115, 133, 165, 188, 197 }) << endl;\n}\n\nint main() {\n    run(NaiveSolution());\n//    problem9.8test.txt: 0 1 2 3 4 4 3 2\n//    problem9.8.txt      2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n\n    run(HeapSolution());\n//    problem9.8test.txt: 0 1 2 3 4 4 3 2\n//    problem9.8.txt      2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n    return 0;\n}\n"
  },
  {
    "path": "dijkstra/main.js",
    "content": "let LineByLine = require('n-readlines');\n\nlet INF = Number(1e9 + 7);\n\nclass NaiveSolution {\n    dijkstra(E) {\n        let dist = new Map();\n        let seen = new Set();\n        let start = 1;\n        dist[start] = 0; seen.add(start);\n        for (;;) {\n            let found = false;\n            let best_v = INF,\n                best_w = INF;\n            for (let [u, v, w] of E) {\n                if (!seen.has(u) || seen.has(v))\n                    continue;\n                found = true;\n                if (best_w > dist[u] + w)\n                    best_v = v,\n                    best_w = dist[u] + w;\n            }\n            if (!found)\n                break;\n            let [v, w] = [best_v, best_w];\n            dist[v] = w; seen.add(v);\n        }\n        return dist;\n    }\n    run(filename, queries) {\n        let E = [];\n        let input = new LineByLine(filename);\n        let line;\n        while (line = input.next()) {\n            let words = String.fromCharCode(...line).trim().split(/\\s+/);\n            let u = Number(words[0]);\n            for (let i = 1; i < words.length; ++i) {\n                let [v, w] = words[i].split(',').map(Number);\n                E.push([ u, v, w ]);\n            }\n        }\n        let dist = this.dijkstra(E);\n        return queries.map(x => dist[x]).join(' ');\n    }\n}\n\nlet heapkey = x => Array.isArray(x) ? x[0] : x;\nlet heappush = (A, x, f = Math.min) => {\n    let P = i => Math.floor((i - 1) / 2);  // parent\n    A.push(x);\n    let N = A.length,\n        i = N - 1;\n    while (0 < i && heapkey(A[i]) == f(heapkey(A[i]), heapkey(A[P(i)]))) {\n        [A[i], A[P(i)]] = [A[P(i)], A[i]];\n        i = P(i);\n    }\n};\nlet heappop = (A, f = Math.min) => {\n    let L = i => 2 * i + 1,  // children\n        R = i => 2 * i + 2;\n    let N = A.length,\n        i = 0;\n    let top = A[0];\n    [A[0], A[N - 1]] = [A[N - 1], A[0]], A.pop(), --N;\n    let ok;\n    do {\n        ok = true;\n        let left = f == Math.min ? Infinity : -Infinity,\n            right = left;\n        if (L(i) < N && heapkey(A[i]) != f(heapkey(A[i]), heapkey(A[L(i)]))) ok = false, left  = heapkey(A[L(i)]);\n        if (R(i) < N && heapkey(A[i]) != f(heapkey(A[i]), heapkey(A[R(i)]))) ok = false, right = heapkey(A[R(i)]);\n        if (!ok) {\n            let j = left == f(left, right) ? L(i) : R(i);\n            [A[i], A[j]] = [A[j], A[i]];\n            i = j;\n        }\n    } while (!ok);\n    return top;\n};\n\nclass HeapSolution {\n    dijkstra(adj) {\n        let dist = {};\n        let seen = new Set();\n        let start = 1;\n        let q = [[ 0, start ]];\n        while (q.length) {\n            let [cost, u] = heappop(q);\n            if (seen.has(u))\n                continue;\n            dist[u] = cost, seen.add(u);\n            for (let [w, v] of (adj[u] || []))\n                heappush(q, [ dist[u] + w, v ]);\n        }\n        return dist;\n    }\n    run(filename, queries) {\n        let adj = {};\n        let input = new LineByLine(filename);\n        let line;\n        while (line = input.next()) {\n            let words = String.fromCharCode(...line).trim().split('\\t');\n            let u = Number(words[0]);\n            if (!(u in adj))\n                adj[u] = [];\n            for (let i = 1; i < words.length; ++i) {\n                let [v, w] = words[i].split(',').map(Number);\n                adj[u].push([ w, v ]);\n            }\n        }\n        let dist = this.dijkstra(adj);\n        return queries.map(x => dist[x]).join(' ');\n    }\n}\n\nlet run = solution => {\n    console.log(solution.run('problem9.8test.txt', [1, 2, 3, 4, 5, 6, 7, 8]));\n    console.log(solution.run('problem9.8.txt', [7, 37, 59, 82, 99, 115, 133, 165, 188, 197]));\n};\n\nrun(new NaiveSolution());\n//    0 1 2 3 4 4 3 2\n//    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n\nrun(new HeapSolution());\n//    0 1 2 3 4 4 3 2\n//    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n"
  },
  {
    "path": "dijkstra/main.kt",
    "content": "import java.io.File\nimport java.util.PriorityQueue\n\nvar INF = (1e9 + 7).toInt()\n\ninterface BaseSolution {\n    fun run(filename: String, queries: Array<Int>): String\n}\n\nclass NaiveSolution : BaseSolution {\n    fun dijkstra(E: List<Triple<Int, Int, Int>>): MutableMap<Int, Int> {\n        var dist = mutableMapOf<Int, Int>()\n        var seen = mutableSetOf<Int>()\n        var start = 1\n        dist[start] = 0; seen.add(start)\n        var found: Boolean;\n        do {\n            found = false\n            var best_v = INF\n            var best_w = INF\n            for ((u, v, w) in E) {\n                if (!seen.contains(u) || seen.contains(v))\n                    continue\n                found = true\n                if (best_w > dist[u]!! + w) {\n                    best_v = v\n                    best_w = dist[u]!! + w\n                }\n            }\n            var v = best_v\n            var w = best_w\n            dist[v] = w; seen.add(v)\n        } while (found)\n        return dist\n    }\n    override fun run(filename: String, queries: Array<Int>): String {\n        var E = mutableListOf<Triple<Int, Int, Int>>()\n        File(filename).forEachLine {\n            var words = it.trim().split(\"\\t\")\n            var u = words[0].toInt()\n            for (i in 1 until words.size) {\n                var (v, w) = words[i].split(\",\").map{ it.toInt() }\n                E.add(Triple(u, v, w))\n            }\n        }\n        var dist = dijkstra(E.toList())\n        return queries.map{ dist[it] }.joinToString(\" \")\n    }\n}\n\nclass HeapSolution : BaseSolution {\n    fun dijkstra(adj: MutableMap<Int, MutableList<Pair<Int, Int>>>): MutableMap<Int, Int> {\n        var dist = mutableMapOf<Int, Int>()\n        var seen = mutableSetOf<Int>()\n        var start = 1\n        dist[start] = 0\n        var q = PriorityQueue<Pair<Int, Int>>(Comparator{ a: Pair<Int, Int>, b: Pair<Int, Int> -> a.first.compareTo(b.first) })\n        q.add(Pair(0, start))\n        while (0 < q.size) {\n            var (cost, u) = q.poll()\n            if (seen.contains(u))\n                continue\n            dist[u] = cost; seen.add(u)\n            for ((w, v) in adj[u]!!) {\n                if (seen.contains(v))\n                    continue\n                q.add(Pair(cost + w, v))\n            }\n        }\n        return dist\n    }\n    override fun run(filename: String, queries: Array<Int>): String {\n        var adj = mutableMapOf<Int, MutableList<Pair<Int, Int>>>()\n        File(filename).forEachLine {\n            var words = it.trim().split(\"\\t\")\n            var u = words[0].toInt()\n            if (!adj.contains(u))\n                adj[u] = mutableListOf()\n            for (i in 1 until words.size) {\n                var (v, w) = words[i].split(\",\").map{ it.toInt() }\n                adj[u]!!.add(Pair(w, v))\n            }\n        }\n        var dist = dijkstra(adj)\n        return queries.map{ dist[it] }.joinToString(\" \")\n    }\n}\n\nfun run(solution: BaseSolution) {\n    println(solution.run(\"problem9.8test.txt\", arrayOf(1, 2, 3, 4, 5, 6, 7, 8)))\n    println(solution.run(\"problem9.8.txt\", arrayOf(7, 37, 59, 82, 99, 115, 133, 165, 188, 197)))\n}\n\nfun main() {\n    run(NaiveSolution())\n    //    0 1 2 3 4 4 3 2\n    //    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n    run(HeapSolution())\n    //    0 1 2 3 4 4 3 2\n    //    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n}\n"
  },
  {
    "path": "dijkstra/main.py",
    "content": "from abc import ABC, abstractmethod\nfrom heapq import heappush, heappop\n\nINF = int(1e9 + 7)\n\nclass BaseSolution(ABC):\n    @abstractmethod\n    def run(self, filename, queries):\n        raise NotImplementedError\n\nclass NaiveSolution(BaseSolution):\n    def dijkstra(self, E):\n        dist = {}\n        seen = set()\n        start = 1\n        dist[start] = 0; seen.add(start)\n        while True:\n            found = False\n            best_v = INF\n            best_w = INF\n            for u, v, w in E:\n                if u not in seen or v in seen:\n                    continue\n                found = True\n                if best_w > dist[u] + w:\n                    best_v = v\n                    best_w = dist[u] + w\n            if not found:\n                break\n            v, w = best_v, best_w\n            dist[v] = w; seen.add(v)\n        return dist\n    def run(self, filename, queries):\n        E = []\n        with open(filename) as fin:\n            while True:\n                line = fin.readline()\n                if not line:\n                    break\n                words = line.split()\n                u = int(words[0])\n                for i in range(1, len(words)):\n                    v, w = map(int, words[i].split(','))\n                    E.append([ u, v, w ])\n        dist = self.dijkstra(E)\n        return ' '.join(str(dist[x]) for x in queries)\n\nclass HeapSolution(BaseSolution):\n    def dijkstra(self, adj, start = 1):\n        dist = {}\n        seen = set()\n        q = [[ 0, start ]]\n        while len(q):\n            cost, u = heappop(q)\n            if u in seen:\n                continue\n            dist[u] = cost; seen.add(u)\n            for w, v in adj[u]:\n                if v not in seen:\n                    heappush(q, [ dist[u] + w, v ])\n        return dist\n    def run(self, filename, queries):\n        adj = {}\n        with open(filename) as fin:\n            while True:\n                line = fin.readline()\n                if not line:\n                    break\n                words = line.split()\n                u = int(words[0])\n                if u not in adj:\n                    adj[u] = []\n                for i in range(1, len(words)):\n                    v, w = map(int, words[i].split(','))\n                    adj[u].append([ w, v ])\n        dist = self.dijkstra(adj)\n        return ' '.join(str(dist[x]) for x in queries)\n\ndef run(solution):\n    print(solution.run('problem9.8test.txt', [1, 2, 3, 4, 5, 6, 7, 8]))\n    print(solution.run('problem9.8.txt', [7, 37, 59, 82, 99, 115, 133, 165, 188, 197]))\n\nrun(NaiveSolution())\n#    0 1 2 3 4 4 3 2\n#    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n\nrun(HeapSolution())\n#    0 1 2 3 4 4 3 2\n#    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n"
  },
  {
    "path": "dijkstra/package.json",
    "content": "{\n  \"name\": \"dijkstra\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "dijkstra/problem9.8.txt",
    "content": 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t133,4296\t\r\n192\t114,6813\t97,6411\t77,561\t39,7454\t22,4606\t104,4219\t27,5344\t85,544\t173,2550\t91,6625\t169,8603\t116,5906\t49,3113\t163,2762\t122,1494\t148,4834\t\r\n193\t152,5444\t167,8116\t114,4000\t55,8583\t58,6166\t189,2375\t159,3786\t96,8831\t79,7737\t21,494\t28,9441\t62,6610\t123,7460\t99,4566\t173,4808\t46,199\t\r\n194\t200,2915\t159,9391\t136,2496\t130,9429\t42,6498\t92,426\t139,6966\t162,1483\t73,8521\t99,5832\t155,6768\t114,949\t46,2429\t79,5784\t135,5726\t\r\n195\t23,3179\t4,2490\t197,5337\t144,652\t136,4279\t6,2233\t158,4912\t186,2099\t200,8114\t61,8928\t46,8206\t164,9730\t119,617\t19,5038\t67,5737\t\r\n196\t188,88\t39,9267\t139,3988\t95,231\t61,5577\t161,9729\t125,4519\t117,3366\t103,696\t46,9632\t26,6754\t112,5663\t128,1760\t119,2824\t185,1339\t\r\n197\t54,2223\t186,1324\t121,6502\t134,6225\t68,8223\t24,9337\t25,3875\t139,1386\t81,5540\t44,4900\t195,5337\t37,9188\t111,4083\t86,9714\t110,751\t136,9068\t185,3140\t104,4174\t175,5909\t\r\n198\t141,2621\t170,8089\t44,2619\t188,9114\t41,7215\t1,1724\t154,5078\t84,5999\t16,2223\t117,3936\t123,3493\t159,8330\t69,6284\t132,2393\t134,4071\t77,5081\t50,3798\t65,3575\t36,6280\t28,366\t128,1860\t189,9430\t\r\n199\t152,2697\t8,1918\t136,7783\t59,8958\t24,2838\t175,3779\t31,5564\t162,7749\t65,11\t76,6878\t9,70\t89,2446\t34,8196\t167,2001\t154,5786\t\r\n200\t108,9976\t103,6851\t145,2753\t41,2622\t187,6767\t190,5999\t16,2848\t194,2915\t5,4009\t172,6888\t39,4319\t176,1709\t60,3269\t138,678\t43,8943\t98,2690\t1,8021\t104,7083\t154,229\t91,1988\t67,475\t76,4623\t195,8114\t37,7541\t54,4899\t\r\n"
  },
  {
    "path": "dijkstra/problem9.8test.txt",
    "content": "1\t2,1\t8,2\n2\t1,1\t3,1\n3\t2,1\t4,1\n4\t3,1\t5,1\n5\t4,1\t6,1\n6\t5,1\t7,1\n7\t6,1\t8,1\n8\t7,1\t1,2\n"
  },
  {
    "path": "floyd_warshall/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(floyd_warshall)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(floyd_warshall main.cpp)"
  },
  {
    "path": "floyd_warshall/main.cpp",
    "content": "/*\n * Programming Problem 18.8: All-Pairs Shortest Paths\n *\n * In this problem, each file describes a directed graph. The first line of the file indicates the number\n * of vertices and edges, respectively. Each subsequent line describes an edge (the first two numbers are its tail\n * and head, respectively) and its length (the third number). NOTE: edge lengths might be negative, and the graphs\n * may or may not be negative cycles.\n *\n * Test cases: (contributed by Matt Davis) What is the shortest shortest path in the graphs described in this file\n * and in this file? (I.e., the minimum, over choices of an origin s and a destination t, of a shortest s-t path in the graph.)\n * (If the graph has a negative cycle, your algorithm should detect that fact.) (Answer: -2 and \"contains a negative cycle,\" respectively.)\n *\n * Challenge data set: Repeat the previous problem for the graphs described in the following files: graph #1, graph #2, graph #3, and graph #4.\n */\n\n#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n\n#define PERF_TEST\n\nusing namespace std;\n\nusing LL = long long;\nusing VL = vector<LL>;\nusing VVL = vector<VL>;\nusing VVVL = vector<VVL>;\nusing Edges = unordered_map<string, LL>;\n\nLL INF = 1e9 + 7;\n\nstring key(int i, int j) {\n    stringstream ss; ss << i << \",\" << j;\n    return ss.str();\n}\n\nVVL floyd_warshall(Edges& E, int N) {\n    VVVL dp(N + 1, VVL(N + 1, VL(N + 1, INF)));\n    for (auto i{ 1 }; i <= N; ++i)\n        for (auto j{ 1 }; j <= N; ++j)\n            if (i == j)\n                dp[0][i][j] = 0;\n            else\n            if (E.find(key(i, j)) != E.end())\n                dp[0][i][j] = E[key(i, j)];\n    for (auto k{ 1 }; k <= N; ++k)\n        for (auto i{ 1 }; i <= N; ++i)\n            for (auto j{ 1 }; j <= N; ++j)\n                dp[k][i][j] = min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j]);\n    return dp[N];\n}\n\nVVL floyd_warshall_memopt(Edges& E, int N) {\n    VVL pre(N + 1, VL(N + 1, INF));\n    for (auto i{ 1 }; i <= N; ++i)\n        for (auto j{ 1 }; j <= N; ++j)\n            if (i == j)\n                pre[i][j] = 0;\n            else\n            if (E.find(key(i, j)) != E.end())\n                pre[i][j] = E[key(i, j)];\n    for (auto k{ 1 }; k <= N; ++k) {\n        VVL cur(N + 1, VL(N + 1, INF));\n        for (auto i{ 1 }; i <= N; ++i)\n            for (auto j{ 1 }; j <= N; ++j)\n                cur[i][j] = min(pre[i][j], pre[i][k] + pre[k][j]);\n        swap(pre, cur);\n    }\n    return pre;\n}\n\nvoid run(const string& filename) {\n    Edges E;\n    fstream fin{ filename };\n    int N, M; fin >> N >> M;\n    for (int u, v, w; fin >> u >> v >> w; E[key(u, v)] = w);\n#ifdef PERF_TEST\n    auto a = floyd_warshall_memopt(E, N);\n#else\n    auto a = floyd_warshall_memopt(E, N),\n         b = floyd_warshall(E, N);\n    assert(a == b);  // 💩 sanity check\n#endif\n    auto cycle = false;\n    for (auto i{ 1 }; i <= N && !cycle; ++i)\n        cycle = a[i][i] < 0;\n    if (cycle) {\n        cout << filename << \": contains a negative cycle\" << endl;\n        return;\n    }\n    auto best = INF;\n    for (auto& row: a)\n        best = min(best, *min_element(row.begin(), row.end()));\n    cout << filename << \": \" << best << endl;\n}\n\nint main() {\n    run(\"problem18.8test1.txt\");  // problem18.8test1.txt: -2\n    run(\"problem18.8test2.txt\");  // problem18.8test2.txt: contains a negative cycle\n    run(\"problem18.8file1.txt\");  // problem18.8file1.txt: contains a negative cycle\n    run(\"problem18.8file2.txt\");  // problem18.8file2.txt: contains a negative cycle\n    run(\"problem18.8file3.txt\");  // problem18.8file3.txt: -19\n//    run(\"problem18.8file4.txt\");\n    return 0;\n}\n"
  },
  {
    "path": "floyd_warshall/main.js",
    "content": "/*\n * Programming Problem 18.8: All-Pairs Shortest Paths\n *\n * In this problem, each file describes a directed graph. The first line of the file indicates the number\n * of vertices and edges, respectively. Each subsequent line describes an edge (the first two numbers are its tail\n * and head, respectively) and its length (the third number). NOTE: edge lengths might be negative, and the graphs\n * may or may not be negative cycles.\n *\n * Test cases: (contributed by Matt Davis) What is the shortest shortest path in the graphs described in this file\n * and in this file? (I.e., the minimum, over choices of an origin s and a destination t, of a shortest s-t path in the graph.)\n * (If the graph has a negative cycle, your algorithm should detect that fact.) (Answer: -2 and \"contains a negative cycle,\" respectively.)\n *\n * Challenge data set: Repeat the previous problem for the graphs described in the following files: graph #1, graph #2, graph #3, and graph #4.\n */\n\nconst LineByLine = require('n-readlines');\nconst assert = require('assert');\n\nlet key = (i, j) => `${i},${j}`;\n\nlet floyd_warshall = (E, N) => {\n    let dp = [...Array(N + 1)].map(_ => [...Array(N + 1)].map(_ => Array(N + 1).fill(Infinity)));\n    for (let i = 1; i <= N; ++i)\n        for (let j = 1; j <= N; ++j)\n            if (i == j)\n                dp[0][i][j] = 0;\n            else\n            if (E.has(key(i, j)))\n                dp[0][i][j] = E.get(key(i, j));\n    for (let k = 1; k <= N; ++k)\n        for (let i = 1; i <= N; ++i)\n            for (let j = 1; j <= N; ++j)\n                dp[k][i][j] = Math.min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j]);\n    return dp[N];\n};\n\nlet floyd_warshall_memopt = (E, N) => {\n    let pre = [...Array(N + 1)].map(_ => Array(N + 1).fill(Infinity));\n    for (let i = 1; i <= N; ++i)\n        for (let j = 1; j <= N; ++j)\n            if (i == j)\n                pre[i][j] = 0;\n            else\n            if (E.has(key(i, j)))\n                pre[i][j] = E.get(key(i, j));\n    for (let k = 1; k <= N; ++k) {\n        let cur = [...Array(N + 1)].map(_ => Array(N + 1).fill(Infinity));\n        for (let i = 1; i <= N; ++i)\n            for (let j = 1; j <= N; ++j)\n                cur[i][j] = Math.min(pre[i][j], pre[i][k] + pre[k][j]);\n        [pre, cur] = [cur, pre];\n    }\n    return pre;\n};\n\nlet run = filename => {\n    let E = new Map();\n    let input = new LineByLine(filename);\n    let [N, _] = input.next().toString('ascii').split(' ').map(Number);\n    let line;\n    while (line = input.next()) {\n        let [u, v, w] = line.toString('ascii').split(' ').map(Number);\n        E.set(key(u, v), w);\n    }\n    let a = floyd_warshall_memopt(E, N);\n    // let b = floyd_warshall(E, N);\n    // for (let i = 1; i <= N; ++i)\n    //     for (let j = 1; j <= N; ++j)\n    //         assert(a[i][j] == b[i][j]);\n    let cycle = false;\n    for (let i = 1; i <= N; ++i)\n        if (a[i][i] < 0)\n            cycle = true;\n    if (cycle) {\n        console.log(`${filename}: contains a negative cycle`);\n        return;\n    }\n    var best = Infinity;\n    for (row of a)\n        best = Math.min(best, ...row);\n    console.log(`${filename}: ${best}`);\n};\n\nrun('problem18.8test1.txt');  // problem18.8test1.txt: -2\nrun('problem18.8test2.txt');  // problem18.8test2.txt: contains a negative cycle\nrun('problem18.8file1.txt');  // problem18.8file1.txt: contains a negative cycle\nrun('problem18.8file2.txt');  // problem18.8file2.txt: contains a negative cycle\nrun('problem18.8file3.txt');  // problem18.8file3.txt: -19\n// run('problem18.8file4.txt');"
  },
  {
    "path": "floyd_warshall/main.kt",
    "content": "/*\n * Programming Problem 18.8: All-Pairs Shortest Paths\n *\n * In this problem, each file describes a directed graph. The first line of the file indicates the number\n * of vertices and edges, respectively. Each subsequent line describes an edge (the first two numbers are its tail\n * and head, respectively) and its length (the third number). NOTE: edge lengths might be negative, and the graphs\n * may or may not be negative cycles.\n *\n * Test cases: (contributed by Matt Davis) What is the shortest shortest path in the graphs described in this file\n * and in this file? (I.e., the minimum, over choices of an origin s and a destination t, of a shortest s-t path in the graph.)\n * (If the graph has a negative cycle, your algorithm should detect that fact.) (Answer: -2 and \"contains a negative cycle,\" respectively.)\n *\n * Challenge data set: Repeat the previous problem for the graphs described in the following files: graph #1, graph #2, graph #3, and graph #4.\n */\n\nimport java.io.File\n\nvar key = { i: Int, j: Int -> \"$i,$j\" }\nvar INF = (1e9 + 7).toInt()\n\nfun floyd_warshall(E: MutableMap<String, Int>, N: Int): Array<IntArray> {\n    var dp = Array(N + 1) { Array(N + 1) { IntArray(N + 1) { INF } } }\n    for (i in 0..N)\n        for (j in 0..N)\n            if (i == j)\n                dp[0][i][j] = 0\n            else\n            if (E.contains(key(i, j)))\n                dp[0][i][j] = E[key(i, j)]!!\n    for (k in 1..N)\n        for (i in 1..N)\n            for (j in 1..N)\n                dp[k][i][j] = Math.min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j])\n    return dp[N]\n}\n\nfun floyd_warshall_memopt(E: MutableMap<String, Int>, N: Int): Array<IntArray> {\n    var pre = Array(N + 1) { IntArray(N + 1) { INF } }\n    for (i in 0..N)\n        for (j in 0..N)\n            if (i == j)\n                pre[i][j] = 0\n            else\n            if (E.contains(key(i, j)))\n                pre[i][j] = E[key(i, j)]!!\n    for (k in 1..N) {\n        var cur = Array(N + 1) { IntArray(N + 1) { INF } }\n        for (i in 1..N)\n            for (j in 1..N)\n                cur[i][j] = Math.min(pre[i][j], pre[i][k] + pre[k][j])\n        pre = cur.also{ cur = pre }\n    }\n    return pre\n}\n\nfun run(filename: String) {\n    var N = 0\n    var E = mutableMapOf<String, Int>()\n    var first = true\n    File(filename).forEachLine {\n        if (!first) {\n            var (u, v, w) = it.trim().split(\" \").map{ it.toInt() }\n            E[key(u, v)] = w\n        } else {\n            N = it.trim().split(\" \").map{ it.toInt() }[0]\n            first = false\n        }\n    }\n    var a = floyd_warshall_memopt(E, N)\n    // var b = floyd_warshall(E, N)\n    // for (i in 1..N)\n    //     for (j in 1..N)\n    //         assert(a[i][j] == b[i][j])  // 💩 sanity check\n    var cycle = false\n    for (i in 1..N)\n        if (a[i][i] < 0)\n            cycle = true\n    if (cycle) {\n        println(\"$filename: contains a negative cycle\")\n        return\n    }\n    var best = INF\n    for (i in 1..N)\n        for (j in 1..N)\n            best = Math.min(best, a[i][j])\n    println(\"$filename: $best\")\n}\n\nfun main() {\n    run(\"problem18.8test1.txt\");  // problem18.8test1.txt: -2\n    run(\"problem18.8test2.txt\");  // problem18.8test2.txt: contains a negative cycle\n    run(\"problem18.8file1.txt\");  // problem18.8file1.txt: contains a negative cycle\n    run(\"problem18.8file2.txt\");  // problem18.8file2.txt: contains a negative cycle\n    run(\"problem18.8file3.txt\");  // problem18.8file3.txt: -19\n    // run(\"problem18.8file4.txt\");\n}"
  },
  {
    "path": "floyd_warshall/main.py",
    "content": "#\n# Programming Problem 18.8: All-Pairs Shortest Paths\n#\n# In this problem, each file describes a directed graph. The first line of the file indicates the number\n# of vertices and edges, respectively. Each subsequent line describes an edge (the first two numbers are its tail\n# and head, respectively) and its length (the third number). NOTE: edge lengths might be negative, and the graphs\n# may or may not be negative cycles.\n#\n# Test cases: (contributed by Matt Davis) What is the shortest shortest path in the graphs described in this file\n# and in this file? (I.e., the minimum, over choices of an origin s and a destination t, of a shortest s-t path in the graph.)\n# (If the graph has a negative cycle, your algorithm should detect that fact.) (Answer: -2 and \"contains a negative cycle,\" respectively.)\n#\n# Challenge data set: Repeat the previous problem for the graphs described in the following files: graph #1, graph #2, graph #3, and graph #4.\n#\n\nkey = lambda i, j: f'{i},{j}'\n\ndef floyd_warshall(E, N):\n    dp = [[[float('inf')] * (N + 1) for _ in range(N + 1)] for _ in range(N + 1)]\n    for i in range(1, N + 1):\n        for j in range(1, N + 1):\n            if i == j:\n                dp[0][i][j] = 0\n            elif key(i, j) in E:\n                dp[0][i][j] = E[key(i, j)]\n    for k in range(1, N + 1):\n        for i in range(1, N + 1):\n            for j in range(1, N + 1):\n                dp[k][i][j] = min(dp[k - 1][i][j], dp[k - 1][i][k] + dp[k - 1][k][j])\n    return dp[N]\n\ndef floyd_warshall_memopt(E, N):\n    pre = [[float('inf')] * (N + 1) for _ in range(N + 1)]\n    for i in range(1, N + 1):\n        for j in range(1, N + 1):\n            if i == j:\n                pre[i][j] = 0\n            elif key(i, j) in E:\n                pre[i][j] = E[key(i, j)]\n    for k in range(1, N + 1):\n        cur = [[float('inf')] * (N + 1) for _ in range(N + 1)]\n        for i in range(1, N + 1):\n            for j in range(1, N + 1):\n                cur[i][j] = min(pre[i][j], pre[i][k] + pre[k][j])\n        pre, cur = cur, pre\n    return pre\n\ndef run(filename):\n    E = {}\n    N = 0\n    first = True\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            if not first:\n                u, v, w = [int(x) for x in line.strip().split(' ')]\n                E[key(u, v)] = w\n            else:\n                N = [int(x) for x in line.strip().split(' ')][0]\n                first = False\n    a = floyd_warshall_memopt(E, N)\n    # b = floyd_warshall(E, N)\n    # for i in range(1, N + 1):\n    #     for j in range(1, N + 1):\n    #         assert(a[i][j] == b[i][j])  # 💩 sanity check\n    cycle = False\n    for i in range(1, N + 1):\n        if a[i][i] < 0:\n            cycle = True\n    if cycle:\n        print(f'{filename}: contains a negative cycle')\n        return\n    best = float('inf')\n    for row in a:\n        best = min(best, *row)\n    print(f'{filename}: {best}')\n\nrun('problem18.8test1.txt')  # problem18.8test1.txt: -2\nrun('problem18.8test2.txt')  # problem18.8test2.txt: contains a negative cycle\nrun('problem18.8file1.txt')  # problem18.8file1.txt: contains a negative cycle\nrun('problem18.8file2.txt')  # problem18.8file2.txt: contains a negative cycle\nrun('problem18.8file3.txt')  # problem18.8file3.txt: -19\n# run('problem18.8file4.txt')"
  },
  {
    "path": "floyd_warshall/package.json",
    "content": "{\n  \"name\": \"floyd_warshall\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"clayton wong\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"assert\": \"^2.0.0\",\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "floyd_warshall/problem18.8file1.txt",
    "content": "1000 47978\n1 14 6\n1 25 47\n1 70 22\n1 82 31\n1 98 17\n1 134 39\n1 146 7\n1 189 44\n1 192 20\n1 261 38\n1 283 30\n1 340 21\n1 380 37\n1 381 24\n1 403 3\n1 422 40\n1 423 40\n1 425 13\n1 518 23\n1 520 38\n1 547 5\n1 558 24\n1 578 32\n1 601 42\n1 604 37\n1 640 38\n1 648 18\n1 699 48\n1 707 10\n1 712 9\n1 723 47\n1 729 26\n1 730 18\n1 769 49\n1 793 32\n1 830 15\n1 841 50\n1 852 16\n1 874 39\n1 880 9\n1 890 6\n1 897 23\n1 917 19\n1 949 22\n1 988 43\n1 993 48\n2 36 29\n2 38 -2\n2 100 37\n2 106 -2\n2 107 12\n2 109 18\n2 112 28\n2 117 50\n2 189 43\n2 190 45\n2 204 27\n2 240 5\n2 252 4\n2 263 32\n2 313 26\n2 345 14\n2 370 9\n2 376 35\n2 421 40\n2 424 50\n2 448 10\n2 511 9\n2 518 41\n2 519 18\n2 532 33\n2 543 10\n2 550 27\n2 553 7\n2 565 39\n2 578 17\n2 609 50\n2 614 11\n2 673 13\n2 675 30\n2 702 4\n2 706 44\n2 732 49\n2 739 14\n2 780 27\n2 791 36\n2 795 46\n2 804 39\n2 824 8\n2 844 34\n2 869 39\n2 883 3\n2 896 40\n2 908 -1\n2 930 37\n2 938 37\n2 941 14\n2 955 3\n2 961 29\n2 972 10\n2 988 43\n3 4 2\n3 28 28\n3 70 -2\n3 125 48\n3 141 28\n3 149 2\n3 184 41\n3 189 7\n3 217 15\n3 229 27\n3 231 17\n3 248 45\n3 256 3\n3 292 10\n3 309 6\n3 341 24\n3 346 -1\n3 391 4\n3 405 14\n3 418 30\n3 433 20\n3 451 4\n3 545 26\n3 547 39\n3 549 1\n3 585 50\n3 586 29\n3 593 31\n3 605 25\n3 613 0\n3 616 39\n3 623 31\n3 661 0\n3 713 34\n3 739 30\n3 837 24\n3 841 40\n3 844 0\n3 848 41\n3 851 36\n3 867 28\n3 888 42\n3 892 15\n3 893 25\n3 898 19\n3 900 14\n3 904 37\n3 912 27\n3 915 21\n3 921 49\n3 940 35\n3 948 5\n3 984 -2\n3 985 31\n4 18 41\n4 28 38\n4 38 37\n4 45 8\n4 48 39\n4 50 17\n4 61 1\n4 63 14\n4 70 0\n4 90 2\n4 98 17\n4 108 45\n4 117 37\n4 216 10\n4 219 45\n4 227 6\n4 247 40\n4 290 46\n4 309 8\n4 317 20\n4 342 35\n4 384 6\n4 386 19\n4 391 36\n4 393 31\n4 454 31\n4 498 47\n4 500 23\n4 519 39\n4 562 50\n4 571 15\n4 579 43\n4 584 6\n4 619 49\n4 658 35\n4 662 6\n4 680 -1\n4 694 43\n4 730 48\n4 758 5\n4 824 14\n4 834 16\n4 856 20\n4 865 9\n4 871 45\n4 925 17\n4 972 22\n4 987 45\n4 994 43\n4 1000 36\n5 6 5\n5 18 16\n5 43 22\n5 45 29\n5 77 20\n5 88 19\n5 111 6\n5 136 1\n5 151 48\n5 159 9\n5 164 37\n5 182 38\n5 201 36\n5 213 24\n5 289 39\n5 315 10\n5 319 7\n5 333 20\n5 347 14\n5 385 39\n5 389 28\n5 432 42\n5 453 35\n5 511 29\n5 512 39\n5 525 5\n5 551 29\n5 557 27\n5 581 23\n5 586 20\n5 587 8\n5 620 45\n5 682 25\n5 708 25\n5 717 20\n5 722 16\n5 725 26\n5 740 17\n5 745 21\n5 808 46\n5 815 25\n5 835 13\n5 848 27\n5 856 24\n5 885 16\n5 893 30\n5 894 26\n5 901 50\n5 919 41\n5 928 7\n5 938 11\n5 954 27\n5 955 43\n5 962 42\n5 964 15\n5 966 45\n5 967 15\n5 978 12\n6 7 28\n6 13 1\n6 43 20\n6 45 40\n6 52 13\n6 65 10\n6 74 41\n6 91 30\n6 101 41\n6 104 38\n6 119 22\n6 133 5\n6 175 40\n6 189 14\n6 192 38\n6 222 29\n6 228 46\n6 261 32\n6 291 25\n6 307 9\n6 309 49\n6 312 17\n6 313 46\n6 407 12\n6 450 -1\n6 475 5\n6 492 44\n6 523 38\n6 562 44\n6 582 42\n6 594 28\n6 602 30\n6 632 26\n6 638 35\n6 665 24\n6 673 44\n6 695 13\n6 697 32\n6 738 14\n6 739 5\n6 763 9\n6 782 19\n6 837 3\n6 865 38\n6 866 8\n6 898 37\n6 919 1\n6 937 26\n6 946 15\n6 951 15\n6 959 5\n6 971 0\n6 972 7\n6 993 -1\n7 3 28\n7 61 -1\n7 70 36\n7 81 38\n7 103 36\n7 117 31\n7 140 24\n7 162 49\n7 173 29\n7 196 12\n7 207 13\n7 241 21\n7 277 38\n7 280 7\n7 286 22\n7 298 4\n7 320 36\n7 338 20\n7 339 21\n7 341 33\n7 363 18\n7 393 -1\n7 438 4\n7 455 4\n7 462 15\n7 486 20\n7 557 34\n7 569 38\n7 593 8\n7 595 43\n7 603 23\n7 616 14\n7 630 45\n7 646 20\n7 652 5\n7 684 24\n7 714 42\n7 731 35\n7 742 3\n7 756 1\n7 770 50\n7 774 26\n7 797 43\n7 801 6\n7 817 46\n7 840 2\n7 852 44\n7 877 44\n7 889 25\n7 912 12\n7 969 42\n8 7 49\n8 15 1\n8 22 29\n8 23 34\n8 50 49\n8 67 28\n8 110 -2\n8 154 26\n8 194 17\n8 198 7\n8 224 27\n8 246 3\n8 280 5\n8 290 25\n8 317 21\n8 319 49\n8 350 20\n8 438 28\n8 464 46\n8 504 18\n8 524 36\n8 544 32\n8 589 17\n8 590 47\n8 629 4\n8 651 40\n8 658 34\n8 674 1\n8 679 49\n8 706 16\n8 747 17\n8 765 8\n8 777 45\n8 789 37\n8 801 13\n8 803 21\n8 813 43\n8 814 36\n8 843 34\n8 858 48\n8 859 43\n8 884 30\n8 887 15\n8 894 -1\n8 909 12\n8 939 14\n8 969 13\n8 971 34\n8 983 4\n9 62 47\n9 68 50\n9 104 44\n9 110 37\n9 127 12\n9 160 20\n9 172 12\n9 204 39\n9 207 41\n9 213 37\n9 250 13\n9 255 11\n9 258 29\n9 271 48\n9 273 27\n9 302 34\n9 304 26\n9 308 22\n9 320 33\n9 370 33\n9 404 11\n9 416 23\n9 458 38\n9 495 11\n9 563 14\n9 568 40\n9 587 36\n9 609 26\n9 610 13\n9 623 22\n9 624 42\n9 670 31\n9 698 14\n9 705 38\n9 735 16\n9 739 13\n9 778 1\n9 781 7\n9 805 47\n9 806 20\n9 823 50\n9 831 1\n9 839 48\n9 926 46\n9 945 25\n9 955 47\n10 21 36\n10 37 13\n10 54 18\n10 104 -2\n10 130 46\n10 137 36\n10 143 46\n10 146 35\n10 213 28\n10 248 39\n10 256 22\n10 262 41\n10 264 23\n10 308 47\n10 324 1\n10 326 25\n10 359 15\n10 363 -1\n10 388 39\n10 428 47\n10 503 22\n10 508 12\n10 512 17\n10 521 8\n10 542 30\n10 551 18\n10 563 38\n10 571 9\n10 579 13\n10 600 32\n10 601 26\n10 619 40\n10 642 26\n10 647 46\n10 670 6\n10 699 33\n10 753 14\n10 756 38\n10 875 44\n10 894 21\n10 913 3\n10 921 42\n10 923 13\n10 932 25\n10 964 9\n11 121 21\n11 129 44\n11 175 41\n11 229 20\n11 240 18\n11 245 37\n11 315 13\n11 377 5\n11 385 10\n11 427 25\n11 493 7\n11 515 37\n11 521 26\n11 546 9\n11 551 37\n11 553 6\n11 613 20\n11 627 41\n11 652 40\n11 672 37\n11 683 23\n11 741 7\n11 795 28\n11 803 38\n11 816 5\n11 823 10\n11 835 46\n11 869 4\n11 911 10\n11 912 23\n11 941 0\n11 974 1\n11 976 46\n11 984 48\n11 989 49\n11 999 36\n12 1 30\n12 30 21\n12 32 0\n12 39 -2\n12 61 46\n12 62 24\n12 64 0\n12 66 27\n12 94 25\n12 97 44\n12 145 29\n12 193 33\n12 210 42\n12 243 44\n12 256 33\n12 304 42\n12 319 20\n12 345 21\n12 401 1\n12 451 33\n12 452 32\n12 493 23\n12 520 1\n12 531 16\n12 572 7\n12 576 21\n12 580 6\n12 657 45\n12 687 3\n12 689 20\n12 769 -2\n12 777 34\n12 791 11\n12 801 13\n12 804 36\n12 816 19\n12 825 3\n12 844 31\n12 850 36\n12 871 47\n12 878 18\n12 899 17\n12 968 8\n12 969 44\n12 996 39\n13 15 36\n13 37 20\n13 109 21\n13 115 1\n13 127 16\n13 129 19\n13 140 27\n13 170 1\n13 180 19\n13 188 17\n13 203 14\n13 239 29\n13 247 29\n13 268 48\n13 339 34\n13 373 39\n13 376 6\n13 442 44\n13 482 4\n13 484 4\n13 510 42\n13 517 16\n13 520 35\n13 558 16\n13 562 13\n13 591 42\n13 595 22\n13 615 8\n13 634 28\n13 671 22\n13 728 37\n13 738 39\n13 772 4\n13 786 39\n13 798 50\n13 837 6\n13 882 39\n13 892 31\n13 904 41\n13 912 29\n13 913 44\n13 921 23\n13 937 36\n13 940 11\n13 984 14\n13 990 41\n14 15 49\n14 27 42\n14 49 -2\n14 52 3\n14 72 2\n14 91 3\n14 121 39\n14 139 49\n14 156 9\n14 191 27\n14 201 10\n14 215 25\n14 220 18\n14 221 39\n14 251 25\n14 261 17\n14 262 44\n14 268 47\n14 281 23\n14 347 9\n14 447 20\n14 473 13\n14 494 30\n14 537 50\n14 560 19\n14 582 40\n14 583 43\n14 621 25\n14 689 0\n14 732 11\n14 772 15\n14 783 5\n14 789 37\n14 843 28\n14 853 28\n14 854 3\n14 918 44\n14 949 38\n14 972 39\n15 30 38\n15 49 17\n15 81 29\n15 125 25\n15 142 21\n15 158 44\n15 171 32\n15 173 4\n15 194 40\n15 199 33\n15 210 11\n15 227 38\n15 228 15\n15 266 20\n15 279 35\n15 304 7\n15 310 15\n15 341 10\n15 348 9\n15 362 16\n15 424 35\n15 467 41\n15 520 35\n15 532 5\n15 582 47\n15 614 33\n15 622 34\n15 645 44\n15 646 35\n15 654 43\n15 685 6\n15 691 1\n15 711 33\n15 733 5\n15 774 1\n15 821 36\n15 844 39\n15 856 25\n15 983 11\n16 2 42\n16 21 21\n16 41 11\n16 76 -1\n16 83 4\n16 112 49\n16 124 1\n16 148 34\n16 150 16\n16 186 17\n16 194 46\n16 222 37\n16 247 24\n16 251 48\n16 265 38\n16 281 29\n16 286 36\n16 300 38\n16 337 24\n16 365 33\n16 367 12\n16 369 4\n16 382 50\n16 387 9\n16 393 14\n16 396 27\n16 433 7\n16 438 1\n16 492 32\n16 516 4\n16 522 35\n16 537 0\n16 551 37\n16 557 4\n16 558 34\n16 609 14\n16 645 9\n16 655 24\n16 657 30\n16 673 45\n16 703 35\n16 707 23\n16 708 39\n16 730 36\n16 769 4\n16 801 47\n16 827 8\n16 853 40\n16 867 28\n16 888 48\n16 930 26\n16 933 0\n16 964 32\n16 973 18\n17 7 18\n17 26 48\n17 88 50\n17 110 27\n17 166 22\n17 175 39\n17 184 20\n17 190 31\n17 197 26\n17 203 9\n17 219 -2\n17 263 0\n17 269 10\n17 293 9\n17 297 11\n17 309 50\n17 317 21\n17 354 33\n17 409 13\n17 437 8\n17 447 26\n17 469 4\n17 519 8\n17 554 -2\n17 559 11\n17 565 33\n17 588 21\n17 593 38\n17 595 0\n17 651 16\n17 668 5\n17 702 9\n17 706 27\n17 716 21\n17 719 24\n17 730 11\n17 777 15\n17 778 37\n17 783 1\n17 788 0\n17 817 6\n17 820 33\n17 877 7\n17 878 12\n17 882 46\n17 899 4\n17 905 38\n17 987 14\n17 992 17\n18 5 -1\n18 20 23\n18 61 44\n18 75 0\n18 100 35\n18 113 0\n18 153 13\n18 167 7\n18 170 29\n18 172 6\n18 175 3\n18 192 15\n18 227 27\n18 282 43\n18 331 40\n18 340 50\n18 353 32\n18 378 22\n18 478 6\n18 511 26\n18 537 0\n18 540 42\n18 554 41\n18 583 29\n18 681 30\n18 709 11\n18 753 26\n18 844 20\n18 880 46\n18 951 1\n18 964 42\n18 997 49\n19 5 4\n19 13 48\n19 40 18\n19 75 8\n19 78 29\n19 87 34\n19 92 8\n19 101 29\n19 103 -1\n19 104 46\n19 130 2\n19 161 33\n19 216 34\n19 278 11\n19 291 25\n19 347 39\n19 399 2\n19 473 25\n19 477 27\n19 513 5\n19 530 46\n19 539 -2\n19 574 45\n19 609 33\n19 677 44\n19 680 49\n19 710 23\n19 716 50\n19 720 21\n19 722 42\n19 755 13\n19 758 42\n19 771 50\n19 803 16\n19 811 46\n19 826 29\n19 915 28\n19 945 20\n19 948 20\n19 949 8\n19 996 12\n20 30 19\n20 100 40\n20 159 11\n20 166 49\n20 213 49\n20 262 40\n20 326 44\n20 336 47\n20 343 22\n20 436 36\n20 463 26\n20 510 24\n20 531 37\n20 539 15\n20 561 37\n20 585 17\n20 606 37\n20 634 31\n20 642 17\n20 647 39\n20 667 3\n20 683 32\n20 710 27\n20 731 31\n20 743 41\n20 744 33\n20 752 24\n20 760 15\n20 777 1\n20 792 4\n20 808 13\n20 813 6\n20 853 23\n20 905 23\n20 918 29\n20 947 39\n21 15 41\n21 19 3\n21 80 48\n21 92 48\n21 116 49\n21 170 39\n21 186 27\n21 215 0\n21 229 48\n21 241 14\n21 260 33\n21 278 48\n21 291 5\n21 396 45\n21 422 1\n21 467 46\n21 472 25\n21 499 13\n21 514 11\n21 537 37\n21 551 45\n21 555 48\n21 573 10\n21 599 30\n21 620 25\n21 631 7\n21 681 34\n21 699 4\n21 736 -1\n21 739 39\n21 746 -1\n21 752 13\n21 822 43\n21 828 36\n21 855 15\n21 880 20\n21 885 39\n21 917 41\n21 931 44\n21 934 33\n21 944 3\n21 947 13\n22 9 1\n22 46 20\n22 72 27\n22 105 47\n22 117 18\n22 142 13\n22 144 2\n22 271 9\n22 307 26\n22 347 21\n22 386 31\n22 393 0\n22 395 24\n22 411 8\n22 416 22\n22 449 45\n22 452 40\n22 473 15\n22 517 12\n22 525 29\n22 529 48\n22 536 14\n22 559 2\n22 625 35\n22 695 15\n22 711 10\n22 777 25\n22 779 3\n22 787 37\n22 800 48\n22 833 24\n22 868 48\n22 899 33\n22 958 31\n22 962 2\n22 976 34\n22 983 42\n22 990 6\n23 8 5\n23 35 4\n23 45 0\n23 58 17\n23 62 5\n23 93 35\n23 112 47\n23 143 7\n23 149 7\n23 154 30\n23 155 40\n23 166 15\n23 168 35\n23 182 39\n23 216 47\n23 260 31\n23 311 45\n23 323 6\n23 355 3\n23 382 44\n23 385 32\n23 388 39\n23 414 46\n23 427 21\n23 443 1\n23 451 42\n23 455 10\n23 473 36\n23 489 39\n23 493 26\n23 512 22\n23 521 29\n23 531 28\n23 551 37\n23 570 5\n23 589 45\n23 602 31\n23 633 26\n23 675 40\n23 696 16\n23 702 28\n23 772 4\n23 782 14\n23 789 50\n23 808 49\n23 837 3\n23 848 11\n23 897 47\n23 899 26\n23 910 35\n23 913 16\n23 917 17\n23 943 19\n23 949 37\n23 959 4\n23 965 45\n23 978 45\n23 991 9\n24 5 18\n24 7 22\n24 17 42\n24 37 31\n24 99 35\n24 101 -1\n24 115 16\n24 153 29\n24 167 23\n24 168 8\n24 213 44\n24 216 28\n24 217 23\n24 291 19\n24 297 8\n24 306 19\n24 313 12\n24 371 46\n24 388 41\n24 431 0\n24 433 40\n24 454 33\n24 473 47\n24 496 48\n24 525 -1\n24 545 21\n24 562 33\n24 574 13\n24 632 5\n24 657 34\n24 671 3\n24 706 -2\n24 719 50\n24 730 46\n24 759 47\n24 765 27\n24 776 11\n24 789 37\n24 799 25\n24 801 25\n24 813 1\n24 819 21\n24 845 26\n24 846 22\n24 912 25\n24 923 16\n24 929 39\n24 932 48\n24 935 33\n24 942 45\n25 28 9\n25 29 -1\n25 38 23\n25 49 19\n25 86 47\n25 91 20\n25 106 49\n25 125 10\n25 143 28\n25 172 13\n25 189 36\n25 231 44\n25 247 24\n25 255 47\n25 259 39\n25 289 14\n25 297 -2\n25 300 43\n25 301 49\n25 326 33\n25 353 26\n25 386 19\n25 425 29\n25 434 28\n25 475 4\n25 487 29\n25 507 12\n25 516 33\n25 519 14\n25 529 19\n25 532 45\n25 541 42\n25 560 39\n25 612 22\n25 627 29\n25 646 41\n25 660 6\n25 666 39\n25 706 45\n25 738 25\n25 754 1\n25 794 17\n25 877 34\n25 889 35\n25 892 41\n25 896 27\n25 923 16\n25 927 13\n25 929 -1\n25 951 33\n26 4 15\n26 11 21\n26 28 50\n26 52 30\n26 99 35\n26 151 1\n26 163 40\n26 189 37\n26 205 21\n26 209 19\n26 255 14\n26 317 24\n26 355 28\n26 360 15\n26 362 35\n26 401 30\n26 402 50\n26 455 47\n26 458 43\n26 465 28\n26 484 12\n26 537 16\n26 540 48\n26 550 48\n26 556 23\n26 561 37\n26 572 20\n26 595 50\n26 603 7\n26 615 10\n26 638 49\n26 649 14\n26 679 10\n26 687 37\n26 711 38\n26 712 5\n26 758 34\n26 760 18\n26 788 5\n26 796 12\n26 816 21\n26 818 24\n26 840 17\n26 871 8\n26 879 1\n26 887 34\n26 889 15\n26 916 8\n26 955 43\n26 969 49\n26 979 16\n26 987 31\n26 999 20\n27 29 2\n27 55 25\n27 56 19\n27 67 40\n27 113 23\n27 115 8\n27 123 1\n27 150 20\n27 164 44\n27 186 32\n27 204 49\n27 221 36\n27 229 30\n27 232 37\n27 264 44\n27 278 40\n27 292 2\n27 308 27\n27 338 15\n27 354 11\n27 366 10\n27 432 44\n27 462 26\n27 484 36\n27 509 8\n27 557 38\n27 594 16\n27 607 19\n27 646 17\n27 681 50\n27 695 48\n27 715 31\n27 723 43\n27 767 1\n27 777 20\n27 805 50\n27 846 13\n27 885 -2\n27 892 37\n27 908 42\n27 912 5\n27 920 22\n27 922 1\n27 943 33\n27 953 46\n27 955 24\n28 14 5\n28 27 6\n28 78 39\n28 87 13\n28 110 -2\n28 126 27\n28 145 31\n28 155 20\n28 190 43\n28 209 22\n28 214 50\n28 227 21\n28 250 20\n28 284 3\n28 391 10\n28 415 37\n28 457 45\n28 492 43\n28 514 30\n28 515 48\n28 518 8\n28 521 -1\n28 540 43\n28 546 34\n28 559 9\n28 560 47\n28 591 23\n28 627 1\n28 650 40\n28 653 45\n28 673 42\n28 674 25\n28 686 21\n28 728 2\n28 762 50\n28 770 31\n28 808 32\n28 809 37\n28 810 47\n28 831 32\n28 890 27\n28 898 49\n28 901 38\n28 905 24\n28 938 39\n28 950 34\n28 952 29\n28 972 34\n28 979 50\n28 983 21\n29 40 22\n29 53 29\n29 94 48\n29 97 10\n29 103 25\n29 106 34\n29 108 9\n29 122 16\n29 206 26\n29 312 34\n29 314 -2\n29 316 21\n29 364 27\n29 366 49\n29 374 2\n29 438 48\n29 454 37\n29 459 26\n29 468 11\n29 479 11\n29 505 25\n29 525 47\n29 552 3\n29 562 25\n29 570 11\n29 577 28\n29 590 35\n29 648 47\n29 653 38\n29 672 22\n29 681 40\n29 682 27\n29 683 35\n29 708 45\n29 726 35\n29 734 15\n29 735 29\n29 747 29\n29 753 30\n29 777 -2\n29 784 6\n29 788 41\n29 789 36\n29 804 32\n29 811 45\n29 828 47\n29 836 0\n29 862 37\n29 910 -2\n29 929 5\n29 946 41\n29 960 14\n29 985 12\n30 1 50\n30 4 33\n30 15 39\n30 16 40\n30 19 13\n30 103 33\n30 132 -2\n30 135 -2\n30 142 14\n30 148 20\n30 166 43\n30 192 39\n30 227 11\n30 231 22\n30 246 40\n30 251 11\n30 286 5\n30 344 13\n30 345 34\n30 387 27\n30 400 29\n30 406 45\n30 408 8\n30 452 38\n30 457 10\n30 460 45\n30 468 33\n30 475 47\n30 495 0\n30 523 33\n30 578 48\n30 595 2\n30 600 13\n30 649 37\n30 672 6\n30 744 19\n30 759 27\n30 772 12\n30 839 -2\n30 859 5\n30 880 40\n30 889 40\n30 937 13\n30 938 19\n30 946 33\n30 969 46\n30 973 38\n30 974 32\n30 978 35\n30 985 39\n30 996 18\n31 1 43\n31 58 12\n31 91 35\n31 110 6\n31 164 20\n31 187 41\n31 189 36\n31 197 45\n31 205 31\n31 215 31\n31 216 35\n31 249 14\n31 323 21\n31 381 30\n31 382 37\n31 423 0\n31 439 34\n31 473 13\n31 476 5\n31 520 50\n31 565 0\n31 566 32\n31 600 43\n31 607 50\n31 614 -1\n31 615 41\n31 627 44\n31 689 24\n31 691 25\n31 700 17\n31 720 31\n31 753 46\n31 780 48\n31 829 12\n31 840 40\n31 857 37\n31 878 50\n31 885 5\n31 890 25\n31 911 35\n31 957 13\n31 977 32\n31 991 32\n32 2 18\n32 21 50\n32 36 23\n32 39 23\n32 63 37\n32 117 43\n32 118 2\n32 133 12\n32 140 49\n32 160 49\n32 174 12\n32 196 33\n32 205 -2\n32 212 36\n32 254 10\n32 287 22\n32 292 37\n32 306 45\n32 312 37\n32 320 1\n32 338 34\n32 350 19\n32 395 18\n32 450 4\n32 473 45\n32 477 40\n32 507 37\n32 555 9\n32 560 33\n32 572 19\n32 604 15\n32 643 35\n32 646 40\n32 666 14\n32 685 32\n32 703 38\n32 728 14\n32 738 42\n32 755 22\n32 764 47\n32 765 25\n32 784 11\n32 787 22\n32 818 50\n32 825 29\n32 842 12\n32 898 11\n32 934 34\n32 939 4\n32 983 49\n32 995 46\n33 2 11\n33 66 46\n33 72 33\n33 94 4\n33 117 13\n33 118 36\n33 142 24\n33 166 8\n33 168 43\n33 190 1\n33 219 24\n33 283 3\n33 323 9\n33 331 40\n33 332 3\n33 342 14\n33 369 17\n33 392 13\n33 401 42\n33 421 28\n33 449 25\n33 455 35\n33 478 22\n33 539 36\n33 598 41\n33 604 36\n33 619 -2\n33 647 43\n33 665 40\n33 679 18\n33 682 21\n33 729 42\n33 743 2\n33 766 48\n33 775 2\n33 792 40\n33 818 -2\n33 826 28\n33 846 18\n33 851 50\n33 854 40\n33 855 10\n33 874 12\n33 881 7\n33 890 21\n33 893 43\n33 899 27\n33 917 39\n33 935 16\n33 936 18\n33 940 50\n33 951 23\n33 954 11\n33 993 15\n34 26 6\n34 29 14\n34 100 14\n34 125 25\n34 134 19\n34 157 44\n34 190 21\n34 191 37\n34 202 43\n34 232 23\n34 238 18\n34 250 32\n34 261 2\n34 293 4\n34 343 27\n34 383 32\n34 421 43\n34 425 10\n34 441 0\n34 470 24\n34 529 9\n34 555 14\n34 563 19\n34 567 -2\n34 577 21\n34 592 37\n34 594 24\n34 596 41\n34 625 21\n34 676 18\n34 740 0\n34 757 27\n34 776 25\n34 791 20\n34 806 21\n34 855 5\n34 872 27\n34 879 50\n34 880 17\n34 894 -2\n34 918 46\n34 950 -1\n34 990 7\n35 21 7\n35 76 41\n35 103 8\n35 106 25\n35 113 41\n35 130 20\n35 136 42\n35 187 28\n35 222 45\n35 231 39\n35 241 32\n35 259 25\n35 271 37\n35 278 26\n35 281 41\n35 295 8\n35 339 37\n35 342 10\n35 347 18\n35 348 1\n35 381 22\n35 414 33\n35 419 10\n35 443 34\n35 483 28\n35 501 19\n35 556 29\n35 557 7\n35 572 35\n35 607 48\n35 616 38\n35 620 30\n35 643 24\n35 646 40\n35 663 42\n35 685 8\n35 700 15\n35 722 32\n35 734 13\n35 746 49\n35 747 17\n35 753 18\n35 803 14\n35 804 30\n35 812 40\n35 845 14\n35 875 24\n35 879 11\n35 885 26\n35 908 46\n35 968 16\n36 4 0\n36 26 43\n36 28 29\n36 49 24\n36 58 40\n36 109 13\n36 170 32\n36 182 3\n36 190 27\n36 192 49\n36 199 21\n36 210 30\n36 220 50\n36 229 8\n36 240 16\n36 253 29\n36 266 28\n36 270 35\n36 286 46\n36 299 -2\n36 301 22\n36 306 20\n36 310 41\n36 316 5\n36 319 29\n36 347 42\n36 361 47\n36 371 36\n36 376 18\n36 420 35\n36 451 16\n36 462 17\n36 477 17\n36 492 26\n36 495 37\n36 509 2\n36 514 29\n36 530 4\n36 628 11\n36 649 17\n36 666 33\n36 682 30\n36 683 -1\n36 700 3\n36 707 0\n36 722 33\n36 735 38\n36 740 37\n36 767 39\n36 777 -2\n36 784 23\n36 855 44\n36 904 -2\n36 939 8\n36 978 11\n36 992 11\n37 10 9\n37 28 39\n37 39 47\n37 63 20\n37 67 7\n37 68 45\n37 69 -1\n37 135 28\n37 272 49\n37 296 12\n37 312 42\n37 354 47\n37 377 40\n37 439 32\n37 458 20\n37 499 4\n37 505 44\n37 515 35\n37 523 6\n37 525 44\n37 535 46\n37 547 34\n37 568 42\n37 574 10\n37 609 39\n37 628 9\n37 644 18\n37 665 21\n37 687 16\n37 698 38\n37 714 14\n37 715 17\n37 731 30\n37 745 18\n37 768 7\n37 784 16\n37 795 27\n37 797 12\n37 803 44\n37 811 38\n37 831 37\n37 841 1\n37 851 3\n37 853 26\n37 860 46\n37 862 50\n37 886 7\n37 892 50\n37 952 16\n37 958 40\n37 987 36\n38 31 19\n38 49 23\n38 57 48\n38 100 4\n38 118 0\n38 128 7\n38 139 25\n38 166 21\n38 170 16\n38 192 35\n38 200 16\n38 204 33\n38 205 21\n38 207 21\n38 220 44\n38 235 21\n38 272 4\n38 293 1\n38 297 39\n38 306 28\n38 308 15\n38 317 -2\n38 319 9\n38 349 30\n38 354 42\n38 355 3\n38 358 27\n38 362 8\n38 369 40\n38 378 34\n38 404 48\n38 426 27\n38 428 6\n38 439 2\n38 440 4\n38 461 23\n38 489 14\n38 496 29\n38 537 34\n38 575 31\n38 577 14\n38 580 37\n38 600 46\n38 612 6\n38 631 -2\n38 637 8\n38 665 47\n38 669 2\n38 677 42\n38 681 20\n38 718 11\n38 828 17\n38 832 9\n38 834 -1\n38 893 16\n38 896 31\n38 920 45\n38 927 29\n38 933 19\n38 960 31\n38 987 50\n39 18 30\n39 52 17\n39 60 44\n39 65 34\n39 84 34\n39 89 27\n39 96 22\n39 98 6\n39 149 38\n39 178 27\n39 194 43\n39 207 11\n39 227 38\n39 268 29\n39 289 48\n39 303 18\n39 321 21\n39 360 23\n39 379 33\n39 380 35\n39 425 49\n39 465 11\n39 468 36\n39 493 7\n39 596 37\n39 611 29\n39 621 0\n39 633 46\n39 642 49\n39 650 2\n39 654 41\n39 655 35\n39 662 25\n39 676 12\n39 693 37\n39 725 17\n39 745 12\n39 751 22\n39 784 26\n39 788 29\n39 815 6\n39 818 21\n39 832 14\n39 852 13\n39 865 26\n39 878 38\n39 917 35\n39 932 49\n39 935 16\n39 985 42\n39 1000 18\n40 9 -2\n40 38 46\n40 47 35\n40 55 41\n40 56 14\n40 69 14\n40 102 44\n40 118 19\n40 119 -2\n40 143 33\n40 155 47\n40 194 25\n40 227 31\n40 246 49\n40 298 33\n40 300 46\n40 307 9\n40 316 10\n40 336 -2\n40 342 16\n40 382 17\n40 391 15\n40 407 37\n40 453 18\n40 480 40\n40 489 33\n40 519 42\n40 551 25\n40 574 15\n40 621 35\n40 698 39\n40 702 5\n40 710 8\n40 724 5\n40 727 17\n40 813 43\n40 824 41\n40 931 16\n40 956 27\n40 982 23\n40 992 27\n40 996 30\n40 998 40\n41 34 1\n41 103 34\n41 111 36\n41 116 24\n41 124 25\n41 160 39\n41 167 36\n41 200 28\n41 209 16\n41 295 18\n41 329 10\n41 401 25\n41 404 22\n41 427 28\n41 431 13\n41 473 43\n41 487 29\n41 488 39\n41 503 9\n41 515 16\n41 544 16\n41 559 10\n41 628 7\n41 669 18\n41 685 6\n41 702 2\n41 714 26\n41 716 41\n41 728 29\n41 729 27\n41 772 9\n41 778 40\n41 804 45\n41 824 49\n41 838 30\n41 839 3\n41 841 36\n41 851 24\n41 875 32\n41 953 8\n41 970 25\n41 977 48\n41 980 21\n42 13 7\n42 19 6\n42 36 14\n42 46 24\n42 122 47\n42 179 40\n42 203 29\n42 223 20\n42 275 6\n42 282 30\n42 296 21\n42 373 -2\n42 376 18\n42 384 -2\n42 450 33\n42 483 8\n42 486 44\n42 519 34\n42 533 27\n42 615 4\n42 621 29\n42 623 32\n42 657 39\n42 665 1\n42 672 34\n42 682 11\n42 701 13\n42 784 18\n42 818 16\n42 847 24\n42 903 37\n42 924 -1\n42 929 28\n42 974 21\n42 986 16\n42 990 35\n43 32 33\n43 53 26\n43 76 34\n43 91 17\n43 111 49\n43 178 28\n43 202 29\n43 205 24\n43 206 21\n43 221 45\n43 226 45\n43 258 19\n43 259 28\n43 273 10\n43 348 36\n43 358 9\n43 373 20\n43 381 2\n43 404 0\n43 405 13\n43 406 10\n43 438 18\n43 439 33\n43 448 39\n43 516 13\n43 518 47\n43 532 21\n43 553 30\n43 568 34\n43 585 29\n43 640 0\n43 646 47\n43 653 5\n43 671 24\n43 703 4\n43 719 45\n43 728 49\n43 734 49\n43 737 18\n43 742 35\n43 755 15\n43 761 16\n43 803 2\n43 815 19\n43 840 27\n43 903 39\n43 975 11\n43 986 27\n44 61 14\n44 73 15\n44 74 49\n44 76 5\n44 89 41\n44 102 46\n44 103 11\n44 149 28\n44 171 41\n44 181 43\n44 188 34\n44 277 -2\n44 292 19\n44 295 29\n44 296 17\n44 310 35\n44 336 19\n44 345 24\n44 400 16\n44 402 21\n44 431 27\n44 443 13\n44 458 11\n44 462 12\n44 498 23\n44 515 26\n44 534 13\n44 537 11\n44 579 40\n44 581 25\n44 585 40\n44 592 43\n44 605 35\n44 610 12\n44 630 4\n44 639 39\n44 642 15\n44 668 44\n44 672 40\n44 687 31\n44 701 33\n44 702 43\n44 706 31\n44 708 16\n44 709 10\n44 740 21\n44 741 47\n44 750 2\n44 752 43\n44 764 18\n44 789 32\n44 892 45\n44 903 32\n44 922 37\n44 963 13\n44 964 50\n44 973 30\n44 982 17\n44 986 28\n44 998 49\n45 8 20\n45 66 38\n45 103 11\n45 111 35\n45 114 28\n45 122 49\n45 158 29\n45 165 3\n45 173 28\n45 177 21\n45 186 37\n45 201 18\n45 240 15\n45 263 3\n45 268 17\n45 276 19\n45 282 41\n45 300 4\n45 334 30\n45 360 38\n45 390 44\n45 419 42\n45 425 32\n45 458 21\n45 496 11\n45 546 22\n45 572 25\n45 591 11\n45 638 3\n45 639 23\n45 700 17\n45 702 25\n45 777 22\n45 783 32\n45 806 13\n45 808 46\n45 811 7\n45 825 33\n45 854 13\n45 858 44\n45 865 4\n45 896 31\n45 903 18\n45 964 15\n45 967 10\n45 984 11\n46 31 36\n46 42 28\n46 66 46\n46 68 32\n46 89 26\n46 99 36\n46 127 39\n46 141 -1\n46 167 13\n46 258 17\n46 260 42\n46 280 19\n46 297 37\n46 317 18\n46 371 29\n46 384 17\n46 392 16\n46 393 40\n46 394 22\n46 478 17\n46 528 40\n46 529 8\n46 538 40\n46 659 34\n46 677 48\n46 746 47\n46 808 37\n46 810 4\n46 848 47\n46 853 44\n46 921 41\n46 952 35\n47 6 27\n47 13 26\n47 87 -2\n47 112 27\n47 114 7\n47 157 16\n47 161 50\n47 166 12\n47 192 39\n47 209 48\n47 215 -2\n47 226 -1\n47 261 19\n47 281 2\n47 296 -1\n47 322 10\n47 351 17\n47 368 43\n47 405 38\n47 443 18\n47 536 16\n47 550 24\n47 571 15\n47 577 19\n47 598 44\n47 622 0\n47 678 22\n47 704 38\n47 747 9\n47 766 33\n47 782 10\n47 794 40\n47 838 23\n47 918 1\n47 924 6\n47 967 39\n47 980 37\n48 5 35\n48 62 25\n48 63 26\n48 100 25\n48 119 31\n48 135 25\n48 148 41\n48 183 23\n48 247 19\n48 262 10\n48 297 26\n48 304 28\n48 312 31\n48 337 24\n48 343 13\n48 353 39\n48 361 19\n48 363 30\n48 369 42\n48 385 26\n48 425 33\n48 446 26\n48 450 3\n48 464 45\n48 471 29\n48 472 18\n48 523 19\n48 575 34\n48 576 0\n48 604 15\n48 610 35\n48 634 3\n48 660 15\n48 664 20\n48 671 37\n48 691 0\n48 698 39\n48 702 22\n48 711 9\n48 775 7\n48 778 38\n48 782 36\n48 790 19\n48 798 29\n48 800 17\n48 820 8\n48 828 1\n48 834 33\n48 847 12\n48 860 19\n48 866 22\n48 880 8\n48 884 26\n48 895 27\n48 904 33\n48 983 12\n48 987 9\n49 3 19\n49 18 12\n49 35 49\n49 88 16\n49 105 8\n49 124 46\n49 139 38\n49 173 20\n49 193 39\n49 204 42\n49 269 18\n49 270 43\n49 293 14\n49 310 43\n49 323 38\n49 334 39\n49 430 33\n49 508 48\n49 511 11\n49 555 39\n49 579 20\n49 607 18\n49 653 7\n49 783 42\n49 850 3\n49 861 49\n49 889 39\n49 912 28\n49 915 18\n49 937 16\n49 944 15\n49 946 5\n49 995 35\n49 997 29\n50 22 4\n50 106 17\n50 157 18\n50 161 16\n50 179 34\n50 202 33\n50 218 17\n50 238 18\n50 291 25\n50 327 44\n50 328 19\n50 332 43\n50 336 24\n50 366 39\n50 372 48\n50 424 29\n50 444 15\n50 520 23\n50 546 22\n50 559 29\n50 573 26\n50 588 44\n50 594 50\n50 630 38\n50 637 25\n50 651 19\n50 672 41\n50 711 3\n50 728 26\n50 741 26\n50 757 32\n50 789 44\n50 811 18\n50 845 34\n50 851 20\n50 865 31\n50 878 20\n50 927 16\n50 935 14\n50 954 37\n50 976 12\n50 984 44\n51 3 46\n51 11 13\n51 15 28\n51 48 23\n51 52 13\n51 77 35\n51 129 20\n51 159 48\n51 160 -2\n51 162 9\n51 178 35\n51 207 21\n51 306 8\n51 317 36\n51 327 -2\n51 348 47\n51 374 17\n51 401 10\n51 403 39\n51 416 7\n51 419 36\n51 423 38\n51 427 34\n51 448 39\n51 449 40\n51 452 7\n51 476 25\n51 485 12\n51 497 -2\n51 523 33\n51 644 43\n51 652 22\n51 660 16\n51 672 19\n51 691 45\n51 704 15\n51 714 43\n51 726 47\n51 733 -2\n51 867 13\n51 886 25\n51 905 16\n51 919 48\n51 934 30\n51 960 26\n51 977 50\n51 979 8\n51 990 16\n51 1000 49\n52 10 38\n52 42 29\n52 69 42\n52 70 33\n52 97 24\n52 148 5\n52 179 33\n52 197 6\n52 200 5\n52 236 22\n52 238 17\n52 274 35\n52 286 17\n52 305 48\n52 312 45\n52 327 43\n52 333 45\n52 335 10\n52 339 33\n52 370 0\n52 375 37\n52 383 12\n52 409 21\n52 413 7\n52 425 25\n52 468 22\n52 488 32\n52 537 19\n52 559 33\n52 560 26\n52 568 46\n52 582 0\n52 590 40\n52 593 -1\n52 620 8\n52 625 16\n52 626 14\n52 636 5\n52 654 35\n52 683 7\n52 702 12\n52 716 29\n52 718 21\n52 735 12\n52 781 7\n52 817 7\n52 824 29\n52 825 30\n52 826 16\n52 831 24\n52 856 10\n52 875 22\n52 890 22\n52 939 29\n52 947 25\n52 969 42\n53 12 36\n53 107 8\n53 112 25\n53 148 12\n53 174 7\n53 250 11\n53 268 6\n53 286 6\n53 295 31\n53 306 18\n53 331 38\n53 443 7\n53 450 46\n53 465 31\n53 467 35\n53 468 19\n53 503 4\n53 536 28\n53 558 38\n53 576 25\n53 652 -2\n53 717 49\n53 739 45\n53 741 33\n53 769 42\n53 837 22\n53 907 19\n53 940 16\n53 968 18\n53 973 8\n54 21 27\n54 30 6\n54 37 46\n54 44 10\n54 74 40\n54 86 39\n54 87 21\n54 91 44\n54 119 50\n54 125 46\n54 142 36\n54 231 21\n54 248 23\n54 267 29\n54 272 37\n54 344 29\n54 358 45\n54 413 17\n54 414 44\n54 433 40\n54 471 25\n54 515 8\n54 550 34\n54 552 50\n54 583 19\n54 592 12\n54 595 41\n54 636 37\n54 697 45\n54 699 49\n54 701 49\n54 737 22\n54 759 31\n54 765 21\n54 792 6\n54 795 3\n54 812 17\n54 820 13\n54 823 44\n54 886 16\n54 899 12\n54 900 38\n54 905 9\n54 908 19\n54 934 32\n54 969 9\n55 3 9\n55 19 16\n55 31 39\n55 41 4\n55 62 20\n55 87 38\n55 119 15\n55 159 21\n55 183 44\n55 204 18\n55 214 50\n55 222 23\n55 244 10\n55 274 41\n55 276 12\n55 277 28\n55 290 23\n55 315 10\n55 325 28\n55 337 18\n55 349 23\n55 370 9\n55 385 11\n55 440 40\n55 482 13\n55 510 18\n55 574 18\n55 642 36\n55 648 40\n55 653 41\n55 685 43\n55 688 -2\n55 692 42\n55 755 28\n55 770 6\n55 797 41\n55 805 11\n55 820 26\n55 829 39\n55 909 18\n55 943 39\n55 972 33\n55 996 15\n56 41 32\n56 216 17\n56 279 9\n56 316 0\n56 325 10\n56 379 31\n56 399 44\n56 414 4\n56 427 3\n56 443 38\n56 447 48\n56 479 31\n56 484 25\n56 485 23\n56 511 11\n56 532 2\n56 539 37\n56 557 7\n56 572 5\n56 574 48\n56 586 14\n56 587 2\n56 600 22\n56 650 37\n56 655 45\n56 656 20\n56 718 14\n56 730 24\n56 732 23\n56 744 41\n56 774 4\n56 780 35\n56 785 42\n56 819 36\n56 837 12\n56 897 21\n56 918 23\n56 929 -2\n56 972 19\n57 15 21\n57 69 15\n57 124 -1\n57 135 7\n57 138 31\n57 143 37\n57 145 0\n57 147 16\n57 173 42\n57 198 19\n57 245 -2\n57 270 46\n57 293 14\n57 331 2\n57 339 4\n57 342 25\n57 351 25\n57 377 50\n57 384 23\n57 406 27\n57 433 18\n57 462 24\n57 465 0\n57 511 37\n57 525 43\n57 531 40\n57 543 17\n57 545 29\n57 559 2\n57 575 11\n57 596 44\n57 611 7\n57 615 48\n57 628 15\n57 629 29\n57 698 -2\n57 699 20\n57 738 41\n57 763 5\n57 764 13\n57 777 26\n57 801 13\n57 820 12\n57 861 25\n57 872 19\n57 896 32\n57 938 44\n57 970 5\n57 995 28\n58 10 5\n58 17 24\n58 24 -1\n58 45 35\n58 56 44\n58 93 10\n58 141 4\n58 143 17\n58 155 42\n58 167 40\n58 175 3\n58 181 2\n58 183 35\n58 184 12\n58 209 3\n58 228 32\n58 288 49\n58 290 47\n58 361 28\n58 390 49\n58 391 37\n58 406 -1\n58 433 19\n58 451 7\n58 452 34\n58 483 42\n58 553 -2\n58 567 21\n58 570 42\n58 626 39\n58 642 3\n58 660 6\n58 662 5\n58 725 19\n58 726 29\n58 739 10\n58 791 44\n58 801 27\n58 805 43\n58 835 49\n58 867 19\n58 898 10\n58 915 32\n58 924 -1\n58 976 19\n58 981 4\n59 54 41\n59 83 34\n59 87 3\n59 90 39\n59 98 12\n59 101 19\n59 130 26\n59 152 31\n59 233 40\n59 237 20\n59 243 4\n59 257 40\n59 339 3\n59 396 31\n59 397 17\n59 430 19\n59 460 19\n59 467 36\n59 507 15\n59 522 45\n59 528 46\n59 544 7\n59 550 34\n59 564 9\n59 597 7\n59 628 39\n59 642 33\n59 661 28\n59 733 1\n59 765 17\n59 768 24\n59 772 30\n59 782 24\n59 835 30\n59 880 42\n59 893 28\n59 917 2\n59 924 9\n59 928 -1\n59 951 4\n59 993 36\n60 9 26\n60 16 34\n60 51 33\n60 63 31\n60 68 14\n60 131 22\n60 178 31\n60 180 35\n60 181 20\n60 217 18\n60 273 36\n60 290 12\n60 295 34\n60 297 -1\n60 310 7\n60 371 39\n60 376 13\n60 381 42\n60 390 15\n60 392 28\n60 406 37\n60 444 25\n60 445 42\n60 459 4\n60 462 27\n60 519 20\n60 556 42\n60 602 17\n60 611 10\n60 621 43\n60 628 20\n60 630 50\n60 649 47\n60 670 43\n60 691 6\n60 698 28\n60 773 10\n60 781 22\n60 827 20\n60 914 29\n60 934 40\n60 953 32\n60 967 47\n60 981 39\n61 16 39\n61 39 20\n61 80 18\n61 128 26\n61 156 42\n61 163 23\n61 176 33\n61 210 46\n61 212 1\n61 242 13\n61 301 12\n61 313 48\n61 321 5\n61 368 43\n61 369 33\n61 379 2\n61 380 46\n61 396 1\n61 409 26\n61 426 50\n61 442 -1\n61 456 4\n61 486 37\n61 502 38\n61 505 17\n61 529 49\n61 531 8\n61 555 33\n61 556 10\n61 574 27\n61 576 48\n61 578 44\n61 591 28\n61 615 50\n61 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28\n111 811 5\n111 818 34\n111 838 50\n111 845 42\n111 885 24\n111 887 7\n111 893 23\n111 895 29\n111 913 43\n111 968 43\n112 20 29\n112 32 12\n112 58 9\n112 73 34\n112 75 5\n112 79 32\n112 88 40\n112 116 35\n112 159 20\n112 172 26\n112 173 21\n112 190 33\n112 200 22\n112 201 28\n112 233 37\n112 235 4\n112 250 7\n112 267 36\n112 286 16\n112 307 9\n112 329 5\n112 375 4\n112 385 18\n112 395 20\n112 412 14\n112 415 34\n112 424 31\n112 427 4\n112 443 42\n112 455 41\n112 479 33\n112 483 38\n112 515 21\n112 521 33\n112 523 47\n112 566 8\n112 580 12\n112 592 33\n112 612 26\n112 653 48\n112 702 17\n112 708 32\n112 711 45\n112 722 45\n112 775 38\n112 803 11\n112 828 14\n112 839 45\n112 855 2\n112 912 8\n112 927 7\n112 941 40\n112 945 19\n112 976 43\n113 25 48\n113 52 44\n113 54 21\n113 98 19\n113 131 15\n113 173 0\n113 239 31\n113 241 27\n113 276 42\n113 285 38\n113 293 44\n113 329 16\n113 379 37\n113 411 1\n113 477 6\n113 514 3\n113 532 37\n113 543 28\n113 567 7\n113 574 -2\n113 585 -2\n113 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10\n126 490 29\n126 491 22\n126 512 12\n126 537 34\n126 562 9\n126 588 28\n126 591 35\n126 593 46\n126 602 35\n126 632 37\n126 647 32\n126 661 20\n126 691 28\n126 716 9\n126 721 28\n126 726 46\n126 729 13\n126 748 -1\n126 759 39\n126 787 43\n126 823 49\n126 848 41\n126 874 9\n126 875 0\n126 905 22\n126 915 9\n126 926 13\n126 937 5\n126 999 10\n127 2 47\n127 52 17\n127 136 13\n127 142 2\n127 198 31\n127 217 29\n127 268 2\n127 272 50\n127 290 16\n127 293 39\n127 328 2\n127 337 28\n127 346 40\n127 347 12\n127 348 6\n127 354 15\n127 364 -2\n127 420 28\n127 436 15\n127 450 50\n127 458 12\n127 464 9\n127 465 13\n127 522 14\n127 540 31\n127 544 29\n127 563 2\n127 575 38\n127 647 11\n127 661 35\n127 679 42\n127 683 39\n127 700 2\n127 704 45\n127 727 5\n127 770 31\n127 772 13\n127 794 18\n127 796 23\n127 865 3\n127 867 47\n127 932 34\n127 943 0\n127 946 3\n127 994 9\n128 5 15\n128 10 17\n128 11 49\n128 18 22\n128 20 24\n128 70 1\n128 84 0\n128 101 13\n128 109 0\n128 122 38\n128 147 45\n128 152 48\n128 179 14\n128 188 35\n128 209 29\n128 268 27\n128 280 27\n128 288 50\n128 307 50\n128 337 11\n128 341 14\n128 370 8\n128 386 37\n128 419 36\n128 442 9\n128 449 45\n128 453 24\n128 455 18\n128 493 37\n128 497 48\n128 583 12\n128 600 0\n128 603 22\n128 607 25\n128 610 9\n128 641 49\n128 658 42\n128 665 33\n128 669 50\n128 676 40\n128 692 36\n128 725 4\n128 727 16\n128 781 5\n128 783 21\n128 797 0\n128 833 13\n128 836 38\n128 837 40\n128 841 46\n128 843 2\n128 849 7\n128 853 11\n128 858 19\n128 926 22\n128 932 15\n128 944 26\n128 995 38\n129 63 20\n129 67 5\n129 86 48\n129 91 -1\n129 110 0\n129 139 5\n129 140 0\n129 154 42\n129 190 26\n129 200 44\n129 214 15\n129 215 30\n129 244 -2\n129 320 32\n129 324 30\n129 354 10\n129 406 -2\n129 410 21\n129 450 32\n129 452 34\n129 465 23\n129 502 4\n129 510 28\n129 528 4\n129 576 11\n129 599 44\n129 617 46\n129 622 16\n129 626 2\n129 632 32\n129 639 26\n129 663 39\n129 664 36\n129 677 19\n129 692 39\n129 731 19\n129 761 17\n129 779 -2\n129 793 30\n129 794 48\n129 854 -2\n129 873 41\n129 876 33\n129 890 49\n129 943 25\n129 961 41\n129 971 49\n129 976 43\n130 4 -1\n130 31 29\n130 34 16\n130 36 36\n130 107 8\n130 125 34\n130 145 15\n130 194 18\n130 197 36\n130 208 33\n130 220 41\n130 236 48\n130 254 -1\n130 289 36\n130 308 29\n130 315 9\n130 327 35\n130 439 14\n130 445 33\n130 457 1\n130 504 13\n130 551 26\n130 586 31\n130 596 7\n130 640 20\n130 649 38\n130 674 39\n130 683 44\n130 736 8\n130 742 7\n130 750 4\n130 755 46\n130 762 39\n130 769 19\n130 780 23\n130 826 19\n130 839 13\n130 847 46\n130 906 27\n130 910 40\n130 927 9\n131 19 22\n131 96 34\n131 113 5\n131 117 37\n131 177 22\n131 223 7\n131 251 44\n131 282 12\n131 317 43\n131 329 23\n131 343 17\n131 360 48\n131 366 44\n131 367 49\n131 374 16\n131 397 41\n131 399 36\n131 412 11\n131 460 40\n131 481 19\n131 544 8\n131 546 23\n131 548 3\n131 554 17\n131 581 36\n131 594 4\n131 627 27\n131 711 23\n131 712 9\n131 718 12\n131 732 26\n131 754 5\n131 758 40\n131 780 19\n131 791 21\n131 795 -1\n131 827 34\n131 838 47\n131 845 5\n131 859 25\n131 873 38\n131 918 17\n131 996 8\n132 57 26\n132 117 44\n132 119 15\n132 151 46\n132 153 35\n132 173 10\n132 186 5\n132 259 37\n132 260 42\n132 271 18\n132 286 19\n132 301 24\n132 355 11\n132 358 31\n132 361 14\n132 383 17\n132 554 35\n132 569 27\n132 585 49\n132 623 35\n132 628 21\n132 653 13\n132 668 22\n132 680 26\n132 691 15\n132 697 -1\n132 704 27\n132 740 1\n132 742 38\n132 766 49\n132 787 17\n132 794 47\n132 797 13\n132 826 49\n132 865 29\n132 873 42\n132 881 32\n132 886 0\n132 909 7\n133 16 23\n133 38 33\n133 89 48\n133 130 8\n133 177 30\n133 193 16\n133 220 30\n133 247 28\n133 288 42\n133 308 10\n133 332 45\n133 411 49\n133 416 0\n133 434 16\n133 460 20\n133 467 24\n133 473 26\n133 512 13\n133 523 16\n133 537 6\n133 589 11\n133 602 49\n133 606 30\n133 625 19\n133 664 50\n133 715 18\n133 775 -1\n133 791 14\n133 806 16\n133 847 40\n133 863 20\n133 873 25\n133 898 47\n133 952 39\n133 962 40\n133 965 48\n133 988 41\n134 15 16\n134 70 13\n134 94 23\n134 109 47\n134 196 31\n134 212 44\n134 245 8\n134 252 11\n134 259 15\n134 286 29\n134 292 26\n134 308 40\n134 310 46\n134 313 33\n134 326 5\n134 355 45\n134 366 10\n134 371 13\n134 387 26\n134 390 30\n134 397 47\n134 405 6\n134 407 15\n134 440 38\n134 452 42\n134 454 23\n134 456 22\n134 460 43\n134 479 7\n134 481 7\n134 494 46\n134 523 2\n134 532 37\n134 546 21\n134 568 2\n134 583 37\n134 596 5\n134 608 47\n134 613 24\n134 617 6\n134 618 29\n134 642 26\n134 652 49\n134 665 15\n134 684 2\n134 693 9\n134 719 3\n134 748 14\n134 766 35\n134 767 16\n134 777 31\n134 807 10\n134 822 41\n134 834 34\n134 873 40\n134 898 33\n134 910 10\n134 913 41\n134 927 47\n134 939 33\n134 960 25\n135 48 23\n135 77 41\n135 101 32\n135 138 16\n135 162 48\n135 166 31\n135 211 32\n135 215 14\n135 226 49\n135 265 11\n135 284 20\n135 293 47\n135 317 36\n135 325 14\n135 345 33\n135 346 43\n135 354 17\n135 363 36\n135 381 6\n135 402 1\n135 412 45\n135 420 21\n135 438 40\n135 456 43\n135 520 15\n135 556 38\n135 559 48\n135 566 7\n135 581 11\n135 586 5\n135 624 37\n135 636 5\n135 640 11\n135 844 8\n135 852 10\n135 862 15\n135 868 13\n135 873 38\n135 881 34\n135 900 21\n135 980 24\n136 26 32\n136 33 41\n136 37 33\n136 41 8\n136 47 21\n136 55 15\n136 65 5\n136 72 41\n136 79 44\n136 123 38\n136 129 10\n136 139 9\n136 147 37\n136 151 13\n136 160 20\n136 172 23\n136 222 40\n136 244 4\n136 292 26\n136 293 24\n136 301 16\n136 305 39\n136 314 34\n136 332 12\n136 350 50\n136 356 20\n136 362 30\n136 389 14\n136 409 23\n136 420 22\n136 442 25\n136 461 25\n136 489 35\n136 496 20\n136 542 25\n136 563 27\n136 565 39\n136 569 30\n136 596 27\n136 626 13\n136 656 10\n136 722 47\n136 732 31\n136 734 6\n136 776 37\n136 781 36\n136 792 43\n136 831 8\n136 924 6\n136 925 9\n136 932 28\n136 947 34\n136 965 45\n136 977 39\n136 985 18\n137 7 47\n137 61 -1\n137 101 45\n137 102 45\n137 122 16\n137 141 42\n137 168 50\n137 169 4\n137 172 21\n137 191 40\n137 203 23\n137 236 34\n137 254 26\n137 273 29\n137 305 22\n137 324 44\n137 341 11\n137 343 41\n137 353 6\n137 376 10\n137 410 33\n137 417 47\n137 434 13\n137 458 1\n137 459 23\n137 465 14\n137 466 34\n137 484 46\n137 488 14\n137 508 19\n137 509 37\n137 535 6\n137 544 33\n137 581 50\n137 599 33\n137 635 17\n137 651 17\n137 683 39\n137 702 26\n137 712 14\n137 720 11\n137 769 14\n137 812 10\n137 869 44\n137 897 5\n137 951 1\n137 971 46\n137 987 7\n138 13 29\n138 33 33\n138 39 6\n138 40 20\n138 60 49\n138 80 32\n138 99 41\n138 101 14\n138 110 28\n138 130 20\n138 169 12\n138 179 32\n138 192 23\n138 219 43\n138 221 38\n138 259 48\n138 270 32\n138 271 35\n138 278 41\n138 317 29\n138 342 22\n138 391 36\n138 426 42\n138 531 46\n138 550 8\n138 612 37\n138 621 29\n138 626 -2\n138 665 14\n138 726 16\n138 795 48\n138 839 32\n138 848 29\n138 860 4\n138 887 46\n138 897 48\n138 899 40\n138 904 21\n138 911 32\n138 923 36\n138 929 39\n138 937 46\n138 954 3\n138 965 13\n138 979 48\n138 985 23\n139 46 6\n139 90 38\n139 91 6\n139 218 43\n139 227 35\n139 232 24\n139 235 39\n139 239 2\n139 265 48\n139 266 9\n139 305 38\n139 311 36\n139 312 39\n139 391 -1\n139 418 29\n139 444 30\n139 446 48\n139 465 49\n139 520 5\n139 557 39\n139 582 8\n139 584 37\n139 599 21\n139 602 44\n139 626 9\n139 665 49\n139 712 1\n139 718 30\n139 785 46\n139 805 6\n139 816 33\n139 818 47\n139 843 31\n139 887 7\n139 947 36\n139 949 47\n139 951 28\n139 964 16\n139 980 19\n139 999 43\n140 19 37\n140 53 23\n140 91 33\n140 102 24\n140 123 24\n140 128 40\n140 242 2\n140 248 49\n140 252 13\n140 255 37\n140 266 36\n140 267 23\n140 277 42\n140 281 4\n140 351 2\n140 363 -1\n140 387 39\n140 395 25\n140 401 11\n140 405 32\n140 416 27\n140 527 21\n140 579 14\n140 598 43\n140 635 7\n140 666 18\n140 675 3\n140 681 27\n140 698 26\n140 725 7\n140 743 25\n140 786 8\n140 803 44\n140 807 12\n140 828 18\n140 850 4\n140 866 8\n140 942 1\n140 983 0\n140 985 35\n141 9 38\n141 25 27\n141 36 41\n141 74 30\n141 115 25\n141 128 43\n141 137 32\n141 171 13\n141 192 42\n141 254 45\n141 281 43\n141 370 8\n141 374 44\n141 375 7\n141 424 32\n141 425 27\n141 454 24\n141 458 15\n141 472 18\n141 518 17\n141 539 32\n141 541 28\n141 549 34\n141 568 39\n141 577 44\n141 616 11\n141 664 6\n141 721 45\n141 726 17\n141 748 46\n141 751 26\n141 756 20\n141 796 5\n141 799 26\n141 816 14\n141 837 20\n141 878 4\n141 884 27\n141 905 35\n141 961 30\n141 967 3\n141 980 30\n142 3 49\n142 18 36\n142 30 21\n142 31 36\n142 97 28\n142 117 25\n142 135 9\n142 157 34\n142 201 32\n142 216 24\n142 247 11\n142 294 43\n142 356 41\n142 414 6\n142 438 36\n142 443 18\n142 485 40\n142 505 34\n142 517 23\n142 530 49\n142 533 15\n142 537 12\n142 542 22\n142 572 40\n142 582 31\n142 665 44\n142 668 9\n142 672 6\n142 692 40\n142 712 36\n142 713 26\n142 718 16\n142 756 31\n142 792 40\n142 796 43\n142 834 14\n142 850 30\n142 866 31\n142 874 35\n142 943 43\n142 957 27\n142 999 45\n143 9 33\n143 37 13\n143 41 41\n143 84 7\n143 104 -2\n143 117 38\n143 124 31\n143 168 20\n143 180 42\n143 190 42\n143 246 28\n143 260 18\n143 265 0\n143 318 32\n143 319 20\n143 348 31\n143 372 24\n143 379 10\n143 387 36\n143 412 31\n143 436 21\n143 447 7\n143 497 20\n143 512 4\n143 536 47\n143 538 44\n143 539 35\n143 590 38\n143 595 31\n143 605 3\n143 607 37\n143 648 14\n143 653 31\n143 679 28\n143 699 45\n143 780 18\n143 783 8\n143 822 23\n143 830 43\n143 834 27\n143 840 39\n143 852 0\n143 870 37\n143 887 50\n143 924 11\n144 17 43\n144 18 45\n144 32 19\n144 57 47\n144 77 27\n144 81 17\n144 125 41\n144 160 47\n144 177 13\n144 186 24\n144 222 17\n144 243 0\n144 265 17\n144 291 -2\n144 292 47\n144 348 35\n144 354 12\n144 362 6\n144 369 48\n144 395 9\n144 404 29\n144 416 47\n144 461 20\n144 480 35\n144 486 43\n144 537 27\n144 570 13\n144 577 39\n144 610 5\n144 630 5\n144 631 4\n144 639 3\n144 661 14\n144 700 41\n144 721 15\n144 737 0\n144 745 49\n144 776 45\n144 786 22\n144 791 22\n144 808 33\n144 843 34\n144 873 46\n144 878 9\n144 884 27\n144 885 23\n144 920 26\n144 969 5\n144 971 30\n144 990 19\n145 11 25\n145 12 50\n145 14 18\n145 58 38\n145 59 7\n145 64 27\n145 76 43\n145 109 1\n145 123 48\n145 143 30\n145 147 38\n145 173 49\n145 204 7\n145 217 11\n145 229 33\n145 280 31\n145 321 46\n145 335 21\n145 417 42\n145 427 42\n145 442 23\n145 481 26\n145 486 32\n145 522 29\n145 527 4\n145 541 47\n145 589 28\n145 604 14\n145 629 22\n145 645 2\n145 707 43\n145 714 12\n145 757 17\n145 768 2\n145 790 39\n145 820 17\n145 845 24\n145 849 20\n145 850 4\n145 851 43\n145 861 44\n145 865 14\n145 922 8\n145 964 20\n145 974 41\n145 975 32\n145 983 19\n146 21 39\n146 51 7\n146 58 35\n146 71 36\n146 108 24\n146 120 12\n146 133 42\n146 138 49\n146 161 50\n146 168 36\n146 190 30\n146 206 26\n146 208 44\n146 277 48\n146 338 -1\n146 366 23\n146 403 16\n146 405 2\n146 428 42\n146 464 34\n146 469 41\n146 500 23\n146 514 26\n146 519 9\n146 521 47\n146 553 8\n146 562 24\n146 567 36\n146 588 8\n146 647 38\n146 652 34\n146 672 22\n146 701 50\n146 716 48\n146 812 46\n146 840 18\n146 846 15\n146 865 37\n146 888 31\n146 893 14\n146 896 13\n146 897 48\n146 909 31\n146 929 21\n146 964 46\n146 966 18\n146 969 11\n146 974 31\n147 28 25\n147 94 32\n147 103 18\n147 139 20\n147 166 19\n147 251 26\n147 278 29\n147 291 50\n147 315 41\n147 363 11\n147 366 20\n147 415 21\n147 460 47\n147 473 -1\n147 489 49\n147 519 34\n147 526 31\n147 554 22\n147 569 34\n147 574 -2\n147 576 13\n147 607 15\n147 666 37\n147 715 22\n147 716 50\n147 719 41\n147 752 16\n147 779 18\n147 824 11\n147 841 50\n147 857 27\n147 867 46\n147 875 25\n147 890 20\n147 932 19\n148 25 5\n148 33 43\n148 42 26\n148 48 7\n148 89 19\n148 143 32\n148 153 12\n148 156 42\n148 166 16\n148 176 33\n148 186 43\n148 195 15\n148 212 26\n148 216 50\n148 314 46\n148 321 5\n148 324 36\n148 333 1\n148 354 8\n148 362 40\n148 364 24\n148 373 37\n148 378 6\n148 381 26\n148 386 15\n148 404 36\n148 425 39\n148 444 10\n148 448 46\n148 500 42\n148 501 28\n148 543 1\n148 553 22\n148 576 45\n148 578 47\n148 581 16\n148 608 44\n148 666 27\n148 676 25\n148 685 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26\n150 162 17\n150 167 45\n150 178 50\n150 181 46\n150 190 24\n150 200 50\n150 210 24\n150 282 4\n150 312 7\n150 333 11\n150 340 12\n150 361 1\n150 376 30\n150 398 24\n150 408 36\n150 410 -1\n150 415 46\n150 452 34\n150 480 37\n150 488 19\n150 492 13\n150 503 42\n150 506 40\n150 512 0\n150 525 26\n150 530 44\n150 589 16\n150 607 5\n150 629 49\n150 644 42\n150 691 25\n150 732 44\n150 743 5\n150 751 32\n150 775 -1\n150 799 12\n150 915 7\n150 922 5\n150 930 -2\n150 936 18\n150 947 24\n150 949 12\n150 954 16\n150 979 50\n150 999 42\n151 38 49\n151 49 8\n151 77 45\n151 91 5\n151 106 32\n151 113 50\n151 130 22\n151 144 47\n151 146 34\n151 147 19\n151 149 12\n151 174 12\n151 180 30\n151 198 9\n151 210 32\n151 235 27\n151 238 21\n151 288 43\n151 304 44\n151 322 30\n151 379 50\n151 381 18\n151 394 46\n151 407 50\n151 435 21\n151 473 28\n151 474 30\n151 477 37\n151 507 4\n151 530 50\n151 548 6\n151 592 15\n151 671 43\n151 701 43\n151 753 40\n151 782 10\n151 832 18\n151 862 46\n151 866 29\n151 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7\n153 610 29\n153 623 22\n153 649 49\n153 659 30\n153 671 42\n153 672 49\n153 695 33\n153 715 10\n153 747 14\n153 752 45\n153 759 39\n153 776 33\n153 823 27\n153 827 33\n153 840 2\n153 859 10\n153 870 12\n153 886 1\n153 887 46\n153 908 24\n153 912 5\n153 991 37\n154 5 38\n154 28 6\n154 48 4\n154 141 29\n154 192 47\n154 204 35\n154 206 20\n154 207 25\n154 266 2\n154 288 8\n154 292 25\n154 299 29\n154 302 49\n154 305 8\n154 326 30\n154 331 23\n154 334 47\n154 365 38\n154 469 37\n154 480 6\n154 482 25\n154 514 36\n154 529 -1\n154 533 19\n154 599 31\n154 608 25\n154 625 22\n154 633 36\n154 637 44\n154 650 47\n154 694 31\n154 702 43\n154 712 32\n154 732 13\n154 760 49\n154 780 50\n154 784 29\n154 792 0\n154 802 39\n154 855 45\n154 861 32\n154 879 7\n154 899 45\n154 926 36\n154 931 8\n154 974 20\n155 17 48\n155 25 7\n155 45 42\n155 140 50\n155 235 29\n155 243 45\n155 262 49\n155 282 12\n155 302 20\n155 305 0\n155 309 29\n155 312 20\n155 323 13\n155 326 28\n155 329 44\n155 330 24\n155 334 31\n155 341 16\n155 363 25\n155 410 4\n155 518 31\n155 522 43\n155 632 12\n155 664 8\n155 706 7\n155 719 43\n155 736 4\n155 750 42\n155 760 21\n155 777 8\n155 792 45\n155 793 4\n155 811 1\n155 840 15\n155 845 44\n155 874 1\n155 880 39\n155 892 19\n155 926 30\n155 928 -2\n155 942 24\n155 960 26\n155 970 18\n156 26 5\n156 28 45\n156 68 -1\n156 79 34\n156 90 39\n156 147 12\n156 157 31\n156 162 22\n156 168 16\n156 194 36\n156 208 40\n156 218 38\n156 309 19\n156 342 -2\n156 369 29\n156 404 15\n156 410 11\n156 412 40\n156 464 49\n156 487 -2\n156 513 45\n156 592 45\n156 601 33\n156 604 25\n156 626 27\n156 638 48\n156 640 6\n156 652 13\n156 654 43\n156 670 20\n156 677 40\n156 686 11\n156 698 39\n156 716 10\n156 728 49\n156 737 35\n156 741 46\n156 779 7\n156 817 -2\n156 860 1\n156 878 13\n156 886 4\n156 900 49\n156 923 38\n156 937 23\n156 979 30\n156 997 26\n157 19 14\n157 31 36\n157 43 4\n157 63 46\n157 93 -1\n157 113 13\n157 125 0\n157 165 38\n157 176 4\n157 196 27\n157 230 14\n157 273 10\n157 301 4\n157 303 31\n157 318 1\n157 323 5\n157 325 40\n157 328 4\n157 379 34\n157 419 28\n157 454 -1\n157 465 34\n157 516 9\n157 531 5\n157 557 37\n157 558 41\n157 584 14\n157 609 49\n157 661 40\n157 667 12\n157 679 7\n157 682 16\n157 686 -2\n157 702 50\n157 718 18\n157 745 48\n157 750 4\n157 784 5\n157 787 41\n157 802 20\n157 812 21\n157 858 -1\n157 892 3\n157 914 32\n157 918 49\n157 974 44\n157 983 24\n158 11 19\n158 16 25\n158 58 16\n158 59 -1\n158 61 17\n158 92 45\n158 98 14\n158 111 2\n158 112 15\n158 132 26\n158 169 5\n158 184 22\n158 193 4\n158 224 41\n158 241 25\n158 275 24\n158 333 50\n158 341 11\n158 367 24\n158 375 48\n158 379 6\n158 424 48\n158 450 42\n158 463 41\n158 480 37\n158 482 19\n158 520 3\n158 538 17\n158 598 4\n158 641 38\n158 644 -2\n158 705 10\n158 707 45\n158 722 36\n158 752 15\n158 756 21\n158 820 41\n158 847 50\n158 850 31\n158 865 1\n158 887 12\n158 892 24\n158 906 -2\n158 916 48\n158 929 34\n158 949 19\n158 984 34\n158 985 46\n158 988 17\n158 993 41\n158 1000 29\n159 6 40\n159 35 17\n159 37 29\n159 62 20\n159 68 43\n159 72 27\n159 124 31\n159 164 6\n159 175 42\n159 178 30\n159 186 20\n159 239 29\n159 285 10\n159 286 39\n159 307 26\n159 313 19\n159 317 48\n159 331 18\n159 399 6\n159 520 10\n159 523 40\n159 563 29\n159 607 42\n159 612 16\n159 639 25\n159 648 36\n159 696 30\n159 698 18\n159 731 34\n159 774 27\n159 775 24\n159 813 44\n159 830 11\n159 846 2\n159 865 48\n159 890 13\n159 901 10\n159 943 41\n159 988 20\n160 33 25\n160 41 4\n160 53 25\n160 68 7\n160 79 49\n160 83 43\n160 95 18\n160 96 45\n160 105 0\n160 131 47\n160 163 11\n160 166 31\n160 208 21\n160 213 49\n160 214 20\n160 217 1\n160 238 46\n160 252 8\n160 265 18\n160 326 7\n160 341 50\n160 345 18\n160 375 38\n160 393 40\n160 415 39\n160 427 43\n160 447 25\n160 476 38\n160 494 -2\n160 501 43\n160 525 41\n160 542 35\n160 554 47\n160 567 16\n160 570 19\n160 574 48\n160 594 13\n160 614 13\n160 629 43\n160 635 3\n160 652 25\n160 679 12\n160 712 43\n160 722 39\n160 741 31\n160 752 24\n160 754 32\n160 759 10\n160 771 38\n160 782 43\n160 785 2\n160 816 3\n160 818 16\n160 828 41\n160 840 50\n160 849 39\n160 871 22\n160 878 23\n160 881 36\n160 895 9\n160 902 39\n160 906 45\n160 921 41\n160 941 28\n161 11 33\n161 17 9\n161 39 44\n161 46 11\n161 54 10\n161 61 17\n161 64 25\n161 66 5\n161 69 15\n161 76 43\n161 79 21\n161 103 16\n161 111 24\n161 142 35\n161 153 11\n161 188 43\n161 258 31\n161 331 35\n161 332 9\n161 351 42\n161 377 20\n161 411 21\n161 454 36\n161 457 45\n161 491 23\n161 506 13\n161 520 41\n161 526 47\n161 529 15\n161 538 40\n161 541 20\n161 559 49\n161 595 47\n161 611 42\n161 626 34\n161 627 34\n161 684 8\n161 699 15\n161 739 10\n161 740 24\n161 760 -2\n161 796 1\n161 804 13\n161 807 15\n161 879 38\n161 881 3\n161 896 24\n161 912 40\n161 915 8\n161 926 39\n161 975 3\n162 71 11\n162 91 33\n162 95 4\n162 100 3\n162 116 13\n162 145 39\n162 156 16\n162 201 13\n162 215 3\n162 217 1\n162 303 2\n162 332 37\n162 337 46\n162 344 26\n162 351 19\n162 355 46\n162 365 46\n162 366 5\n162 388 21\n162 390 14\n162 439 39\n162 458 43\n162 479 40\n162 486 33\n162 493 6\n162 513 13\n162 515 19\n162 528 39\n162 534 2\n162 541 16\n162 549 45\n162 582 22\n162 592 41\n162 602 14\n162 603 48\n162 642 45\n162 687 44\n162 701 17\n162 703 38\n162 708 30\n162 755 17\n162 774 37\n162 783 5\n162 808 33\n162 813 9\n162 846 20\n162 859 13\n162 905 22\n162 930 8\n162 965 15\n162 975 26\n162 983 11\n162 989 25\n163 48 39\n163 81 13\n163 120 32\n163 126 24\n163 191 28\n163 201 36\n163 240 31\n163 264 7\n163 270 36\n163 303 22\n163 305 8\n163 329 10\n163 353 39\n163 360 35\n163 395 -1\n163 408 36\n163 447 26\n163 450 22\n163 473 30\n163 480 40\n163 489 25\n163 492 -2\n163 549 3\n163 560 36\n163 595 28\n163 612 38\n163 624 5\n163 630 11\n163 634 45\n163 636 22\n163 667 15\n163 675 31\n163 696 2\n163 697 47\n163 713 50\n163 716 40\n163 744 46\n163 748 9\n163 842 17\n163 845 46\n163 848 5\n163 854 34\n163 887 44\n163 900 5\n163 912 2\n163 915 18\n163 922 5\n163 924 16\n163 925 36\n163 935 43\n163 936 20\n163 944 36\n163 945 36\n163 971 42\n163 981 48\n163 992 30\n164 2 50\n164 6 3\n164 33 43\n164 38 35\n164 67 48\n164 69 45\n164 70 -1\n164 81 38\n164 88 39\n164 115 44\n164 119 34\n164 144 18\n164 157 15\n164 179 49\n164 194 18\n164 234 11\n164 242 12\n164 253 0\n164 271 35\n164 289 20\n164 293 47\n164 347 45\n164 402 31\n164 407 4\n164 425 50\n164 447 28\n164 452 17\n164 537 48\n164 540 29\n164 555 31\n164 564 34\n164 576 24\n164 637 42\n164 658 18\n164 688 5\n164 704 49\n164 708 7\n164 724 44\n164 736 22\n164 745 -1\n164 757 28\n164 760 49\n164 795 31\n164 814 31\n164 856 28\n165 14 4\n165 45 7\n165 61 0\n165 74 17\n165 177 0\n165 181 27\n165 214 48\n165 241 28\n165 247 5\n165 289 33\n165 307 32\n165 322 3\n165 331 16\n165 454 12\n165 463 23\n165 466 6\n165 486 14\n165 525 27\n165 551 21\n165 555 20\n165 562 25\n165 636 3\n165 723 39\n165 733 4\n165 746 0\n165 787 5\n165 788 7\n165 797 10\n165 798 49\n165 822 18\n165 850 10\n165 856 46\n165 887 13\n165 905 36\n165 914 50\n165 935 37\n165 957 35\n166 20 38\n166 35 25\n166 44 22\n166 46 41\n166 54 34\n166 58 3\n166 68 34\n166 81 45\n166 100 36\n166 120 8\n166 145 9\n166 146 45\n166 155 45\n166 224 6\n166 232 13\n166 244 25\n166 258 48\n166 266 13\n166 277 4\n166 290 42\n166 297 34\n166 300 46\n166 322 5\n166 376 37\n166 474 4\n166 486 48\n166 523 10\n166 533 40\n166 546 35\n166 574 49\n166 575 16\n166 587 4\n166 592 37\n166 595 7\n166 624 1\n166 637 9\n166 649 41\n166 663 26\n166 709 0\n166 718 17\n166 786 27\n166 803 -2\n166 809 17\n166 855 30\n166 857 -2\n166 860 11\n166 876 40\n166 920 7\n166 927 28\n166 964 22\n166 966 19\n166 977 39\n167 5 50\n167 16 4\n167 42 3\n167 68 48\n167 70 25\n167 89 28\n167 92 7\n167 98 46\n167 99 50\n167 111 27\n167 118 12\n167 134 13\n167 136 -2\n167 202 -2\n167 222 50\n167 279 36\n167 315 30\n167 340 46\n167 341 19\n167 361 1\n167 392 18\n167 393 40\n167 452 14\n167 468 21\n167 546 32\n167 549 49\n167 589 22\n167 614 42\n167 648 30\n167 739 8\n167 744 2\n167 750 30\n167 759 13\n167 770 30\n167 775 16\n167 792 39\n167 795 15\n167 839 33\n167 884 32\n167 904 26\n167 908 3\n167 909 28\n167 921 1\n167 927 11\n167 931 12\n167 951 10\n167 968 50\n167 982 34\n167 997 12\n168 19 44\n168 27 20\n168 59 49\n168 76 40\n168 81 15\n168 98 4\n168 103 28\n168 181 28\n168 197 38\n168 223 18\n168 279 43\n168 292 19\n168 303 14\n168 305 -2\n168 332 49\n168 340 45\n168 377 35\n168 378 19\n168 400 45\n168 459 47\n168 496 15\n168 517 49\n168 521 13\n168 548 19\n168 564 22\n168 602 18\n168 624 10\n168 642 18\n168 656 8\n168 666 8\n168 674 2\n168 679 21\n168 709 41\n168 719 9\n168 734 17\n168 797 2\n168 807 49\n168 823 37\n168 864 15\n168 872 13\n168 879 26\n168 897 16\n168 901 14\n168 908 13\n168 921 33\n168 923 33\n168 931 9\n168 950 33\n168 977 11\n168 979 12\n168 991 0\n169 28 19\n169 33 10\n169 86 37\n169 91 34\n169 101 38\n169 113 37\n169 129 -1\n169 143 -2\n169 149 14\n169 156 32\n169 162 9\n169 168 11\n169 204 21\n169 243 25\n169 253 46\n169 286 28\n169 287 26\n169 292 35\n169 300 15\n169 306 34\n169 326 38\n169 332 35\n169 335 26\n169 361 35\n169 468 21\n169 478 26\n169 525 40\n169 530 15\n169 561 44\n169 567 17\n169 573 41\n169 574 44\n169 591 46\n169 594 25\n169 690 15\n169 708 32\n169 749 46\n169 756 24\n169 760 42\n169 761 10\n169 779 6\n169 812 29\n169 926 28\n169 929 49\n169 944 13\n169 956 42\n169 959 15\n169 990 3\n169 995 33\n170 34 36\n170 55 17\n170 88 13\n170 105 8\n170 111 21\n170 130 15\n170 145 10\n170 243 31\n170 310 6\n170 323 7\n170 328 38\n170 346 26\n170 405 20\n170 410 41\n170 444 39\n170 455 9\n170 462 10\n170 465 8\n170 496 39\n170 514 27\n170 526 43\n170 527 20\n170 535 9\n170 543 10\n170 570 35\n170 583 36\n170 598 45\n170 611 39\n170 612 46\n170 622 27\n170 649 27\n170 663 20\n170 677 42\n170 680 35\n170 681 30\n170 692 36\n170 733 23\n170 745 8\n170 768 30\n170 787 49\n170 812 50\n170 823 6\n170 845 17\n170 848 47\n170 877 30\n170 930 25\n170 940 17\n170 976 12\n171 26 33\n171 36 42\n171 103 46\n171 119 -2\n171 146 27\n171 150 -1\n171 175 19\n171 177 24\n171 201 28\n171 203 21\n171 233 0\n171 248 38\n171 287 44\n171 295 10\n171 338 40\n171 370 39\n171 395 45\n171 416 20\n171 431 47\n171 432 5\n171 439 17\n171 451 37\n171 460 13\n171 464 30\n171 467 10\n171 470 27\n171 477 0\n171 483 2\n171 485 30\n171 486 31\n171 509 7\n171 517 11\n171 521 36\n171 529 40\n171 531 9\n171 554 21\n171 574 39\n171 590 38\n171 622 28\n171 626 46\n171 634 45\n171 673 19\n171 689 23\n171 697 32\n171 710 0\n171 730 1\n171 816 3\n171 817 46\n171 829 40\n171 835 47\n171 852 48\n171 853 9\n171 856 27\n171 931 25\n171 939 48\n171 940 49\n171 949 40\n171 961 37\n171 986 45\n171 995 34\n171 997 31\n172 6 -2\n172 31 -1\n172 32 32\n172 56 22\n172 75 41\n172 90 1\n172 91 17\n172 102 39\n172 128 14\n172 151 21\n172 161 30\n172 188 9\n172 194 41\n172 225 47\n172 265 -2\n172 284 43\n172 330 8\n172 335 42\n172 387 12\n172 391 7\n172 397 -2\n172 418 28\n172 461 24\n172 474 48\n172 485 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46\n179 617 28\n179 637 49\n179 639 50\n179 645 0\n179 646 27\n179 650 27\n179 652 36\n179 793 42\n179 794 29\n179 811 6\n179 823 15\n179 842 34\n179 861 46\n179 898 4\n179 907 36\n179 986 19\n179 1000 30\n180 6 49\n180 12 45\n180 37 13\n180 42 13\n180 53 48\n180 75 18\n180 87 28\n180 133 32\n180 145 36\n180 153 27\n180 174 28\n180 178 10\n180 216 11\n180 253 7\n180 261 31\n180 272 46\n180 291 36\n180 304 46\n180 332 13\n180 334 29\n180 344 47\n180 379 44\n180 463 20\n180 496 11\n180 555 9\n180 575 48\n180 605 44\n180 611 13\n180 627 29\n180 648 50\n180 656 35\n180 688 25\n180 705 36\n180 731 27\n180 751 49\n180 757 46\n180 804 24\n180 835 37\n180 870 35\n180 874 12\n180 883 16\n180 890 35\n180 901 47\n180 913 47\n180 943 44\n180 953 22\n181 28 7\n181 50 8\n181 76 38\n181 88 33\n181 107 10\n181 117 5\n181 118 43\n181 234 20\n181 304 15\n181 310 4\n181 318 47\n181 337 32\n181 359 24\n181 372 -2\n181 376 49\n181 378 1\n181 396 23\n181 399 7\n181 410 24\n181 427 13\n181 468 1\n181 492 32\n181 494 -1\n181 677 40\n181 719 43\n181 801 24\n181 803 25\n181 825 24\n181 834 6\n181 835 0\n181 848 12\n181 869 37\n181 911 1\n181 925 20\n181 990 38\n182 27 14\n182 32 11\n182 58 22\n182 67 12\n182 85 7\n182 96 50\n182 108 44\n182 175 1\n182 184 7\n182 196 22\n182 213 46\n182 217 7\n182 246 37\n182 247 29\n182 265 4\n182 314 11\n182 318 4\n182 321 31\n182 330 40\n182 339 2\n182 378 44\n182 402 47\n182 422 25\n182 452 28\n182 455 27\n182 459 25\n182 463 20\n182 527 6\n182 551 0\n182 554 49\n182 588 15\n182 674 17\n182 686 40\n182 691 3\n182 701 36\n182 705 23\n182 725 26\n182 748 39\n182 774 9\n182 801 29\n182 828 13\n182 864 8\n182 878 33\n182 882 7\n182 906 31\n182 924 48\n182 960 44\n182 962 1\n183 18 15\n183 22 10\n183 25 14\n183 40 23\n183 47 9\n183 83 8\n183 126 22\n183 160 3\n183 176 20\n183 217 38\n183 220 42\n183 248 14\n183 266 2\n183 267 7\n183 281 41\n183 285 24\n183 289 37\n183 291 50\n183 347 20\n183 364 41\n183 378 24\n183 402 5\n183 414 45\n183 420 47\n183 458 42\n183 466 11\n183 472 37\n183 476 19\n183 490 9\n183 512 26\n183 518 25\n183 604 17\n183 607 28\n183 613 10\n183 643 11\n183 645 17\n183 647 16\n183 723 1\n183 760 22\n183 764 36\n183 803 -2\n183 859 15\n183 872 21\n183 878 47\n183 889 32\n183 935 19\n183 937 7\n183 953 44\n183 973 16\n184 16 43\n184 39 6\n184 65 4\n184 66 0\n184 74 39\n184 100 4\n184 103 1\n184 128 2\n184 153 40\n184 154 36\n184 165 7\n184 171 -2\n184 189 18\n184 199 4\n184 206 -1\n184 218 46\n184 222 17\n184 243 15\n184 248 0\n184 254 18\n184 309 48\n184 321 27\n184 322 6\n184 347 44\n184 355 28\n184 378 4\n184 418 36\n184 432 6\n184 452 23\n184 490 27\n184 595 20\n184 597 16\n184 606 25\n184 615 34\n184 673 45\n184 692 36\n184 697 17\n184 716 4\n184 721 36\n184 725 33\n184 736 16\n184 753 12\n184 813 26\n184 867 0\n184 873 4\n184 907 5\n184 948 46\n184 953 10\n184 966 47\n184 975 4\n184 994 16\n185 4 36\n185 8 45\n185 20 3\n185 25 25\n185 27 24\n185 66 20\n185 75 10\n185 83 12\n185 88 0\n185 159 19\n185 167 12\n185 171 16\n185 172 7\n185 201 -1\n185 224 18\n185 238 3\n185 258 36\n185 274 27\n185 344 49\n185 391 14\n185 398 1\n185 425 18\n185 428 33\n185 438 24\n185 456 30\n185 492 38\n185 498 17\n185 503 42\n185 504 7\n185 569 32\n185 586 42\n185 593 4\n185 605 19\n185 620 17\n185 628 45\n185 646 15\n185 663 34\n185 692 29\n185 718 17\n185 767 30\n185 778 31\n185 807 14\n185 823 45\n185 838 41\n185 893 44\n185 909 49\n185 935 28\n185 968 27\n185 971 18\n186 7 12\n186 28 14\n186 34 34\n186 35 36\n186 61 29\n186 88 17\n186 98 22\n186 141 18\n186 148 27\n186 215 26\n186 232 24\n186 255 12\n186 278 45\n186 282 25\n186 288 45\n186 291 33\n186 318 7\n186 345 8\n186 346 46\n186 347 2\n186 371 26\n186 403 35\n186 446 24\n186 508 28\n186 519 15\n186 537 45\n186 565 40\n186 597 18\n186 612 33\n186 620 29\n186 669 0\n186 701 45\n186 707 31\n186 749 17\n186 793 -1\n186 795 4\n186 839 6\n186 858 8\n186 861 34\n186 873 31\n186 917 1\n186 924 6\n186 926 46\n186 992 21\n187 13 -2\n187 38 23\n187 48 32\n187 54 3\n187 56 50\n187 59 27\n187 84 47\n187 106 8\n187 109 39\n187 149 21\n187 178 49\n187 182 36\n187 208 30\n187 220 14\n187 225 8\n187 232 40\n187 263 29\n187 277 36\n187 302 25\n187 310 7\n187 387 17\n187 389 43\n187 396 48\n187 467 41\n187 487 12\n187 508 45\n187 519 -2\n187 535 42\n187 546 38\n187 584 8\n187 597 24\n187 598 50\n187 645 36\n187 722 2\n187 763 16\n187 783 9\n187 798 28\n187 799 34\n187 804 47\n187 810 40\n187 817 45\n187 837 25\n187 844 49\n187 856 2\n187 874 1\n187 883 50\n187 915 29\n187 945 43\n187 947 12\n187 984 5\n187 986 4\n188 31 37\n188 36 40\n188 58 45\n188 87 4\n188 93 41\n188 156 29\n188 163 35\n188 173 42\n188 207 26\n188 213 31\n188 226 18\n188 230 32\n188 231 8\n188 262 12\n188 281 29\n188 286 13\n188 289 22\n188 337 15\n188 354 44\n188 361 27\n188 368 1\n188 408 15\n188 456 31\n188 469 25\n188 474 7\n188 506 13\n188 554 40\n188 576 29\n188 580 44\n188 607 7\n188 618 27\n188 647 49\n188 657 41\n188 663 32\n188 676 7\n188 677 21\n188 696 29\n188 714 18\n188 736 33\n188 747 41\n188 775 11\n188 779 18\n188 780 20\n188 785 10\n188 865 -2\n188 918 44\n188 930 35\n188 966 40\n188 968 0\n188 989 -2\n188 995 39\n189 12 14\n189 34 26\n189 42 1\n189 92 18\n189 96 41\n189 110 42\n189 112 34\n189 116 20\n189 117 44\n189 119 39\n189 145 43\n189 249 22\n189 255 16\n189 258 0\n189 268 22\n189 277 32\n189 290 39\n189 297 14\n189 361 9\n189 404 43\n189 410 41\n189 419 35\n189 460 26\n189 472 45\n189 473 10\n189 490 32\n189 506 46\n189 509 29\n189 536 25\n189 599 47\n189 605 40\n189 615 33\n189 638 34\n189 681 25\n189 731 39\n189 738 31\n189 741 46\n189 767 43\n189 770 28\n189 799 45\n189 800 37\n189 810 16\n189 843 50\n189 895 3\n189 904 48\n189 917 33\n190 6 20\n190 18 1\n190 30 14\n190 45 49\n190 90 15\n190 94 28\n190 145 32\n190 151 34\n190 188 12\n190 207 23\n190 227 29\n190 248 12\n190 312 2\n190 325 32\n190 327 15\n190 338 7\n190 386 19\n190 401 0\n190 408 8\n190 413 27\n190 425 6\n190 426 5\n190 459 4\n190 473 15\n190 492 37\n190 493 12\n190 548 31\n190 572 42\n190 581 45\n190 595 16\n190 596 24\n190 669 41\n190 670 19\n190 693 48\n190 719 18\n190 728 26\n190 732 44\n190 736 5\n190 750 -1\n190 763 0\n190 769 1\n190 864 1\n190 894 15\n190 903 18\n190 907 31\n190 915 0\n190 959 48\n190 961 40\n190 964 33\n190 966 6\n190 985 29\n191 15 27\n191 25 40\n191 32 33\n191 41 20\n191 60 0\n191 64 27\n191 67 19\n191 94 39\n191 134 28\n191 148 38\n191 150 42\n191 161 5\n191 168 48\n191 188 29\n191 198 -1\n191 208 49\n191 251 28\n191 254 36\n191 259 14\n191 280 18\n191 282 43\n191 322 24\n191 332 6\n191 336 5\n191 349 21\n191 355 13\n191 356 17\n191 387 47\n191 436 30\n191 458 27\n191 489 6\n191 499 10\n191 500 43\n191 525 21\n191 530 33\n191 584 22\n191 587 37\n191 594 2\n191 596 7\n191 636 17\n191 679 34\n191 685 46\n191 706 20\n191 733 6\n191 748 6\n191 753 29\n191 785 9\n191 814 9\n191 817 20\n191 877 50\n191 885 9\n191 944 6\n191 965 14\n191 999 8\n192 6 42\n192 23 47\n192 26 33\n192 27 31\n192 89 29\n192 100 12\n192 101 10\n192 108 35\n192 149 29\n192 161 5\n192 266 28\n192 292 13\n192 314 18\n192 367 30\n192 368 39\n192 381 49\n192 382 7\n192 386 49\n192 401 3\n192 436 5\n192 439 -1\n192 440 27\n192 458 1\n192 469 16\n192 492 39\n192 556 34\n192 571 10\n192 585 44\n192 639 4\n192 667 42\n192 675 36\n192 682 49\n192 718 36\n192 735 21\n192 754 -2\n192 789 22\n192 796 35\n192 841 33\n192 848 9\n192 857 50\n192 867 3\n192 877 36\n192 919 22\n192 925 38\n192 929 48\n192 931 11\n192 937 21\n192 939 34\n192 952 0\n193 7 35\n193 58 16\n193 60 6\n193 104 28\n193 138 35\n193 164 -2\n193 182 30\n193 204 32\n193 205 6\n193 206 1\n193 207 43\n193 214 44\n193 222 17\n193 234 31\n193 247 24\n193 265 38\n193 270 42\n193 280 24\n193 284 27\n193 300 38\n193 311 34\n193 317 28\n193 319 4\n193 352 9\n193 362 47\n193 406 39\n193 431 33\n193 441 1\n193 494 13\n193 503 -1\n193 554 34\n193 556 47\n193 557 25\n193 585 20\n193 726 8\n193 732 39\n193 751 11\n193 761 8\n193 780 28\n193 785 36\n193 821 49\n193 834 50\n193 845 44\n193 879 4\n193 880 47\n193 912 23\n193 927 34\n193 938 41\n193 973 44\n193 990 27\n194 9 12\n194 10 46\n194 29 16\n194 41 43\n194 46 -1\n194 53 24\n194 115 6\n194 119 36\n194 134 35\n194 165 9\n194 168 27\n194 178 12\n194 186 16\n194 187 6\n194 188 42\n194 189 39\n194 207 7\n194 227 6\n194 239 1\n194 252 24\n194 268 45\n194 325 20\n194 344 38\n194 376 14\n194 381 6\n194 398 43\n194 418 48\n194 424 48\n194 441 48\n194 444 18\n194 467 14\n194 498 33\n194 507 3\n194 525 43\n194 526 34\n194 558 28\n194 571 32\n194 576 10\n194 577 40\n194 615 19\n194 625 21\n194 632 28\n194 637 42\n194 692 29\n194 712 22\n194 741 40\n194 743 49\n194 809 11\n194 826 18\n194 854 44\n194 870 34\n194 882 14\n194 917 9\n194 934 23\n194 936 49\n194 946 6\n194 953 2\n195 1 36\n195 23 46\n195 54 16\n195 114 28\n195 151 14\n195 153 11\n195 181 14\n195 184 29\n195 194 30\n195 199 2\n195 232 49\n195 253 32\n195 331 43\n195 381 45\n195 383 1\n195 435 50\n195 458 26\n195 546 49\n195 587 48\n195 622 13\n195 647 8\n195 649 21\n195 655 32\n195 672 32\n195 688 35\n195 731 34\n195 746 31\n195 755 19\n195 787 22\n195 870 11\n195 874 37\n196 33 35\n196 55 44\n196 74 19\n196 96 26\n196 104 5\n196 110 25\n196 124 21\n196 165 34\n196 168 44\n196 180 20\n196 220 8\n196 256 48\n196 266 43\n196 270 13\n196 286 19\n196 337 18\n196 347 25\n196 357 33\n196 359 49\n196 371 7\n196 376 4\n196 398 34\n196 419 39\n196 452 40\n196 465 40\n196 483 8\n196 517 21\n196 548 37\n196 599 8\n196 615 0\n196 636 5\n196 669 4\n196 693 45\n196 719 45\n196 733 27\n196 744 42\n196 748 36\n196 754 37\n196 767 10\n196 780 14\n196 793 36\n196 816 24\n196 832 49\n196 836 22\n196 846 8\n196 848 40\n196 870 41\n196 890 50\n196 897 50\n196 904 36\n196 929 26\n196 940 27\n196 987 11\n197 12 32\n197 16 48\n197 23 9\n197 24 19\n197 36 33\n197 81 4\n197 103 30\n197 106 38\n197 146 3\n197 156 47\n197 166 19\n197 169 20\n197 201 24\n197 207 26\n197 218 4\n197 247 -2\n197 284 26\n197 287 20\n197 288 16\n197 320 9\n197 339 33\n197 355 11\n197 391 27\n197 403 0\n197 430 2\n197 450 36\n197 470 40\n197 477 12\n197 485 13\n197 489 14\n197 507 9\n197 537 10\n197 565 5\n197 581 20\n197 618 20\n197 647 13\n197 652 31\n197 654 37\n197 659 35\n197 681 16\n197 699 0\n197 722 20\n197 734 32\n197 764 -1\n197 784 1\n197 818 16\n197 828 33\n197 848 27\n197 859 6\n197 871 45\n197 872 3\n197 913 22\n197 915 42\n197 924 38\n197 931 2\n197 973 47\n197 975 43\n198 19 24\n198 59 34\n198 119 46\n198 156 10\n198 184 38\n198 255 18\n198 278 8\n198 331 9\n198 341 43\n198 353 37\n198 359 38\n198 376 29\n198 412 5\n198 439 25\n198 472 50\n198 485 26\n198 495 12\n198 500 -2\n198 559 43\n198 624 18\n198 627 16\n198 636 32\n198 646 35\n198 661 38\n198 683 32\n198 702 4\n198 705 24\n198 720 50\n198 726 19\n198 779 39\n198 838 40\n198 856 7\n198 883 3\n198 964 40\n198 996 31\n199 3 8\n199 19 15\n199 34 7\n199 36 12\n199 47 5\n199 52 20\n199 53 17\n199 104 26\n199 218 17\n199 222 5\n199 248 17\n199 278 19\n199 282 22\n199 297 41\n199 310 7\n199 335 42\n199 339 33\n199 366 19\n199 372 11\n199 382 1\n199 411 42\n199 438 19\n199 442 18\n199 465 18\n199 498 31\n199 500 1\n199 514 18\n199 525 32\n199 542 30\n199 574 10\n199 603 1\n199 622 3\n199 657 35\n199 664 20\n199 702 46\n199 735 40\n199 761 45\n199 772 27\n199 800 47\n199 817 32\n199 825 17\n199 841 15\n199 849 44\n199 864 48\n199 866 19\n199 870 10\n199 880 43\n199 895 49\n199 906 40\n199 955 32\n199 962 37\n199 970 35\n200 21 18\n200 46 30\n200 70 24\n200 79 -2\n200 89 15\n200 95 32\n200 99 34\n200 116 24\n200 132 11\n200 155 13\n200 161 9\n200 166 33\n200 173 3\n200 179 13\n200 191 22\n200 203 32\n200 212 19\n200 222 20\n200 223 2\n200 228 46\n200 237 49\n200 258 33\n200 273 33\n200 280 14\n200 295 3\n200 308 44\n200 334 34\n200 340 22\n200 357 21\n200 358 2\n200 407 6\n200 415 41\n200 423 15\n200 454 22\n200 466 42\n200 485 10\n200 525 49\n200 533 0\n200 541 16\n200 608 7\n200 668 32\n200 670 17\n200 683 35\n200 693 13\n200 702 41\n200 719 4\n200 743 7\n200 744 14\n200 746 33\n200 757 33\n200 763 18\n200 769 25\n200 807 14\n200 864 25\n200 868 19\n200 871 34\n200 882 13\n200 911 38\n200 921 24\n200 939 44\n200 947 15\n200 974 37\n200 999 3\n201 3 31\n201 7 20\n201 18 30\n201 30 5\n201 55 15\n201 57 49\n201 66 14\n201 124 21\n201 158 21\n201 179 25\n201 209 24\n201 216 0\n201 222 4\n201 245 36\n201 261 10\n201 268 50\n201 290 38\n201 295 20\n201 366 41\n201 390 10\n201 414 1\n201 459 12\n201 461 9\n201 462 3\n201 483 40\n201 507 33\n201 512 0\n201 516 48\n201 572 8\n201 594 35\n201 606 22\n201 619 5\n201 707 38\n201 708 17\n201 736 41\n201 744 33\n201 780 23\n201 807 28\n201 832 7\n201 835 7\n201 837 25\n201 853 1\n201 868 1\n201 871 7\n201 873 9\n201 897 -2\n201 907 28\n201 964 15\n201 971 21\n201 989 -2\n202 6 24\n202 9 25\n202 13 9\n202 66 49\n202 68 -1\n202 76 4\n202 122 49\n202 126 17\n202 156 22\n202 182 48\n202 183 10\n202 187 43\n202 208 31\n202 222 36\n202 238 4\n202 248 43\n202 253 1\n202 256 36\n202 259 13\n202 263 25\n202 282 37\n202 302 24\n202 313 4\n202 317 24\n202 345 2\n202 356 31\n202 408 22\n202 416 19\n202 424 41\n202 440 35\n202 442 24\n202 449 33\n202 485 33\n202 492 10\n202 537 18\n202 544 1\n202 554 9\n202 566 26\n202 575 29\n202 588 9\n202 594 44\n202 600 24\n202 621 4\n202 675 7\n202 676 17\n202 692 23\n202 693 22\n202 699 26\n202 721 4\n202 750 47\n202 765 24\n202 844 21\n202 871 13\n202 933 32\n202 976 36\n202 992 17\n203 56 26\n203 62 24\n203 68 27\n203 70 39\n203 87 31\n203 118 31\n203 127 35\n203 200 44\n203 211 39\n203 224 35\n203 274 46\n203 275 21\n203 313 49\n203 315 15\n203 327 27\n203 329 39\n203 388 33\n203 392 47\n203 447 8\n203 472 14\n203 476 33\n203 500 33\n203 501 19\n203 517 11\n203 546 34\n203 549 42\n203 562 33\n203 564 7\n203 566 7\n203 584 35\n203 589 27\n203 590 42\n203 597 37\n203 626 41\n203 643 36\n203 650 30\n203 652 45\n203 743 6\n203 750 32\n203 790 3\n203 815 5\n203 835 42\n203 846 26\n203 895 5\n203 902 8\n203 905 20\n203 908 18\n203 927 9\n203 932 43\n203 950 47\n203 983 40\n203 984 31\n204 42 12\n204 57 47\n204 58 11\n204 69 26\n204 71 45\n204 107 6\n204 108 -2\n204 126 1\n204 131 5\n204 133 46\n204 140 33\n204 145 10\n204 149 9\n204 150 39\n204 169 46\n204 176 46\n204 180 8\n204 188 39\n204 194 5\n204 199 15\n204 206 19\n204 213 9\n204 236 19\n204 251 -2\n204 256 48\n204 274 14\n204 281 36\n204 300 18\n204 318 2\n204 333 -1\n204 364 41\n204 381 25\n204 458 11\n204 475 -2\n204 493 11\n204 508 29\n204 523 44\n204 541 31\n204 547 31\n204 567 16\n204 591 43\n204 624 6\n204 667 23\n204 669 26\n204 674 29\n204 697 5\n204 702 19\n204 738 39\n204 779 15\n204 780 31\n204 788 -2\n204 805 35\n204 813 18\n204 823 43\n204 850 2\n204 868 11\n204 872 47\n204 903 7\n204 946 32\n204 956 25\n204 980 27\n204 990 11\n204 992 29\n205 5 -2\n205 18 10\n205 35 11\n205 55 18\n205 97 2\n205 108 49\n205 109 12\n205 152 33\n205 181 41\n205 185 49\n205 254 19\n205 293 16\n205 326 40\n205 335 36\n205 338 22\n205 353 44\n205 372 41\n205 412 44\n205 442 47\n205 459 16\n205 562 15\n205 581 34\n205 592 19\n205 596 11\n205 602 42\n205 612 11\n205 656 41\n205 740 14\n205 751 43\n205 778 42\n205 784 28\n205 786 36\n205 826 21\n205 837 32\n205 865 37\n205 867 17\n205 869 13\n205 900 49\n205 935 44\n205 939 0\n205 954 38\n205 987 46\n206 6 47\n206 28 45\n206 46 5\n206 80 22\n206 134 26\n206 158 26\n206 204 31\n206 218 29\n206 230 47\n206 254 44\n206 278 9\n206 287 15\n206 336 15\n206 337 15\n206 346 47\n206 378 44\n206 385 24\n206 395 43\n206 406 26\n206 407 22\n206 415 25\n206 419 48\n206 466 39\n206 478 38\n206 526 25\n206 539 42\n206 552 2\n206 572 11\n206 594 50\n206 598 24\n206 653 43\n206 667 8\n206 672 48\n206 675 49\n206 678 34\n206 702 32\n206 748 50\n206 778 14\n206 803 26\n206 838 35\n206 863 14\n206 880 45\n206 903 7\n206 939 49\n206 947 20\n206 970 46\n206 999 20\n207 22 41\n207 23 10\n207 27 27\n207 43 48\n207 45 15\n207 48 50\n207 107 25\n207 120 10\n207 198 35\n207 212 44\n207 217 34\n207 224 34\n207 247 30\n207 278 18\n207 283 42\n207 303 16\n207 370 26\n207 388 31\n207 411 9\n207 424 12\n207 453 47\n207 495 50\n207 502 43\n207 506 11\n207 528 8\n207 556 31\n207 598 37\n207 638 50\n207 654 9\n207 733 30\n207 734 34\n207 738 2\n207 779 42\n207 789 10\n207 804 24\n207 819 8\n207 820 39\n207 847 37\n207 874 36\n207 878 7\n207 882 6\n207 917 25\n207 921 31\n207 929 24\n207 982 23\n207 991 15\n208 1 34\n208 44 13\n208 59 17\n208 89 40\n208 105 13\n208 158 -2\n208 162 3\n208 184 39\n208 189 18\n208 201 47\n208 237 8\n208 277 47\n208 289 31\n208 307 23\n208 341 33\n208 425 45\n208 458 20\n208 515 21\n208 560 20\n208 606 45\n208 624 39\n208 626 8\n208 710 38\n208 714 26\n208 722 9\n208 730 13\n208 760 2\n208 823 30\n208 842 -2\n208 845 17\n208 863 39\n208 889 15\n208 945 48\n208 995 39\n209 2 50\n209 13 -1\n209 85 19\n209 93 31\n209 122 42\n209 127 20\n209 140 31\n209 147 50\n209 162 -2\n209 174 0\n209 185 3\n209 188 1\n209 195 11\n209 223 1\n209 226 5\n209 233 17\n209 256 38\n209 306 15\n209 309 7\n209 331 26\n209 332 36\n209 344 14\n209 353 16\n209 388 31\n209 393 25\n209 408 30\n209 427 26\n209 459 39\n209 505 44\n209 517 3\n209 557 28\n209 586 50\n209 641 39\n209 673 33\n209 696 31\n209 737 39\n209 768 48\n209 786 36\n209 853 8\n209 864 40\n209 866 14\n209 876 16\n209 900 8\n209 903 5\n209 966 25\n209 970 9\n209 980 26\n209 988 6\n210 14 8\n210 25 37\n210 46 45\n210 64 22\n210 65 48\n210 86 23\n210 102 45\n210 107 -2\n210 112 17\n210 155 45\n210 162 39\n210 180 41\n210 195 6\n210 209 24\n210 345 -1\n210 349 48\n210 350 5\n210 365 14\n210 375 -1\n210 401 9\n210 439 13\n210 502 43\n210 534 28\n210 545 14\n210 574 3\n210 590 4\n210 610 4\n210 655 48\n210 679 39\n210 761 50\n210 767 13\n210 773 24\n210 777 41\n210 793 41\n210 842 4\n210 844 26\n210 851 44\n210 868 29\n210 884 13\n210 918 14\n210 921 16\n210 945 -2\n210 955 3\n210 959 20\n210 961 6\n210 964 44\n210 999 3\n210 1000 46\n211 2 34\n211 3 49\n211 7 18\n211 14 41\n211 23 47\n211 35 0\n211 103 31\n211 153 29\n211 194 7\n211 201 39\n211 217 49\n211 243 47\n211 249 37\n211 279 -1\n211 288 1\n211 302 32\n211 351 33\n211 383 3\n211 400 46\n211 405 0\n211 459 42\n211 557 25\n211 573 15\n211 583 16\n211 616 25\n211 647 -1\n211 648 0\n211 739 33\n211 758 16\n211 792 11\n211 799 44\n211 800 5\n211 809 40\n211 823 18\n211 873 9\n211 920 38\n211 929 42\n211 933 40\n211 947 3\n211 949 24\n211 953 23\n211 973 37\n212 14 32\n212 36 19\n212 37 36\n212 69 9\n212 113 5\n212 114 32\n212 123 22\n212 141 9\n212 206 12\n212 233 16\n212 243 48\n212 275 5\n212 330 37\n212 389 8\n212 402 31\n212 413 12\n212 425 14\n212 456 23\n212 483 14\n212 490 41\n212 502 26\n212 528 23\n212 530 34\n212 580 50\n212 594 49\n212 601 11\n212 615 33\n212 640 29\n212 649 43\n212 685 49\n212 698 24\n212 701 24\n212 712 23\n212 726 13\n212 751 44\n212 917 9\n212 940 31\n212 942 2\n212 964 28\n212 968 7\n213 1 35\n213 9 29\n213 12 47\n213 36 29\n213 83 42\n213 107 15\n213 144 18\n213 173 37\n213 205 42\n213 211 37\n213 239 40\n213 241 13\n213 248 24\n213 271 5\n213 275 48\n213 276 22\n213 280 26\n213 291 10\n213 366 41\n213 378 27\n213 380 44\n213 393 29\n213 403 14\n213 404 49\n213 424 36\n213 441 29\n213 445 49\n213 482 4\n213 493 38\n213 504 43\n213 548 15\n213 567 24\n213 579 45\n213 596 32\n213 603 12\n213 621 14\n213 697 22\n213 717 24\n213 803 13\n213 808 36\n213 809 19\n213 811 33\n213 861 15\n213 884 32\n213 887 18\n213 911 47\n213 930 34\n213 934 35\n213 937 41\n213 951 29\n213 982 24\n213 988 44\n213 992 18\n214 17 42\n214 36 50\n214 37 44\n214 50 -1\n214 74 34\n214 112 16\n214 116 40\n214 134 2\n214 135 14\n214 156 26\n214 188 3\n214 225 -1\n214 229 9\n214 256 36\n214 285 30\n214 296 9\n214 298 19\n214 316 47\n214 324 48\n214 326 46\n214 328 21\n214 339 33\n214 352 3\n214 374 -1\n214 375 39\n214 376 43\n214 429 45\n214 460 32\n214 477 0\n214 494 10\n214 516 21\n214 544 -2\n214 567 34\n214 631 7\n214 632 13\n214 665 1\n214 678 38\n214 679 5\n214 682 21\n214 809 -1\n214 858 41\n214 868 18\n214 892 45\n214 896 11\n214 900 17\n214 907 -2\n214 910 47\n214 932 27\n214 952 14\n214 963 37\n215 32 34\n215 46 45\n215 51 40\n215 62 29\n215 70 41\n215 87 31\n215 114 37\n215 154 38\n215 207 26\n215 208 27\n215 214 38\n215 259 0\n215 300 26\n215 345 45\n215 353 34\n215 363 46\n215 369 41\n215 377 6\n215 398 36\n215 413 35\n215 418 47\n215 425 30\n215 447 11\n215 470 16\n215 519 2\n215 527 45\n215 545 30\n215 560 32\n215 562 49\n215 617 27\n215 619 14\n215 646 15\n215 650 50\n215 669 46\n215 682 35\n215 735 14\n215 754 -1\n215 783 19\n215 809 43\n215 833 42\n215 836 22\n215 850 36\n215 885 28\n215 886 46\n215 895 18\n215 899 6\n215 919 40\n215 982 8\n216 6 25\n216 18 50\n216 50 -1\n216 61 28\n216 87 45\n216 89 3\n216 96 48\n216 139 41\n216 165 -2\n216 195 39\n216 248 42\n216 283 26\n216 294 15\n216 295 12\n216 303 19\n216 421 10\n216 432 50\n216 462 -1\n216 463 45\n216 478 32\n216 485 35\n216 506 28\n216 527 9\n216 543 32\n216 549 22\n216 577 6\n216 600 10\n216 658 27\n216 697 29\n216 718 16\n216 729 17\n216 762 46\n216 785 31\n216 809 23\n216 824 31\n216 848 7\n216 904 18\n216 927 19\n216 942 -1\n216 957 33\n216 973 35\n216 988 20\n216 992 15\n217 7 50\n217 91 38\n217 98 5\n217 108 28\n217 111 10\n217 112 13\n217 124 21\n217 125 35\n217 141 4\n217 144 8\n217 242 14\n217 252 14\n217 266 48\n217 273 23\n217 313 42\n217 354 16\n217 391 23\n217 402 7\n217 404 46\n217 443 3\n217 472 13\n217 475 50\n217 494 33\n217 502 36\n217 521 11\n217 525 32\n217 565 48\n217 581 33\n217 612 4\n217 618 23\n217 641 25\n217 656 29\n217 667 34\n217 684 36\n217 692 15\n217 708 43\n217 709 40\n217 716 21\n217 719 49\n217 727 10\n217 780 14\n217 808 48\n217 809 6\n217 814 21\n217 827 42\n217 868 8\n217 882 48\n217 909 47\n217 911 1\n217 930 3\n217 943 20\n217 949 3\n217 958 3\n217 987 31\n218 7 -2\n218 30 30\n218 32 4\n218 55 30\n218 156 2\n218 255 -1\n218 258 24\n218 268 15\n218 303 27\n218 326 40\n218 337 13\n218 374 42\n218 477 42\n218 488 47\n218 490 14\n218 597 24\n218 616 10\n218 656 20\n218 659 -2\n218 666 40\n218 680 11\n218 683 20\n218 702 25\n218 709 0\n218 717 33\n218 794 25\n218 808 47\n218 844 9\n218 859 36\n218 877 36\n218 898 36\n218 901 0\n218 914 32\n218 922 48\n218 938 39\n218 970 27\n218 972 24\n218 997 14\n219 61 18\n219 77 6\n219 81 47\n219 146 45\n219 175 9\n219 209 12\n219 240 36\n219 255 10\n219 269 15\n219 310 1\n219 336 22\n219 364 21\n219 372 24\n219 381 23\n219 413 36\n219 467 13\n219 489 20\n219 531 46\n219 539 41\n219 540 1\n219 547 39\n219 559 29\n219 583 43\n219 596 17\n219 608 25\n219 619 27\n219 644 18\n219 673 50\n219 713 44\n219 735 19\n219 740 8\n219 771 33\n219 773 41\n219 778 29\n219 793 12\n219 800 34\n219 810 50\n219 820 15\n219 843 26\n219 861 16\n219 875 50\n219 881 1\n219 905 39\n219 914 42\n219 917 41\n219 923 12\n219 935 16\n219 939 43\n219 967 45\n219 976 37\n219 983 39\n220 28 28\n220 46 29\n220 49 8\n220 88 26\n220 107 17\n220 130 38\n220 133 10\n220 176 17\n220 201 12\n220 226 24\n220 239 48\n220 253 31\n220 294 33\n220 302 5\n220 317 36\n220 343 19\n220 355 21\n220 380 28\n220 399 42\n220 401 3\n220 446 15\n220 487 34\n220 534 31\n220 543 39\n220 544 28\n220 572 8\n220 633 31\n220 695 34\n220 700 6\n220 712 50\n220 720 33\n220 736 35\n220 738 10\n220 740 28\n220 772 5\n220 783 8\n220 799 12\n220 803 10\n220 805 34\n220 813 22\n220 825 38\n220 892 36\n220 934 49\n220 952 15\n220 991 21\n221 43 49\n221 76 34\n221 105 41\n221 235 2\n221 395 3\n221 432 6\n221 440 35\n221 451 28\n221 468 36\n221 474 41\n221 482 29\n221 503 1\n221 570 30\n221 583 42\n221 585 8\n221 602 37\n221 605 17\n221 606 11\n221 617 40\n221 633 34\n221 653 25\n221 669 4\n221 679 44\n221 710 24\n221 725 30\n221 747 50\n221 748 19\n221 753 29\n221 833 18\n221 864 8\n221 867 15\n221 888 15\n221 891 49\n221 940 36\n221 950 42\n221 960 48\n222 15 28\n222 22 29\n222 55 17\n222 72 22\n222 78 12\n222 167 15\n222 183 25\n222 203 23\n222 237 11\n222 260 14\n222 277 48\n222 325 30\n222 335 24\n222 340 34\n222 348 43\n222 380 15\n222 382 48\n222 388 1\n222 400 22\n222 421 3\n222 424 49\n222 427 41\n222 455 15\n222 478 20\n222 489 12\n222 495 30\n222 501 17\n222 524 44\n222 528 11\n222 543 30\n222 553 32\n222 560 31\n222 568 24\n222 577 39\n222 584 36\n222 605 33\n222 612 -1\n222 614 26\n222 666 23\n222 668 44\n222 669 -2\n222 686 17\n222 718 50\n222 743 6\n222 749 16\n222 757 39\n222 789 46\n222 791 26\n222 815 37\n222 819 48\n222 872 29\n222 891 11\n222 915 35\n222 923 35\n222 935 18\n223 23 30\n223 57 21\n223 62 50\n223 139 10\n223 189 36\n223 208 23\n223 269 24\n223 294 32\n223 333 7\n223 340 42\n223 390 36\n223 451 29\n223 483 25\n223 507 47\n223 542 15\n223 544 16\n223 553 14\n223 564 27\n223 572 47\n223 582 45\n223 612 12\n223 625 31\n223 709 45\n223 712 43\n223 714 30\n223 728 42\n223 796 50\n223 801 40\n223 901 15\n223 917 49\n223 929 45\n223 958 44\n223 965 34\n224 22 39\n224 43 -2\n224 47 28\n224 115 27\n224 144 31\n224 150 15\n224 217 32\n224 247 11\n224 257 11\n224 258 4\n224 282 44\n224 304 34\n224 332 31\n224 339 42\n224 397 26\n224 421 15\n224 473 42\n224 542 33\n224 592 16\n224 609 11\n224 617 21\n224 643 27\n224 659 45\n224 660 38\n224 677 15\n224 772 4\n224 789 12\n224 803 48\n224 813 46\n224 817 2\n224 852 47\n224 864 47\n224 867 39\n224 885 19\n224 888 50\n224 922 26\n224 964 16\n224 994 25\n224 998 11\n225 16 17\n225 42 47\n225 48 35\n225 119 34\n225 132 21\n225 151 27\n225 152 38\n225 171 44\n225 186 18\n225 204 21\n225 213 31\n225 224 8\n225 231 7\n225 236 22\n225 256 -1\n225 273 36\n225 274 17\n225 280 9\n225 284 11\n225 296 35\n225 320 28\n225 332 17\n225 333 27\n225 352 50\n225 369 50\n225 375 15\n225 416 33\n225 419 42\n225 443 15\n225 510 41\n225 530 28\n225 563 12\n225 595 34\n225 617 43\n225 619 21\n225 649 14\n225 667 9\n225 689 37\n225 707 1\n225 720 19\n225 734 39\n225 741 19\n225 788 50\n225 803 25\n225 809 20\n225 812 33\n225 828 40\n225 869 12\n225 885 14\n225 898 38\n225 908 5\n225 916 25\n225 918 19\n225 947 23\n225 987 36\n226 13 35\n226 44 20\n226 45 6\n226 48 18\n226 52 38\n226 63 48\n226 88 24\n226 132 1\n226 162 25\n226 169 34\n226 177 43\n226 204 21\n226 244 33\n226 262 9\n226 265 10\n226 270 44\n226 282 9\n226 349 17\n226 380 8\n226 385 50\n226 398 7\n226 401 42\n226 411 35\n226 439 50\n226 446 11\n226 524 30\n226 581 24\n226 596 40\n226 604 8\n226 615 40\n226 627 38\n226 629 24\n226 630 33\n226 637 30\n226 639 10\n226 663 36\n226 669 7\n226 704 48\n226 719 18\n226 733 30\n226 741 17\n226 801 45\n226 811 40\n226 822 24\n226 839 34\n226 851 42\n226 878 44\n226 883 3\n226 897 32\n226 926 48\n226 931 47\n226 952 16\n226 969 31\n227 2 1\n227 24 22\n227 29 27\n227 50 20\n227 55 42\n227 72 26\n227 86 41\n227 143 10\n227 162 28\n227 185 45\n227 281 5\n227 307 3\n227 319 21\n227 346 6\n227 361 -2\n227 370 41\n227 413 28\n227 462 43\n227 499 8\n227 564 24\n227 593 36\n227 594 20\n227 676 13\n227 716 0\n227 729 6\n227 764 20\n227 784 47\n227 790 8\n227 795 49\n227 796 3\n227 820 49\n227 831 48\n227 880 20\n227 886 35\n227 926 28\n227 974 39\n227 977 4\n228 4 6\n228 14 34\n228 37 48\n228 38 7\n228 61 46\n228 101 29\n228 112 36\n228 113 1\n228 123 1\n228 143 21\n228 191 37\n228 193 22\n228 216 29\n228 240 39\n228 265 16\n228 288 32\n228 306 13\n228 312 28\n228 326 0\n228 336 44\n228 341 15\n228 380 23\n228 385 50\n228 386 17\n228 413 41\n228 432 11\n228 440 30\n228 490 27\n228 495 2\n228 565 33\n228 589 18\n228 595 23\n228 601 38\n228 614 44\n228 650 37\n228 676 45\n228 677 27\n228 703 49\n228 748 32\n228 757 15\n228 767 28\n228 785 48\n228 793 35\n228 826 8\n228 839 38\n228 895 14\n228 901 23\n228 908 0\n228 936 28\n228 965 35\n229 26 23\n229 43 49\n229 50 0\n229 82 17\n229 98 47\n229 101 11\n229 115 24\n229 122 5\n229 173 44\n229 179 0\n229 182 17\n229 188 16\n229 195 18\n229 197 34\n229 240 0\n229 269 30\n229 303 10\n229 308 45\n229 367 42\n229 371 37\n229 380 19\n229 393 -1\n229 416 24\n229 425 47\n229 435 38\n229 449 40\n229 484 9\n229 496 43\n229 500 13\n229 510 24\n229 526 42\n229 538 46\n229 550 30\n229 566 40\n229 587 25\n229 605 12\n229 623 36\n229 644 28\n229 654 10\n229 666 27\n229 675 37\n229 719 13\n229 722 42\n229 741 41\n229 759 35\n229 768 32\n229 816 26\n229 824 11\n229 859 34\n229 864 14\n229 867 33\n229 881 2\n229 889 27\n229 899 2\n229 965 5\n230 10 47\n230 26 24\n230 31 40\n230 80 2\n230 110 47\n230 126 29\n230 138 18\n230 220 41\n230 247 27\n230 329 34\n230 342 45\n230 347 2\n230 568 45\n230 671 37\n230 717 -2\n230 749 7\n230 818 13\n230 844 31\n230 878 16\n230 927 0\n230 929 9\n231 14 46\n231 25 -1\n231 33 8\n231 35 11\n231 43 34\n231 47 27\n231 57 9\n231 70 33\n231 97 11\n231 106 39\n231 219 10\n231 234 29\n231 238 32\n231 253 17\n231 285 36\n231 296 35\n231 302 15\n231 330 37\n231 335 48\n231 351 13\n231 364 31\n231 384 -2\n231 429 4\n231 433 29\n231 489 18\n231 510 8\n231 542 4\n231 640 14\n231 661 47\n231 698 45\n231 708 26\n231 780 36\n231 783 28\n231 784 18\n231 797 19\n231 871 -2\n231 896 27\n231 929 50\n231 940 38\n231 947 46\n231 950 41\n231 972 41\n231 973 20\n232 15 33\n232 21 46\n232 39 27\n232 43 50\n232 77 12\n232 97 7\n232 98 50\n232 103 35\n232 145 43\n232 156 15\n232 166 25\n232 171 26\n232 176 43\n232 191 37\n232 201 47\n232 203 35\n232 221 19\n232 225 0\n232 238 14\n232 249 31\n232 258 2\n232 298 17\n232 308 27\n232 345 -2\n232 347 40\n232 357 32\n232 365 30\n232 382 12\n232 385 17\n232 394 15\n232 404 -2\n232 409 39\n232 411 8\n232 427 33\n232 429 21\n232 468 23\n232 542 42\n232 548 19\n232 574 23\n232 580 0\n232 660 29\n232 669 9\n232 671 35\n232 677 37\n232 698 49\n232 717 7\n232 722 37\n232 729 4\n232 751 24\n232 792 11\n232 803 36\n232 806 49\n232 807 3\n232 818 10\n232 835 42\n232 880 7\n232 884 2\n232 887 39\n232 916 46\n232 952 38\n232 974 40\n232 992 25\n233 37 47\n233 40 6\n233 56 41\n233 58 13\n233 65 0\n233 72 32\n233 82 5\n233 93 38\n233 108 4\n233 207 39\n233 218 38\n233 292 17\n233 295 10\n233 314 47\n233 345 11\n233 358 -1\n233 393 7\n233 401 14\n233 420 47\n233 455 37\n233 483 37\n233 489 0\n233 497 45\n233 516 18\n233 518 13\n233 582 7\n233 613 35\n233 638 33\n233 658 41\n233 671 40\n233 701 44\n233 718 18\n233 725 26\n233 726 12\n233 769 2\n233 795 42\n233 797 19\n233 806 49\n233 816 -2\n233 818 20\n233 877 50\n233 900 21\n234 2 27\n234 12 28\n234 18 22\n234 19 36\n234 28 27\n234 36 40\n234 48 39\n234 62 48\n234 69 48\n234 75 3\n234 80 8\n234 92 20\n234 95 10\n234 110 34\n234 113 9\n234 126 18\n234 138 9\n234 152 24\n234 155 24\n234 167 21\n234 171 32\n234 187 15\n234 203 18\n234 215 26\n234 218 27\n234 253 34\n234 273 41\n234 294 46\n234 317 29\n234 338 28\n234 343 14\n234 354 32\n234 373 48\n234 380 -1\n234 381 6\n234 388 36\n234 411 33\n234 450 34\n234 484 22\n234 509 19\n234 520 45\n234 521 46\n234 556 5\n234 600 41\n234 670 17\n234 710 41\n234 733 19\n234 765 50\n234 777 30\n234 790 17\n234 795 20\n234 814 29\n234 821 8\n234 831 15\n234 846 16\n234 877 40\n234 891 47\n234 897 20\n234 996 29\n235 7 29\n235 80 16\n235 184 5\n235 205 22\n235 354 33\n235 377 21\n235 394 32\n235 418 18\n235 444 -2\n235 448 42\n235 452 14\n235 500 7\n235 514 30\n235 529 37\n235 548 46\n235 569 3\n235 587 50\n235 676 47\n235 704 50\n235 713 33\n235 718 41\n235 763 23\n235 768 17\n235 771 19\n235 774 32\n235 811 49\n235 831 16\n235 886 43\n235 898 32\n235 904 35\n235 920 47\n235 937 45\n235 945 41\n235 951 34\n235 958 44\n235 969 6\n235 975 40\n235 978 31\n235 983 29\n235 986 40\n235 993 32\n236 5 23\n236 34 50\n236 74 19\n236 98 24\n236 142 22\n236 145 47\n236 173 29\n236 199 40\n236 206 46\n236 213 34\n236 218 34\n236 237 24\n236 260 44\n236 289 17\n236 330 33\n236 341 30\n236 363 5\n236 394 25\n236 408 14\n236 410 42\n236 415 42\n236 437 29\n236 445 36\n236 472 28\n236 549 18\n236 578 24\n236 586 43\n236 600 32\n236 612 50\n236 619 4\n236 659 12\n236 673 48\n236 687 7\n236 697 44\n236 707 4\n236 732 33\n236 738 43\n236 750 31\n236 784 2\n236 805 23\n236 829 8\n236 834 22\n236 864 -2\n236 874 36\n236 898 14\n236 903 37\n236 956 12\n236 958 7\n236 997 50\n237 6 2\n237 12 5\n237 14 4\n237 17 12\n237 41 47\n237 46 37\n237 50 22\n237 67 26\n237 81 35\n237 108 6\n237 117 47\n237 126 28\n237 142 22\n237 146 12\n237 156 21\n237 160 40\n237 238 41\n237 245 25\n237 253 17\n237 263 36\n237 279 29\n237 289 14\n237 321 10\n237 341 3\n237 355 16\n237 369 24\n237 374 14\n237 375 22\n237 383 32\n237 386 -1\n237 402 29\n237 428 16\n237 446 1\n237 465 0\n237 516 2\n237 524 22\n237 533 48\n237 560 3\n237 623 44\n237 624 39\n237 628 1\n237 634 10\n237 639 23\n237 641 31\n237 643 18\n237 662 47\n237 734 50\n237 741 0\n237 745 16\n237 753 1\n237 786 24\n237 788 36\n237 792 43\n237 801 43\n237 876 46\n237 907 13\n237 914 47\n237 927 18\n237 935 2\n237 982 40\n238 20 33\n238 39 19\n238 58 15\n238 90 -2\n238 91 19\n238 119 26\n238 140 35\n238 165 35\n238 187 6\n238 217 1\n238 222 50\n238 228 -1\n238 233 2\n238 250 37\n238 253 30\n238 258 19\n238 287 38\n238 292 28\n238 300 8\n238 325 41\n238 360 0\n238 363 12\n238 381 34\n238 395 32\n238 407 24\n238 411 23\n238 414 20\n238 432 -2\n238 440 34\n238 451 43\n238 487 36\n238 491 39\n238 512 4\n238 523 32\n238 524 24\n238 558 8\n238 601 38\n238 623 26\n238 665 43\n238 684 36\n238 690 35\n238 705 -2\n238 714 49\n238 716 18\n238 762 41\n238 847 11\n238 850 6\n238 865 9\n238 897 17\n238 898 5\n238 919 36\n238 946 50\n238 948 35\n239 22 17\n239 25 1\n239 28 5\n239 49 37\n239 138 24\n239 196 27\n239 201 24\n239 217 18\n239 219 0\n239 259 20\n239 293 33\n239 329 22\n239 338 18\n239 363 8\n239 364 40\n239 424 42\n239 426 -1\n239 435 -1\n239 472 39\n239 527 22\n239 538 0\n239 570 34\n239 582 2\n239 651 43\n239 669 31\n239 726 32\n239 727 -1\n239 731 11\n239 734 6\n239 780 30\n239 790 30\n239 806 1\n239 824 42\n239 861 10\n239 868 50\n239 919 10\n239 982 -2\n239 984 -1\n240 6 34\n240 49 34\n240 50 32\n240 138 45\n240 163 29\n240 167 46\n240 193 38\n240 201 47\n240 223 15\n240 282 29\n240 283 10\n240 286 41\n240 323 19\n240 349 44\n240 351 27\n240 374 24\n240 382 14\n240 390 9\n240 425 47\n240 426 21\n240 491 10\n240 496 29\n240 500 37\n240 534 48\n240 539 33\n240 610 10\n240 632 15\n240 639 47\n240 644 17\n240 649 9\n240 660 8\n240 661 11\n240 664 24\n240 666 24\n240 694 12\n240 698 19\n240 739 19\n240 749 5\n240 784 44\n240 851 47\n240 857 16\n240 874 27\n240 875 26\n240 884 35\n240 907 50\n240 911 7\n240 923 48\n240 952 45\n240 982 35\n241 37 23\n241 40 18\n241 57 29\n241 74 11\n241 88 11\n241 115 2\n241 121 44\n241 140 12\n241 160 18\n241 163 46\n241 168 50\n241 189 44\n241 196 38\n241 211 23\n241 217 20\n241 232 25\n241 244 23\n241 299 45\n241 329 11\n241 352 42\n241 366 16\n241 368 7\n241 402 24\n241 417 37\n241 423 46\n241 435 18\n241 451 37\n241 457 34\n241 478 26\n241 520 40\n241 600 47\n241 646 32\n241 659 14\n241 662 -2\n241 667 41\n241 671 24\n241 680 40\n241 719 1\n241 725 17\n241 733 17\n241 737 17\n241 826 18\n241 871 34\n241 876 28\n241 877 33\n241 892 18\n241 900 20\n241 908 13\n241 912 4\n241 921 43\n241 974 12\n241 987 49\n242 17 36\n242 70 28\n242 92 32\n242 96 48\n242 98 40\n242 121 22\n242 136 8\n242 146 14\n242 149 33\n242 170 40\n242 179 33\n242 190 37\n242 233 49\n242 282 45\n242 296 35\n242 320 31\n242 381 33\n242 415 10\n242 421 3\n242 431 8\n242 474 37\n242 476 46\n242 624 4\n242 634 -2\n242 647 45\n242 655 31\n242 670 44\n242 685 15\n242 690 39\n242 701 47\n242 707 25\n242 718 17\n242 734 10\n242 738 34\n242 743 18\n242 771 2\n242 776 27\n242 792 37\n242 802 21\n242 807 16\n242 824 9\n242 829 8\n242 857 -1\n242 875 37\n242 896 7\n242 932 15\n242 954 10\n242 972 40\n243 48 28\n243 49 19\n243 58 35\n243 85 -1\n243 131 32\n243 133 27\n243 138 7\n243 171 11\n243 181 36\n243 208 37\n243 220 47\n243 228 34\n243 250 20\n243 302 8\n243 311 32\n243 319 18\n243 329 46\n243 369 16\n243 391 21\n243 423 12\n243 431 30\n243 444 40\n243 451 47\n243 486 39\n243 526 19\n243 564 25\n243 609 37\n243 615 49\n243 626 16\n243 641 29\n243 650 13\n243 661 45\n243 686 22\n243 693 37\n243 695 45\n243 697 50\n243 714 40\n243 726 15\n243 756 0\n243 780 38\n243 784 17\n243 786 6\n243 796 22\n243 797 14\n243 818 12\n243 855 31\n243 862 36\n243 869 11\n243 902 19\n243 915 23\n243 926 48\n244 2 4\n244 20 29\n244 24 15\n244 33 1\n244 40 47\n244 43 8\n244 58 49\n244 70 17\n244 73 7\n244 124 16\n244 138 2\n244 141 12\n244 164 38\n244 205 9\n244 240 18\n244 245 42\n244 251 35\n244 278 0\n244 287 2\n244 325 3\n244 344 13\n244 356 9\n244 379 46\n244 387 4\n244 398 33\n244 425 32\n244 449 19\n244 457 17\n244 486 21\n244 513 18\n244 519 28\n244 575 11\n244 665 9\n244 696 7\n244 701 6\n244 714 25\n244 737 47\n244 745 13\n244 763 43\n244 793 13\n244 819 49\n244 835 29\n244 871 33\n244 915 40\n244 922 30\n244 928 38\n244 930 25\n244 931 27\n245 8 26\n245 21 12\n245 75 27\n245 77 23\n245 103 45\n245 118 22\n245 214 36\n245 232 20\n245 246 9\n245 253 33\n245 368 44\n245 412 46\n245 421 15\n245 477 46\n245 513 10\n245 515 27\n245 561 0\n245 573 41\n245 624 9\n245 642 25\n245 669 17\n245 672 34\n245 674 43\n245 687 22\n245 731 33\n245 780 34\n245 792 27\n245 796 31\n245 837 28\n245 843 20\n245 859 13\n245 888 46\n245 936 16\n245 945 28\n245 994 48\n246 4 37\n246 25 32\n246 98 37\n246 103 50\n246 105 38\n246 118 20\n246 125 27\n246 135 48\n246 140 48\n246 156 8\n246 175 27\n246 179 1\n246 209 47\n246 221 38\n246 226 36\n246 268 50\n246 320 29\n246 395 38\n246 423 34\n246 424 3\n246 473 46\n246 488 10\n246 496 37\n246 502 24\n246 507 0\n246 519 32\n246 528 23\n246 556 22\n246 568 47\n246 578 32\n246 593 30\n246 602 26\n246 604 48\n246 605 12\n246 626 28\n246 642 7\n246 648 8\n246 649 3\n246 724 18\n246 727 43\n246 737 4\n246 750 14\n246 754 34\n246 796 28\n246 801 30\n246 816 17\n246 817 3\n246 899 9\n246 984 50\n246 987 35\n246 992 31\n246 998 19\n247 18 44\n247 29 50\n247 31 39\n247 38 -1\n247 53 30\n247 71 47\n247 74 43\n247 75 1\n247 102 8\n247 106 48\n247 128 42\n247 144 24\n247 186 12\n247 202 48\n247 213 40\n247 218 35\n247 227 22\n247 253 18\n247 254 50\n247 258 37\n247 275 17\n247 317 37\n247 332 20\n247 369 21\n247 383 4\n247 404 5\n247 440 8\n247 448 13\n247 478 9\n247 521 2\n247 537 47\n247 567 -2\n247 579 18\n247 583 1\n247 587 33\n247 634 5\n247 641 38\n247 642 45\n247 692 48\n247 693 7\n247 712 24\n247 715 29\n247 728 48\n247 730 39\n247 742 10\n247 813 40\n247 844 23\n247 848 35\n247 871 44\n247 872 39\n247 875 19\n247 882 46\n247 932 36\n247 939 14\n247 947 48\n247 963 40\n248 6 49\n248 58 46\n248 91 -2\n248 147 8\n248 175 34\n248 193 0\n248 214 27\n248 261 11\n248 276 28\n248 292 4\n248 293 43\n248 294 5\n248 301 15\n248 323 29\n248 332 -2\n248 340 21\n248 350 28\n248 353 48\n248 364 27\n248 412 11\n248 416 44\n248 427 38\n248 465 50\n248 473 33\n248 487 29\n248 514 21\n248 551 36\n248 553 33\n248 577 45\n248 581 10\n248 603 39\n248 635 10\n248 649 6\n248 650 16\n248 659 24\n248 667 47\n248 680 27\n248 681 34\n248 684 42\n248 701 35\n248 731 4\n248 742 37\n248 755 27\n248 775 34\n248 804 45\n248 875 6\n248 906 47\n248 916 44\n248 968 31\n248 975 3\n248 985 20\n248 998 33\n249 49 48\n249 62 8\n249 81 2\n249 121 38\n249 125 22\n249 141 33\n249 183 11\n249 184 15\n249 194 23\n249 196 39\n249 199 -2\n249 240 9\n249 246 15\n249 258 4\n249 295 14\n249 326 33\n249 344 10\n249 349 7\n249 387 33\n249 388 23\n249 441 46\n249 480 14\n249 508 48\n249 548 17\n249 550 48\n249 598 17\n249 609 50\n249 620 32\n249 633 20\n249 645 17\n249 660 17\n249 666 25\n249 705 5\n249 707 9\n249 710 42\n249 713 40\n249 717 0\n249 742 18\n249 744 22\n249 765 1\n249 768 11\n249 839 0\n249 866 18\n249 871 27\n249 897 36\n249 908 31\n249 926 2\n249 928 22\n249 966 39\n249 988 0\n250 6 1\n250 76 41\n250 101 39\n250 105 15\n250 167 15\n250 177 36\n250 193 24\n250 243 6\n250 260 42\n250 265 39\n250 268 35\n250 283 4\n250 300 31\n250 321 39\n250 331 2\n250 348 14\n250 352 2\n250 456 47\n250 458 19\n250 483 37\n250 487 7\n250 528 19\n250 569 44\n250 581 -1\n250 589 2\n250 592 25\n250 596 2\n250 601 31\n250 606 38\n250 638 18\n250 657 46\n250 658 29\n250 664 16\n250 665 29\n250 683 48\n250 690 11\n250 718 40\n250 737 27\n250 752 48\n250 816 28\n250 837 4\n250 851 9\n250 867 21\n250 886 10\n250 910 5\n250 916 40\n250 935 -2\n250 953 33\n250 957 -1\n250 981 39\n251 1 7\n251 27 13\n251 88 37\n251 90 8\n251 116 6\n251 120 36\n251 151 29\n251 188 34\n251 268 49\n251 282 19\n251 292 41\n251 311 38\n251 320 50\n251 423 13\n251 429 17\n251 479 21\n251 486 31\n251 551 18\n251 584 11\n251 608 39\n251 623 45\n251 653 35\n251 684 17\n251 688 11\n251 703 49\n251 726 35\n251 752 48\n251 771 24\n251 778 5\n251 780 4\n251 788 42\n251 882 14\n251 887 42\n251 888 35\n251 916 28\n251 918 22\n251 927 49\n251 941 12\n251 957 1\n251 969 12\n251 987 10\n252 57 28\n252 60 -2\n252 93 40\n252 95 16\n252 100 37\n252 149 36\n252 208 42\n252 308 46\n252 312 8\n252 332 26\n252 358 18\n252 431 50\n252 456 50\n252 463 17\n252 468 1\n252 470 1\n252 488 27\n252 500 4\n252 507 24\n252 545 13\n252 564 49\n252 578 3\n252 595 19\n252 596 15\n252 606 37\n252 622 6\n252 636 41\n252 639 40\n252 674 43\n252 677 7\n252 684 24\n252 725 -2\n252 759 41\n252 784 -1\n252 810 30\n252 813 5\n252 821 21\n252 826 18\n252 864 21\n252 884 25\n252 903 6\n252 928 -1\n252 940 -1\n252 944 21\n252 968 49\n252 971 6\n253 8 34\n253 53 29\n253 68 46\n253 143 36\n253 155 36\n253 203 43\n253 225 33\n253 236 37\n253 306 48\n253 319 23\n253 342 30\n253 343 30\n253 344 33\n253 411 5\n253 492 39\n253 518 14\n253 520 7\n253 570 24\n253 603 32\n253 637 23\n253 695 23\n253 707 49\n253 726 26\n253 742 24\n253 749 25\n253 765 35\n253 775 14\n253 839 48\n253 856 11\n253 865 -2\n253 894 44\n253 935 22\n253 939 4\n254 15 19\n254 30 41\n254 35 27\n254 72 32\n254 93 28\n254 96 39\n254 135 32\n254 174 13\n254 186 10\n254 193 9\n254 212 6\n254 236 21\n254 265 3\n254 266 11\n254 280 44\n254 312 20\n254 322 9\n254 335 12\n254 340 13\n254 366 10\n254 373 41\n254 408 41\n254 416 32\n254 489 35\n254 510 49\n254 511 24\n254 518 34\n254 549 45\n254 566 4\n254 580 30\n254 581 36\n254 632 13\n254 644 14\n254 656 45\n254 662 -2\n254 692 14\n254 693 39\n254 696 12\n254 701 45\n254 707 37\n254 719 23\n254 739 31\n254 757 16\n254 780 7\n254 790 1\n254 800 49\n254 807 12\n254 811 9\n254 818 50\n254 839 16\n254 851 49\n254 854 35\n254 877 30\n254 907 19\n254 909 10\n254 923 50\n254 951 10\n254 998 48\n255 15 6\n255 20 9\n255 21 48\n255 26 37\n255 34 47\n255 37 48\n255 52 17\n255 60 44\n255 135 8\n255 137 47\n255 153 40\n255 161 18\n255 171 35\n255 181 17\n255 205 3\n255 219 46\n255 239 37\n255 240 41\n255 256 18\n255 265 8\n255 271 18\n255 273 34\n255 276 25\n255 284 5\n255 298 20\n255 328 30\n255 332 16\n255 368 18\n255 455 33\n255 470 9\n255 502 7\n255 503 36\n255 513 43\n255 545 0\n255 563 46\n255 564 25\n255 605 35\n255 611 25\n255 615 24\n255 618 15\n255 621 8\n255 673 35\n255 700 13\n255 753 17\n255 795 42\n255 799 47\n255 802 18\n255 807 50\n255 820 44\n255 836 20\n255 910 12\n255 958 23\n255 961 13\n255 966 18\n255 971 6\n256 26 49\n256 44 40\n256 73 15\n256 82 34\n256 88 24\n256 132 15\n256 158 41\n256 164 33\n256 193 11\n256 196 14\n256 198 20\n256 231 7\n256 265 26\n256 269 41\n256 283 34\n256 300 28\n256 350 3\n256 382 44\n256 388 26\n256 406 34\n256 448 15\n256 449 20\n256 494 22\n256 517 39\n256 543 12\n256 550 41\n256 558 23\n256 572 26\n256 596 37\n256 651 39\n256 674 5\n256 677 29\n256 702 25\n256 726 35\n256 745 4\n256 783 46\n256 802 27\n256 810 24\n256 812 28\n256 815 7\n256 823 33\n256 918 33\n256 925 27\n256 959 33\n256 971 12\n256 975 30\n256 990 26\n257 11 7\n257 39 22\n257 44 17\n257 107 15\n257 111 30\n257 192 8\n257 197 17\n257 234 14\n257 235 34\n257 249 4\n257 260 11\n257 286 25\n257 366 42\n257 373 21\n257 375 23\n257 394 14\n257 402 42\n257 412 16\n257 436 50\n257 454 31\n257 478 46\n257 483 35\n257 533 36\n257 544 17\n257 547 37\n257 556 3\n257 576 50\n257 591 7\n257 630 4\n257 667 40\n257 693 22\n257 697 43\n257 702 19\n257 713 37\n257 735 23\n257 773 24\n257 786 21\n257 858 11\n257 892 26\n257 914 36\n257 932 27\n257 946 25\n257 982 45\n258 57 26\n258 85 50\n258 127 32\n258 138 36\n258 148 47\n258 152 45\n258 187 33\n258 189 11\n258 190 16\n258 200 21\n258 205 44\n258 219 11\n258 322 25\n258 345 19\n258 347 21\n258 362 42\n258 377 26\n258 421 45\n258 429 -1\n258 443 19\n258 457 32\n258 501 24\n258 520 33\n258 534 45\n258 560 48\n258 602 36\n258 604 29\n258 610 26\n258 641 44\n258 647 11\n258 713 22\n258 714 -2\n258 720 46\n258 737 25\n258 738 45\n258 758 20\n258 794 35\n258 850 14\n258 887 18\n258 910 34\n258 920 29\n258 961 10\n258 968 39\n259 55 4\n259 60 38\n259 65 47\n259 79 -1\n259 105 16\n259 107 3\n259 136 18\n259 137 1\n259 144 1\n259 163 27\n259 168 3\n259 171 25\n259 190 11\n259 213 3\n259 252 7\n259 255 31\n259 258 15\n259 316 25\n259 319 11\n259 361 18\n259 372 31\n259 373 22\n259 378 34\n259 410 26\n259 485 43\n259 508 32\n259 511 15\n259 520 12\n259 557 42\n259 581 29\n259 584 49\n259 623 24\n259 630 23\n259 652 17\n259 655 44\n259 709 18\n259 715 50\n259 718 40\n259 816 28\n259 857 50\n259 883 47\n259 885 49\n259 898 36\n259 910 39\n259 932 40\n259 943 34\n259 944 14\n259 947 40\n259 994 20\n260 11 9\n260 22 28\n260 29 20\n260 61 29\n260 74 15\n260 80 16\n260 101 28\n260 105 31\n260 179 12\n260 184 18\n260 199 -1\n260 232 34\n260 252 15\n260 465 14\n260 469 16\n260 474 28\n260 492 6\n260 507 42\n260 519 1\n260 542 42\n260 571 7\n260 622 27\n260 627 44\n260 638 32\n260 687 43\n260 717 9\n260 759 5\n260 763 19\n260 765 41\n260 789 10\n260 815 24\n260 848 0\n260 854 8\n260 864 46\n260 866 -1\n260 883 3\n260 891 33\n260 901 14\n260 914 7\n260 932 46\n260 960 5\n260 979 21\n261 51 36\n261 99 44\n261 121 47\n261 125 32\n261 162 26\n261 167 -2\n261 198 33\n261 238 5\n261 260 35\n261 274 14\n261 280 33\n261 305 47\n261 313 11\n261 380 26\n261 410 3\n261 474 10\n261 490 23\n261 513 26\n261 541 37\n261 543 15\n261 564 4\n261 566 14\n261 594 10\n261 600 31\n261 609 26\n261 617 5\n261 619 3\n261 622 7\n261 630 23\n261 680 45\n261 684 1\n261 740 26\n261 758 49\n261 773 6\n261 774 46\n261 802 24\n261 835 28\n261 842 36\n261 845 13\n261 848 42\n261 862 33\n261 882 50\n261 893 6\n261 911 -2\n261 920 33\n261 922 31\n261 926 41\n261 934 23\n261 955 13\n261 964 -2\n261 995 37\n261 996 19\n262 19 19\n262 66 29\n262 68 48\n262 117 7\n262 118 22\n262 138 45\n262 147 22\n262 164 33\n262 186 49\n262 212 26\n262 251 31\n262 274 40\n262 284 42\n262 309 11\n262 330 -2\n262 335 47\n262 359 21\n262 370 24\n262 404 26\n262 410 7\n262 459 31\n262 475 18\n262 476 19\n262 495 47\n262 499 48\n262 504 27\n262 506 49\n262 540 37\n262 570 50\n262 584 45\n262 606 23\n262 614 24\n262 631 42\n262 637 10\n262 655 32\n262 681 39\n262 708 13\n262 742 9\n262 746 0\n262 753 1\n262 777 17\n262 789 6\n262 893 25\n262 961 38\n262 986 38\n263 6 -2\n263 10 45\n263 26 31\n263 28 23\n263 61 44\n263 66 31\n263 78 48\n263 80 4\n263 87 33\n263 117 33\n263 137 34\n263 142 1\n263 145 47\n263 153 38\n263 168 39\n263 194 32\n263 205 45\n263 206 48\n263 246 11\n263 253 19\n263 267 44\n263 269 9\n263 300 3\n263 316 2\n263 321 42\n263 355 35\n263 359 19\n263 403 14\n263 406 5\n263 414 33\n263 425 42\n263 445 26\n263 457 11\n263 468 42\n263 474 -1\n263 477 8\n263 512 1\n263 540 50\n263 592 2\n263 693 44\n263 717 20\n263 731 12\n263 734 12\n263 772 30\n263 812 25\n263 835 40\n263 837 21\n263 841 31\n263 845 25\n263 863 12\n263 875 45\n263 924 -1\n263 957 6\n263 965 2\n263 969 32\n264 60 32\n264 63 29\n264 94 0\n264 118 6\n264 125 45\n264 144 39\n264 173 11\n264 179 39\n264 191 41\n264 192 27\n264 211 43\n264 249 40\n264 253 34\n264 284 44\n264 350 44\n264 357 18\n264 387 49\n264 465 46\n264 478 23\n264 502 13\n264 513 33\n264 526 3\n264 528 33\n264 560 -2\n264 573 38\n264 599 39\n264 617 42\n264 618 9\n264 621 30\n264 656 5\n264 662 8\n264 685 11\n264 686 19\n264 708 50\n264 752 43\n264 793 27\n264 810 3\n264 815 16\n264 822 46\n264 834 37\n264 842 37\n264 856 25\n264 859 15\n264 883 40\n264 889 8\n264 905 41\n264 938 46\n264 949 11\n264 979 22\n265 25 36\n265 96 35\n265 97 24\n265 104 33\n265 118 16\n265 155 42\n265 169 42\n265 177 25\n265 200 30\n265 208 1\n265 214 12\n265 218 20\n265 259 29\n265 285 13\n265 328 28\n265 330 40\n265 335 15\n265 366 47\n265 415 19\n265 418 12\n265 450 26\n265 465 49\n265 499 40\n265 524 10\n265 537 48\n265 551 15\n265 561 -2\n265 609 12\n265 612 25\n265 625 13\n265 659 21\n265 676 34\n265 678 33\n265 680 19\n265 688 23\n265 716 46\n265 720 37\n265 745 14\n265 753 50\n265 795 33\n265 822 13\n265 869 18\n265 875 48\n265 893 1\n265 897 46\n265 914 41\n265 933 17\n265 963 49\n266 25 38\n266 69 -2\n266 104 46\n266 114 14\n266 128 28\n266 132 43\n266 142 14\n266 160 0\n266 191 14\n266 230 35\n266 247 41\n266 285 6\n266 289 -1\n266 328 29\n266 342 4\n266 360 48\n266 387 48\n266 397 3\n266 409 48\n266 410 30\n266 449 31\n266 494 50\n266 503 1\n266 529 41\n266 550 14\n266 562 41\n266 574 30\n266 605 45\n266 611 50\n266 617 3\n266 619 25\n266 625 36\n266 631 31\n266 636 31\n266 638 3\n266 639 12\n266 658 29\n266 660 43\n266 666 34\n266 677 11\n266 716 49\n266 746 41\n266 753 0\n266 800 40\n266 811 17\n266 813 14\n266 827 37\n266 875 11\n266 914 29\n266 981 42\n266 992 13\n267 32 20\n267 37 38\n267 45 19\n267 54 44\n267 60 33\n267 78 7\n267 94 12\n267 130 33\n267 143 17\n267 168 46\n267 198 40\n267 252 5\n267 280 39\n267 281 49\n267 313 14\n267 320 7\n267 341 11\n267 425 16\n267 482 0\n267 491 5\n267 505 37\n267 519 22\n267 565 6\n267 568 48\n267 610 41\n267 664 18\n267 744 24\n267 749 48\n267 765 14\n267 796 41\n267 798 8\n267 799 27\n267 849 33\n267 858 13\n267 891 48\n267 897 28\n267 946 8\n267 978 42\n267 993 11\n268 4 48\n268 16 25\n268 24 29\n268 28 19\n268 30 23\n268 32 19\n268 49 12\n268 84 22\n268 94 13\n268 112 1\n268 127 43\n268 157 18\n268 170 50\n268 209 11\n268 254 20\n268 261 49\n268 295 26\n268 383 33\n268 490 37\n268 523 46\n268 527 43\n268 529 16\n268 638 20\n268 698 44\n268 706 35\n268 712 23\n268 714 32\n268 731 15\n268 827 31\n268 837 12\n268 860 31\n268 871 40\n268 886 -1\n268 892 14\n268 903 13\n268 912 22\n268 956 22\n268 977 28\n268 993 13\n269 11 24\n269 14 24\n269 35 42\n269 66 15\n269 80 19\n269 92 14\n269 93 49\n269 108 35\n269 122 48\n269 136 50\n269 137 24\n269 139 32\n269 161 9\n269 169 4\n269 179 48\n269 203 41\n269 244 17\n269 301 38\n269 349 5\n269 388 16\n269 408 20\n269 411 35\n269 435 -2\n269 462 20\n269 485 24\n269 489 38\n269 491 16\n269 532 1\n269 557 15\n269 567 47\n269 576 49\n269 588 49\n269 607 48\n269 620 9\n269 641 41\n269 651 41\n269 661 50\n269 669 27\n269 674 4\n269 675 0\n269 680 45\n269 694 5\n269 723 15\n269 818 5\n269 819 12\n269 842 28\n269 891 1\n269 899 45\n269 937 9\n269 947 34\n270 15 20\n270 39 -2\n270 48 37\n270 59 38\n270 62 28\n270 66 5\n270 131 2\n270 147 17\n270 154 38\n270 159 38\n270 193 45\n270 212 29\n270 214 30\n270 250 36\n270 251 19\n270 263 16\n270 266 21\n270 293 11\n270 333 11\n270 335 19\n270 384 -2\n270 385 38\n270 400 48\n270 469 27\n270 497 32\n270 506 15\n270 519 33\n270 561 28\n270 577 15\n270 607 3\n270 644 44\n270 724 31\n270 764 0\n270 765 38\n270 773 27\n270 784 20\n270 792 24\n270 816 16\n270 829 36\n270 837 28\n270 857 0\n270 869 16\n270 906 2\n270 922 34\n270 930 38\n270 989 25\n271 28 -2\n271 34 3\n271 42 12\n271 62 29\n271 94 1\n271 178 6\n271 198 28\n271 250 50\n271 279 36\n271 282 27\n271 311 46\n271 316 32\n271 340 17\n271 345 42\n271 347 17\n271 358 5\n271 359 17\n271 373 17\n271 383 28\n271 393 27\n271 396 14\n271 407 23\n271 452 23\n271 464 40\n271 465 3\n271 481 18\n271 494 33\n271 510 15\n271 516 31\n271 549 37\n271 592 41\n271 647 37\n271 655 18\n271 659 19\n271 675 14\n271 682 46\n271 685 37\n271 688 1\n271 716 45\n271 725 37\n271 727 23\n271 728 0\n271 871 44\n271 878 13\n271 900 11\n271 979 15\n272 26 0\n272 28 24\n272 69 28\n272 101 14\n272 111 6\n272 129 38\n272 148 6\n272 231 9\n272 243 40\n272 257 6\n272 261 23\n272 267 42\n272 299 8\n272 320 40\n272 330 -1\n272 332 0\n272 349 17\n272 355 37\n272 401 -1\n272 409 21\n272 429 23\n272 443 -1\n272 461 3\n272 488 27\n272 499 7\n272 509 16\n272 524 11\n272 570 7\n272 580 44\n272 599 8\n272 631 36\n272 646 31\n272 661 32\n272 702 42\n272 749 43\n272 750 -1\n272 772 44\n272 791 23\n272 811 2\n272 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615 30\n277 619 42\n277 622 30\n277 679 22\n277 690 43\n277 714 -1\n277 724 15\n277 732 26\n277 742 7\n277 778 39\n277 789 28\n277 860 35\n277 867 5\n277 904 20\n277 950 45\n277 953 12\n277 975 48\n277 979 12\n278 1 0\n278 13 14\n278 52 43\n278 80 20\n278 140 4\n278 182 24\n278 202 29\n278 259 -2\n278 269 40\n278 298 37\n278 324 8\n278 333 38\n278 337 28\n278 350 7\n278 395 43\n278 448 35\n278 468 7\n278 484 1\n278 488 28\n278 549 44\n278 552 12\n278 553 10\n278 561 37\n278 569 31\n278 596 32\n278 615 19\n278 616 44\n278 623 32\n278 640 13\n278 641 31\n278 649 19\n278 668 14\n278 679 16\n278 716 31\n278 724 3\n278 738 23\n278 765 13\n278 776 17\n278 799 31\n278 828 34\n278 845 47\n278 847 5\n278 901 9\n278 908 24\n278 911 -1\n278 930 36\n278 969 39\n278 972 42\n279 37 22\n279 50 27\n279 54 45\n279 69 35\n279 70 2\n279 81 4\n279 118 35\n279 175 40\n279 185 10\n279 187 10\n279 237 36\n279 238 32\n279 240 14\n279 261 49\n279 284 21\n279 290 46\n279 291 4\n279 296 27\n279 309 9\n279 310 45\n279 322 10\n279 384 17\n279 434 23\n279 453 47\n279 458 25\n279 476 14\n279 484 15\n279 487 17\n279 495 35\n279 498 31\n279 518 46\n279 537 8\n279 541 46\n279 557 31\n279 560 5\n279 561 36\n279 563 14\n279 596 44\n279 603 0\n279 640 34\n279 647 7\n279 651 30\n279 678 19\n279 682 16\n279 689 24\n279 701 30\n279 705 46\n279 707 -2\n279 710 50\n279 720 18\n279 731 23\n279 738 24\n279 747 17\n279 766 47\n279 783 14\n279 784 46\n279 816 25\n279 830 22\n279 845 13\n279 885 18\n279 933 34\n279 940 12\n279 983 49\n279 989 7\n280 2 27\n280 35 31\n280 58 41\n280 80 17\n280 139 32\n280 144 -2\n280 185 31\n280 215 -1\n280 229 41\n280 253 4\n280 295 23\n280 308 34\n280 336 20\n280 361 25\n280 385 16\n280 392 44\n280 438 17\n280 452 8\n280 456 46\n280 496 21\n280 498 39\n280 519 34\n280 528 8\n280 534 29\n280 543 43\n280 568 46\n280 571 22\n280 617 50\n280 619 49\n280 629 26\n280 633 12\n280 637 20\n280 656 24\n280 697 45\n280 739 10\n280 760 -2\n280 798 6\n280 802 7\n280 875 49\n280 922 27\n280 944 40\n280 948 15\n280 955 -2\n281 1 23\n281 4 23\n281 31 21\n281 34 48\n281 72 -1\n281 80 28\n281 127 20\n281 128 45\n281 135 0\n281 150 37\n281 195 17\n281 198 22\n281 258 7\n281 268 29\n281 282 32\n281 286 33\n281 291 45\n281 336 9\n281 346 11\n281 361 22\n281 424 32\n281 430 9\n281 505 25\n281 519 40\n281 536 40\n281 537 21\n281 546 24\n281 562 7\n281 589 23\n281 603 19\n281 646 16\n281 686 37\n281 696 32\n281 717 14\n281 726 11\n281 746 7\n281 748 11\n281 816 31\n281 820 46\n281 875 43\n281 893 1\n281 900 30\n281 939 14\n281 991 6\n282 34 34\n282 50 40\n282 144 40\n282 203 -1\n282 242 36\n282 290 37\n282 300 33\n282 305 21\n282 313 13\n282 318 30\n282 329 50\n282 347 1\n282 375 40\n282 428 8\n282 453 42\n282 457 48\n282 494 8\n282 522 14\n282 545 25\n282 581 5\n282 586 10\n282 587 33\n282 666 18\n282 677 25\n282 698 9\n282 728 1\n282 753 16\n282 762 11\n282 796 -2\n282 800 9\n282 801 -2\n282 824 31\n282 838 19\n282 842 27\n282 890 14\n282 898 32\n282 915 10\n282 961 49\n282 996 2\n283 17 9\n283 18 27\n283 35 8\n283 89 11\n283 104 46\n283 138 38\n283 153 43\n283 163 21\n283 211 50\n283 225 -1\n283 243 39\n283 249 2\n283 264 44\n283 287 43\n283 309 35\n283 315 40\n283 351 7\n283 428 42\n283 438 48\n283 463 24\n283 490 37\n283 500 34\n283 506 22\n283 537 36\n283 545 12\n283 550 12\n283 568 17\n283 589 33\n283 593 12\n283 596 39\n283 611 42\n283 650 39\n283 699 44\n283 714 45\n283 747 31\n283 758 9\n283 775 18\n283 784 20\n283 787 27\n283 804 20\n283 812 38\n283 819 40\n283 830 23\n283 882 36\n283 886 -2\n283 912 -1\n283 926 44\n283 947 41\n283 964 46\n284 4 38\n284 21 34\n284 43 47\n284 109 43\n284 148 29\n284 153 33\n284 184 46\n284 203 5\n284 210 24\n284 239 46\n284 249 35\n284 276 39\n284 349 34\n284 355 46\n284 434 8\n284 439 50\n284 460 41\n284 476 32\n284 507 43\n284 517 14\n284 526 23\n284 554 44\n284 574 23\n284 606 15\n284 617 9\n284 624 2\n284 627 12\n284 628 35\n284 651 31\n284 661 9\n284 665 48\n284 680 35\n284 692 26\n284 705 39\n284 722 25\n284 726 24\n284 807 32\n284 837 13\n284 845 14\n284 874 37\n284 908 8\n284 914 38\n284 976 25\n285 18 24\n285 27 49\n285 42 32\n285 93 40\n285 101 11\n285 117 46\n285 135 49\n285 136 34\n285 157 32\n285 166 50\n285 181 36\n285 223 -1\n285 258 42\n285 267 44\n285 274 20\n285 289 48\n285 291 2\n285 299 23\n285 318 19\n285 319 8\n285 320 9\n285 350 35\n285 358 2\n285 378 17\n285 381 45\n285 437 33\n285 446 43\n285 483 17\n285 498 46\n285 513 3\n285 537 24\n285 586 10\n285 603 7\n285 636 28\n285 651 10\n285 670 35\n285 694 36\n285 706 49\n285 707 13\n285 713 22\n285 724 38\n285 730 20\n285 744 50\n285 767 27\n285 769 15\n285 834 22\n285 850 39\n285 851 50\n285 852 49\n285 858 6\n285 868 9\n285 873 30\n285 929 32\n285 958 9\n286 18 -1\n286 25 17\n286 55 -2\n286 86 24\n286 89 32\n286 99 35\n286 112 32\n286 135 11\n286 152 41\n286 159 32\n286 194 37\n286 222 40\n286 263 21\n286 279 13\n286 296 30\n286 309 40\n286 316 11\n286 365 43\n286 370 27\n286 379 31\n286 405 5\n286 454 26\n286 472 12\n286 524 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4\n288 102 8\n288 124 11\n288 129 7\n288 130 33\n288 169 20\n288 170 48\n288 203 1\n288 206 22\n288 214 27\n288 218 6\n288 227 7\n288 269 24\n288 285 12\n288 291 39\n288 356 3\n288 367 41\n288 484 8\n288 486 14\n288 513 48\n288 515 50\n288 521 40\n288 550 49\n288 588 27\n288 596 20\n288 617 41\n288 652 8\n288 662 22\n288 679 48\n288 720 39\n288 756 45\n288 783 11\n288 795 50\n288 840 13\n288 891 26\n288 900 29\n288 909 34\n288 927 -1\n288 942 17\n288 969 1\n288 975 10\n288 987 34\n288 996 1\n289 3 11\n289 25 28\n289 49 26\n289 84 9\n289 113 -1\n289 144 9\n289 156 27\n289 189 43\n289 191 33\n289 192 16\n289 215 5\n289 230 37\n289 231 37\n289 232 35\n289 266 16\n289 270 42\n289 308 13\n289 311 16\n289 324 34\n289 340 30\n289 344 0\n289 353 5\n289 372 26\n289 375 25\n289 377 8\n289 393 47\n289 395 7\n289 401 30\n289 405 7\n289 426 6\n289 446 19\n289 480 2\n289 491 13\n289 525 36\n289 554 50\n289 563 14\n289 597 38\n289 734 32\n289 738 20\n289 748 25\n289 757 43\n289 787 33\n289 814 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726 50\n291 727 12\n291 732 46\n291 746 25\n291 763 50\n291 773 1\n291 776 36\n291 789 48\n291 795 2\n291 864 25\n291 902 23\n291 913 5\n291 940 36\n291 944 27\n291 959 8\n291 962 25\n291 969 35\n292 15 43\n292 25 35\n292 28 38\n292 30 7\n292 74 16\n292 117 43\n292 130 35\n292 141 46\n292 155 35\n292 162 7\n292 178 28\n292 213 32\n292 215 2\n292 217 7\n292 338 8\n292 358 11\n292 363 41\n292 386 46\n292 392 5\n292 413 37\n292 421 6\n292 494 31\n292 503 31\n292 514 41\n292 557 6\n292 583 35\n292 608 46\n292 660 4\n292 676 27\n292 683 6\n292 700 23\n292 721 35\n292 726 -2\n292 755 17\n292 767 16\n292 778 6\n292 801 32\n292 846 21\n292 853 36\n292 854 1\n292 855 45\n292 861 4\n292 866 22\n292 873 36\n292 899 7\n292 913 22\n292 924 39\n292 959 37\n292 975 18\n292 980 35\n293 10 38\n293 13 32\n293 15 12\n293 20 21\n293 30 32\n293 39 3\n293 40 39\n293 56 16\n293 128 32\n293 132 31\n293 149 1\n293 165 -1\n293 212 23\n293 236 17\n293 252 4\n293 256 16\n293 278 2\n293 300 17\n293 313 2\n293 315 13\n293 318 6\n293 363 14\n293 406 35\n293 428 22\n293 458 10\n293 463 49\n293 495 33\n293 501 22\n293 526 35\n293 530 48\n293 543 37\n293 555 15\n293 576 44\n293 583 37\n293 586 44\n293 599 6\n293 603 5\n293 617 24\n293 631 14\n293 640 50\n293 654 29\n293 699 -2\n293 715 3\n293 717 46\n293 727 6\n293 743 41\n293 747 7\n293 785 28\n293 788 24\n293 794 38\n293 822 8\n293 833 27\n293 840 38\n293 849 24\n293 875 43\n293 984 34\n294 26 45\n294 69 11\n294 88 10\n294 125 10\n294 128 0\n294 167 40\n294 178 38\n294 203 35\n294 209 12\n294 228 11\n294 233 -2\n294 238 13\n294 246 0\n294 260 29\n294 307 49\n294 325 41\n294 332 24\n294 380 39\n294 406 17\n294 410 2\n294 417 33\n294 444 14\n294 451 -2\n294 470 34\n294 478 7\n294 490 35\n294 519 2\n294 524 6\n294 532 20\n294 534 49\n294 563 14\n294 573 24\n294 577 21\n294 579 18\n294 588 31\n294 633 41\n294 639 9\n294 643 17\n294 719 -1\n294 732 36\n294 746 34\n294 795 10\n294 814 34\n294 816 35\n294 829 28\n294 832 8\n294 854 28\n294 856 33\n294 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6\n299 783 32\n299 786 1\n299 797 33\n299 798 13\n299 802 9\n299 817 6\n299 833 43\n299 857 19\n299 869 19\n299 910 21\n299 917 18\n299 929 24\n299 941 0\n299 972 17\n299 977 2\n300 2 -2\n300 63 -1\n300 81 -1\n300 87 31\n300 100 21\n300 139 44\n300 187 -1\n300 199 3\n300 204 31\n300 214 29\n300 236 25\n300 266 24\n300 278 24\n300 311 49\n300 312 2\n300 326 40\n300 347 50\n300 376 9\n300 387 35\n300 405 10\n300 442 47\n300 450 27\n300 504 44\n300 537 45\n300 582 34\n300 614 43\n300 619 38\n300 630 34\n300 642 29\n300 648 44\n300 683 22\n300 684 47\n300 698 27\n300 709 33\n300 734 19\n300 811 38\n300 843 38\n300 848 39\n300 887 19\n300 909 34\n300 911 39\n300 915 1\n300 922 45\n300 934 15\n300 947 10\n300 952 -1\n301 3 49\n301 7 44\n301 26 2\n301 61 9\n301 73 17\n301 87 14\n301 141 17\n301 186 3\n301 291 22\n301 292 41\n301 318 8\n301 358 1\n301 365 -2\n301 390 17\n301 402 4\n301 405 28\n301 443 2\n301 462 29\n301 467 44\n301 475 0\n301 481 30\n301 482 -2\n301 489 13\n301 563 39\n301 567 34\n301 590 34\n301 618 47\n301 637 35\n301 638 18\n301 657 25\n301 663 30\n301 667 49\n301 681 -2\n301 696 36\n301 710 8\n301 728 5\n301 756 24\n301 776 42\n301 777 19\n301 803 33\n301 878 15\n301 881 28\n301 885 21\n301 913 2\n301 916 42\n301 932 17\n301 947 31\n301 983 47\n302 8 35\n302 10 27\n302 22 26\n302 70 1\n302 86 7\n302 93 4\n302 120 24\n302 138 48\n302 140 8\n302 153 14\n302 165 26\n302 168 41\n302 189 36\n302 221 21\n302 229 13\n302 242 13\n302 253 14\n302 255 32\n302 278 29\n302 280 4\n302 294 40\n302 303 49\n302 328 25\n302 343 7\n302 349 49\n302 353 -1\n302 361 11\n302 394 -2\n302 420 45\n302 421 11\n302 432 7\n302 462 1\n302 471 39\n302 488 27\n302 492 47\n302 508 13\n302 548 49\n302 561 33\n302 611 38\n302 618 32\n302 684 8\n302 702 24\n302 722 34\n302 736 6\n302 781 22\n302 813 26\n302 858 22\n302 866 44\n302 901 18\n302 903 47\n302 905 10\n302 959 50\n302 971 42\n302 977 1\n303 51 11\n303 54 48\n303 69 46\n303 78 49\n303 81 46\n303 84 7\n303 116 21\n303 123 34\n303 144 35\n303 152 45\n303 161 27\n303 187 13\n303 209 11\n303 248 11\n303 253 32\n303 276 48\n303 297 39\n303 320 34\n303 344 19\n303 376 40\n303 409 9\n303 451 23\n303 475 37\n303 498 26\n303 512 44\n303 522 33\n303 576 21\n303 580 4\n303 605 28\n303 641 27\n303 664 44\n303 677 21\n303 680 44\n303 706 28\n303 757 7\n303 759 11\n303 760 26\n303 763 7\n303 765 36\n303 779 49\n303 780 5\n303 788 16\n303 803 43\n303 815 29\n303 850 24\n303 858 9\n303 891 27\n303 903 29\n303 916 5\n303 922 23\n303 945 22\n303 974 26\n304 46 12\n304 108 50\n304 115 46\n304 153 49\n304 171 18\n304 184 6\n304 207 9\n304 324 26\n304 328 41\n304 332 45\n304 337 29\n304 392 18\n304 400 9\n304 432 25\n304 437 23\n304 491 46\n304 497 7\n304 514 19\n304 541 22\n304 544 26\n304 547 27\n304 562 1\n304 566 41\n304 596 11\n304 647 22\n304 659 13\n304 661 2\n304 666 13\n304 697 16\n304 701 34\n304 710 13\n304 729 26\n304 737 16\n304 747 13\n304 779 46\n304 819 29\n304 823 40\n304 827 47\n304 838 15\n304 845 3\n304 859 22\n304 870 24\n304 876 3\n304 887 21\n304 916 14\n304 931 18\n305 19 1\n305 47 34\n305 49 5\n305 53 8\n305 99 19\n305 108 26\n305 116 40\n305 121 26\n305 148 46\n305 171 44\n305 200 35\n305 231 0\n305 323 43\n305 340 6\n305 345 -2\n305 355 32\n305 360 17\n305 368 26\n305 369 50\n305 371 50\n305 372 31\n305 379 39\n305 382 2\n305 392 10\n305 398 5\n305 412 27\n305 419 40\n305 435 -2\n305 443 23\n305 459 21\n305 471 40\n305 522 0\n305 558 13\n305 571 5\n305 573 41\n305 581 5\n305 636 22\n305 685 39\n305 696 22\n305 730 25\n305 744 40\n305 777 38\n305 782 29\n305 786 46\n305 802 1\n305 841 49\n305 884 37\n305 918 8\n305 922 16\n305 930 31\n305 986 24\n305 993 32\n306 10 23\n306 17 30\n306 24 32\n306 40 47\n306 49 32\n306 57 32\n306 67 21\n306 95 45\n306 100 28\n306 124 -2\n306 140 11\n306 147 -1\n306 162 16\n306 192 18\n306 197 22\n306 232 -2\n306 240 37\n306 245 16\n306 269 13\n306 270 5\n306 310 24\n306 315 33\n306 322 34\n306 376 37\n306 440 31\n306 450 18\n306 468 -1\n306 489 16\n306 526 2\n306 537 -2\n306 544 32\n306 594 2\n306 668 29\n306 670 -1\n306 673 47\n306 731 42\n306 736 5\n306 740 27\n306 745 29\n306 758 16\n306 832 20\n306 837 28\n306 849 14\n306 851 12\n306 853 28\n306 862 39\n306 886 39\n306 917 47\n306 919 33\n306 964 23\n306 994 16\n307 6 5\n307 32 26\n307 55 10\n307 64 20\n307 102 -1\n307 110 38\n307 112 48\n307 138 36\n307 148 4\n307 150 9\n307 161 45\n307 168 24\n307 177 29\n307 181 32\n307 196 40\n307 224 23\n307 230 30\n307 233 28\n307 236 27\n307 255 9\n307 259 39\n307 283 36\n307 324 26\n307 329 21\n307 422 25\n307 428 2\n307 468 9\n307 474 19\n307 511 40\n307 532 46\n307 629 45\n307 633 -2\n307 677 28\n307 679 23\n307 681 46\n307 702 38\n307 721 14\n307 740 17\n307 741 9\n307 763 14\n307 780 44\n307 802 40\n307 896 38\n307 920 40\n307 924 18\n307 927 19\n307 942 12\n307 960 50\n307 963 9\n307 1000 18\n308 90 26\n308 102 26\n308 136 38\n308 176 38\n308 188 33\n308 191 20\n308 193 19\n308 214 3\n308 255 9\n308 269 30\n308 280 19\n308 304 45\n308 312 49\n308 365 3\n308 373 8\n308 383 36\n308 384 36\n308 396 0\n308 417 33\n308 445 24\n308 448 2\n308 449 28\n308 468 6\n308 482 34\n308 487 45\n308 491 45\n308 518 15\n308 540 6\n308 557 45\n308 561 0\n308 577 8\n308 579 32\n308 589 20\n308 607 40\n308 610 35\n308 617 17\n308 622 22\n308 625 23\n308 717 29\n308 766 39\n308 817 15\n308 821 41\n308 837 11\n308 893 26\n308 960 13\n308 987 2\n309 34 4\n309 67 1\n309 69 10\n309 74 39\n309 78 14\n309 82 10\n309 86 1\n309 105 37\n309 118 49\n309 120 41\n309 152 20\n309 153 11\n309 181 35\n309 210 8\n309 216 13\n309 245 -1\n309 274 34\n309 275 40\n309 283 16\n309 296 23\n309 339 49\n309 351 27\n309 354 19\n309 431 23\n309 454 24\n309 477 2\n309 492 23\n309 535 44\n309 538 3\n309 550 45\n309 557 42\n309 590 11\n309 630 39\n309 646 43\n309 661 44\n309 690 11\n309 699 31\n309 700 2\n309 731 47\n309 738 5\n309 749 43\n309 768 33\n309 771 3\n309 790 18\n309 818 39\n309 821 49\n309 840 -2\n309 849 18\n309 858 26\n309 867 15\n309 874 23\n309 876 36\n309 891 22\n309 915 36\n309 922 38\n309 938 38\n309 983 26\n310 22 22\n310 43 20\n310 88 31\n310 128 12\n310 169 25\n310 173 34\n310 191 33\n310 210 31\n310 218 6\n310 259 13\n310 289 15\n310 299 49\n310 314 15\n310 322 47\n310 327 48\n310 375 14\n310 420 50\n310 421 6\n310 493 10\n310 510 43\n310 518 35\n310 521 3\n310 583 22\n310 611 12\n310 641 36\n310 661 5\n310 663 36\n310 696 43\n310 745 4\n310 878 10\n310 902 13\n310 919 15\n310 929 32\n310 937 44\n310 950 27\n310 953 41\n310 958 25\n310 967 23\n310 998 34\n311 5 11\n311 31 36\n311 49 48\n311 61 17\n311 68 34\n311 70 33\n311 89 27\n311 94 5\n311 104 0\n311 123 9\n311 135 25\n311 146 41\n311 157 21\n311 163 23\n311 185 13\n311 218 32\n311 223 4\n311 224 24\n311 243 18\n311 268 20\n311 289 20\n311 308 37\n311 315 1\n311 348 42\n311 362 14\n311 371 28\n311 378 21\n311 397 21\n311 410 24\n311 416 17\n311 431 8\n311 439 44\n311 442 29\n311 469 26\n311 487 41\n311 491 10\n311 492 18\n311 505 22\n311 510 9\n311 546 20\n311 637 15\n311 642 16\n311 646 42\n311 655 43\n311 664 20\n311 673 44\n311 704 40\n311 743 13\n311 744 33\n311 746 4\n311 763 40\n311 796 47\n311 799 30\n311 810 23\n311 813 42\n311 832 26\n311 870 44\n311 900 33\n311 920 31\n311 944 24\n311 963 45\n311 976 44\n312 46 13\n312 52 -1\n312 61 1\n312 85 5\n312 103 10\n312 140 34\n312 142 37\n312 206 48\n312 289 22\n312 329 6\n312 362 12\n312 370 23\n312 407 34\n312 414 30\n312 426 25\n312 473 25\n312 532 17\n312 565 16\n312 583 29\n312 597 10\n312 624 34\n312 652 -2\n312 690 8\n312 695 37\n312 708 47\n312 749 31\n312 776 21\n312 810 48\n312 833 43\n312 863 2\n312 884 27\n312 906 11\n312 916 46\n312 929 22\n312 935 24\n312 944 25\n312 966 35\n313 9 13\n313 34 19\n313 36 21\n313 100 47\n313 142 39\n313 246 12\n313 305 39\n313 362 20\n313 363 2\n313 372 20\n313 375 1\n313 387 36\n313 390 6\n313 395 35\n313 412 45\n313 431 35\n313 434 37\n313 438 26\n313 452 46\n313 462 35\n313 470 31\n313 480 16\n313 482 48\n313 507 3\n313 527 36\n313 528 26\n313 547 38\n313 557 36\n313 588 40\n313 635 20\n313 682 41\n313 694 6\n313 709 1\n313 725 13\n313 756 45\n313 760 11\n313 779 22\n313 813 46\n313 814 21\n313 818 36\n313 819 33\n313 867 40\n313 904 13\n313 924 19\n313 934 8\n313 952 23\n313 959 50\n314 28 31\n314 30 37\n314 95 13\n314 113 6\n314 130 43\n314 155 42\n314 170 28\n314 182 31\n314 191 4\n314 193 0\n314 203 44\n314 207 9\n314 222 30\n314 224 39\n314 245 2\n314 260 10\n314 266 31\n314 273 24\n314 337 17\n314 359 30\n314 366 13\n314 398 23\n314 400 20\n314 407 39\n314 425 41\n314 483 42\n314 514 46\n314 521 40\n314 539 23\n314 541 30\n314 549 45\n314 566 39\n314 568 13\n314 577 45\n314 611 26\n314 633 35\n314 638 49\n314 699 -1\n314 726 42\n314 748 38\n314 761 29\n314 838 34\n314 858 47\n314 861 27\n314 909 27\n314 930 2\n314 966 -2\n314 971 23\n314 976 17\n315 100 14\n315 109 2\n315 149 0\n315 180 21\n315 200 3\n315 208 7\n315 218 1\n315 226 16\n315 239 1\n315 258 8\n315 273 26\n315 299 40\n315 302 40\n315 363 18\n315 383 16\n315 483 48\n315 502 35\n315 535 35\n315 544 11\n315 590 17\n315 606 22\n315 663 22\n315 670 33\n315 675 22\n315 712 9\n315 726 24\n315 743 2\n315 747 28\n315 771 41\n315 795 10\n315 803 21\n315 837 26\n315 881 33\n315 885 27\n315 886 20\n315 897 41\n315 904 28\n315 905 23\n315 913 26\n315 916 6\n315 926 32\n315 956 18\n315 959 34\n315 963 35\n316 7 33\n316 46 26\n316 52 19\n316 102 12\n316 126 5\n316 141 3\n316 153 23\n316 176 33\n316 239 12\n316 245 8\n316 247 18\n316 300 48\n316 326 22\n316 338 -1\n316 394 50\n316 397 40\n316 484 32\n316 503 23\n316 562 19\n316 575 22\n316 582 44\n316 586 17\n316 605 39\n316 622 17\n316 646 4\n316 653 0\n316 697 39\n316 720 45\n316 721 10\n316 740 44\n316 767 33\n316 768 15\n316 769 21\n316 792 11\n316 793 10\n316 830 24\n316 834 42\n316 845 44\n316 847 14\n316 854 24\n316 882 43\n316 908 15\n316 911 18\n316 914 30\n316 974 17\n316 976 16\n316 980 2\n316 996 8\n317 7 40\n317 21 3\n317 23 35\n317 40 14\n317 62 11\n317 82 26\n317 108 15\n317 133 17\n317 137 48\n317 159 46\n317 186 11\n317 190 2\n317 206 24\n317 214 2\n317 219 33\n317 247 32\n317 335 36\n317 370 23\n317 391 7\n317 413 26\n317 423 40\n317 426 30\n317 434 32\n317 437 41\n317 438 38\n317 447 36\n317 470 39\n317 478 18\n317 491 48\n317 504 39\n317 557 14\n317 564 36\n317 579 36\n317 604 46\n317 609 4\n317 630 24\n317 636 32\n317 643 39\n317 719 33\n317 721 36\n317 723 40\n317 731 4\n317 790 23\n317 793 40\n317 806 28\n317 813 44\n317 838 9\n317 840 39\n317 864 21\n317 865 1\n317 902 29\n317 913 50\n317 918 15\n317 925 12\n317 970 36\n317 991 24\n318 70 43\n318 90 -1\n318 97 32\n318 118 26\n318 138 29\n318 162 28\n318 167 21\n318 169 37\n318 197 26\n318 213 13\n318 254 24\n318 269 34\n318 275 36\n318 277 29\n318 302 3\n318 308 35\n318 330 -1\n318 331 30\n318 332 12\n318 353 38\n318 367 34\n318 436 4\n318 437 14\n318 463 30\n318 486 10\n318 524 40\n318 544 14\n318 564 41\n318 601 30\n318 639 48\n318 657 33\n318 678 35\n318 705 5\n318 723 28\n318 754 -2\n318 769 46\n318 783 36\n318 786 25\n318 795 12\n318 810 30\n318 878 -2\n318 886 46\n318 895 38\n318 908 21\n318 933 39\n318 996 10\n319 32 22\n319 99 16\n319 116 45\n319 133 37\n319 171 44\n319 195 21\n319 199 4\n319 216 50\n319 243 13\n319 281 0\n319 291 50\n319 297 18\n319 316 21\n319 353 14\n319 404 31\n319 413 34\n319 432 32\n319 456 26\n319 474 37\n319 479 16\n319 482 47\n319 509 47\n319 519 19\n319 523 41\n319 541 46\n319 543 35\n319 552 17\n319 569 47\n319 590 41\n319 608 22\n319 628 11\n319 647 11\n319 651 12\n319 665 9\n319 670 18\n319 677 40\n319 695 10\n319 719 34\n319 739 37\n319 760 42\n319 795 39\n319 823 13\n319 836 46\n319 842 40\n319 844 46\n319 863 25\n319 878 23\n319 910 9\n319 940 4\n319 966 12\n319 968 14\n319 988 16\n319 991 23\n319 999 24\n320 15 8\n320 35 44\n320 77 10\n320 80 15\n320 159 30\n320 167 0\n320 213 34\n320 218 19\n320 274 9\n320 298 24\n320 312 42\n320 319 0\n320 341 41\n320 346 7\n320 373 28\n320 394 38\n320 456 34\n320 461 42\n320 465 33\n320 489 23\n320 491 20\n320 492 8\n320 528 11\n320 541 13\n320 565 4\n320 572 36\n320 579 31\n320 611 46\n320 614 3\n320 624 26\n320 631 25\n320 635 50\n320 649 27\n320 658 12\n320 737 38\n320 761 21\n320 774 24\n320 789 21\n320 790 41\n320 800 46\n320 803 1\n320 808 43\n320 813 48\n320 835 45\n320 855 42\n320 885 9\n320 904 11\n320 908 35\n320 918 45\n320 933 32\n320 937 31\n320 953 29\n320 955 43\n320 995 0\n320 1000 4\n321 5 46\n321 11 19\n321 17 10\n321 110 5\n321 148 9\n321 149 49\n321 159 13\n321 161 30\n321 162 6\n321 167 20\n321 188 50\n321 205 40\n321 206 11\n321 235 27\n321 240 8\n321 300 48\n321 339 45\n321 375 25\n321 380 40\n321 388 0\n321 422 22\n321 426 31\n321 436 5\n321 439 41\n321 441 44\n321 455 32\n321 476 48\n321 477 1\n321 478 28\n321 481 13\n321 501 8\n321 504 50\n321 529 26\n321 532 34\n321 535 45\n321 560 19\n321 568 11\n321 606 32\n321 621 33\n321 629 41\n321 639 8\n321 649 19\n321 658 34\n321 660 8\n321 688 15\n321 692 2\n321 695 13\n321 722 10\n321 729 -2\n321 760 3\n321 764 33\n321 767 21\n321 795 -2\n321 820 14\n321 880 11\n321 903 29\n321 910 36\n322 40 28\n322 45 33\n322 68 2\n322 73 49\n322 78 39\n322 142 27\n322 144 26\n322 163 42\n322 175 40\n322 194 47\n322 240 2\n322 259 42\n322 260 44\n322 291 35\n322 297 27\n322 316 18\n322 351 48\n322 358 20\n322 364 22\n322 382 36\n322 393 29\n322 395 48\n322 422 50\n322 430 44\n322 432 49\n322 441 24\n322 455 47\n322 474 8\n322 555 36\n322 623 49\n322 641 44\n322 654 50\n322 664 3\n322 694 6\n322 718 3\n322 762 6\n322 776 39\n322 830 31\n322 845 13\n322 851 38\n322 857 0\n322 864 45\n322 901 40\n322 935 25\n322 947 26\n322 953 32\n322 961 14\n323 52 50\n323 69 21\n323 109 3\n323 133 30\n323 164 38\n323 172 37\n323 176 18\n323 220 19\n323 221 1\n323 236 18\n323 249 36\n323 277 1\n323 278 9\n323 279 34\n323 320 47\n323 326 37\n323 350 37\n323 411 46\n323 416 23\n323 428 37\n323 435 48\n323 444 5\n323 457 24\n323 459 27\n323 465 35\n323 470 24\n323 480 27\n323 482 29\n323 500 33\n323 534 43\n323 560 23\n323 591 50\n323 607 17\n323 610 18\n323 666 40\n323 702 31\n323 708 26\n323 710 48\n323 717 36\n323 774 47\n323 784 35\n323 881 28\n323 886 33\n323 894 41\n323 906 14\n323 949 2\n323 959 8\n323 966 32\n323 972 6\n323 982 28\n324 9 45\n324 25 40\n324 41 39\n324 100 46\n324 157 18\n324 169 31\n324 191 0\n324 192 34\n324 200 11\n324 205 48\n324 239 21\n324 246 18\n324 250 -2\n324 271 7\n324 283 39\n324 297 0\n324 307 0\n324 326 26\n324 452 3\n324 467 28\n324 496 16\n324 518 24\n324 521 36\n324 537 25\n324 551 45\n324 555 45\n324 587 15\n324 590 27\n324 611 20\n324 613 12\n324 618 5\n324 620 11\n324 654 3\n324 683 16\n324 695 11\n324 698 17\n324 735 50\n324 764 15\n324 791 18\n324 800 49\n324 803 30\n324 821 34\n324 873 25\n324 896 19\n325 10 48\n325 48 21\n325 93 4\n325 102 19\n325 124 41\n325 142 42\n325 152 45\n325 193 45\n325 224 24\n325 235 32\n325 263 32\n325 332 3\n325 370 45\n325 410 30\n325 411 39\n325 424 29\n325 429 20\n325 469 44\n325 472 39\n325 478 26\n325 483 8\n325 488 46\n325 497 11\n325 511 28\n325 583 5\n325 610 47\n325 620 3\n325 626 16\n325 643 7\n325 654 50\n325 655 35\n325 671 8\n325 727 41\n325 738 23\n325 741 47\n325 762 9\n325 766 6\n325 772 24\n325 829 0\n325 843 40\n325 866 18\n325 892 48\n325 895 -2\n325 899 4\n325 942 49\n325 972 25\n326 21 27\n326 28 49\n326 43 35\n326 62 10\n326 78 43\n326 82 9\n326 86 36\n326 89 15\n326 117 19\n326 123 2\n326 210 27\n326 224 42\n326 254 33\n326 271 11\n326 282 18\n326 285 28\n326 325 1\n326 375 25\n326 399 50\n326 436 23\n326 450 4\n326 471 6\n326 477 29\n326 501 47\n326 516 37\n326 521 32\n326 547 47\n326 564 30\n326 577 49\n326 649 20\n326 684 17\n326 720 20\n326 737 17\n326 750 9\n326 753 17\n326 755 33\n326 769 17\n326 773 50\n326 839 4\n326 868 32\n326 870 35\n326 921 43\n326 932 1\n327 18 3\n327 58 22\n327 170 1\n327 185 15\n327 195 31\n327 214 45\n327 223 45\n327 229 27\n327 236 5\n327 252 20\n327 268 20\n327 303 46\n327 347 32\n327 375 45\n327 383 10\n327 409 39\n327 420 33\n327 512 37\n327 521 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817 -2\n353 830 46\n353 836 28\n353 841 4\n353 844 25\n353 892 21\n354 30 36\n354 66 19\n354 94 -2\n354 113 10\n354 141 10\n354 163 23\n354 192 30\n354 207 10\n354 208 47\n354 216 44\n354 237 44\n354 251 41\n354 273 35\n354 318 33\n354 356 4\n354 382 25\n354 420 41\n354 421 40\n354 425 29\n354 459 33\n354 472 23\n354 483 47\n354 484 2\n354 493 37\n354 529 25\n354 551 31\n354 552 20\n354 562 7\n354 571 1\n354 600 16\n354 620 32\n354 651 3\n354 681 37\n354 703 50\n354 732 50\n354 755 19\n354 787 40\n354 817 6\n354 854 35\n354 873 14\n354 877 50\n354 881 26\n354 885 10\n354 903 47\n354 931 31\n354 984 21\n354 995 28\n355 5 40\n355 10 47\n355 32 21\n355 73 42\n355 106 33\n355 114 44\n355 130 7\n355 155 46\n355 157 12\n355 222 27\n355 224 0\n355 235 34\n355 237 45\n355 241 23\n355 256 38\n355 268 3\n355 294 10\n355 298 37\n355 307 34\n355 308 28\n355 334 48\n355 341 44\n355 347 3\n355 367 49\n355 403 24\n355 446 27\n355 462 43\n355 493 13\n355 548 -2\n355 557 26\n355 565 46\n355 574 5\n355 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726 -1\n410 744 32\n410 798 7\n410 807 12\n410 882 39\n410 885 42\n410 907 36\n410 945 11\n410 951 36\n410 967 8\n410 968 28\n410 971 33\n410 994 20\n411 23 6\n411 24 20\n411 67 16\n411 98 37\n411 99 17\n411 101 40\n411 104 5\n411 121 20\n411 126 46\n411 141 39\n411 172 24\n411 182 24\n411 226 19\n411 230 43\n411 242 22\n411 251 34\n411 274 45\n411 277 11\n411 279 29\n411 298 3\n411 360 44\n411 369 24\n411 373 20\n411 412 7\n411 423 11\n411 424 0\n411 450 42\n411 461 50\n411 509 16\n411 510 46\n411 513 15\n411 522 38\n411 543 11\n411 558 29\n411 561 19\n411 578 15\n411 590 48\n411 642 41\n411 659 21\n411 682 9\n411 684 6\n411 702 21\n411 707 34\n411 716 5\n411 765 34\n411 796 17\n411 818 2\n411 831 0\n411 845 40\n411 865 2\n411 924 24\n411 941 43\n411 948 9\n411 951 19\n412 3 23\n412 15 5\n412 74 44\n412 88 21\n412 113 7\n412 123 35\n412 151 38\n412 157 42\n412 167 16\n412 188 22\n412 196 20\n412 270 28\n412 305 22\n412 318 6\n412 338 28\n412 339 37\n412 376 25\n412 381 7\n412 420 49\n412 453 49\n412 582 47\n412 591 3\n412 601 22\n412 608 6\n412 628 30\n412 653 34\n412 662 34\n412 681 17\n412 704 5\n412 725 37\n412 755 9\n412 764 29\n412 772 41\n412 785 20\n412 810 32\n412 817 22\n412 822 50\n412 853 36\n412 865 39\n412 995 8\n413 13 20\n413 42 48\n413 58 20\n413 82 48\n413 89 19\n413 94 0\n413 97 2\n413 111 23\n413 121 -2\n413 125 20\n413 140 37\n413 155 1\n413 159 34\n413 175 27\n413 202 46\n413 237 -2\n413 270 40\n413 283 34\n413 342 20\n413 550 19\n413 557 22\n413 593 31\n413 599 13\n413 626 27\n413 634 39\n413 645 8\n413 657 10\n413 668 7\n413 728 26\n413 769 17\n413 775 25\n413 799 39\n413 802 37\n413 817 13\n413 845 45\n413 860 33\n413 873 35\n413 912 13\n413 915 28\n413 920 15\n413 984 21\n413 991 35\n414 26 28\n414 30 25\n414 47 30\n414 55 30\n414 79 32\n414 93 35\n414 101 48\n414 109 40\n414 112 18\n414 122 29\n414 186 28\n414 241 39\n414 259 2\n414 285 9\n414 299 44\n414 315 47\n414 331 15\n414 360 28\n414 445 -2\n414 454 23\n414 478 29\n414 480 39\n414 484 3\n414 492 22\n414 514 12\n414 523 1\n414 527 27\n414 590 16\n414 601 36\n414 638 12\n414 641 39\n414 654 29\n414 655 4\n414 678 28\n414 690 50\n414 694 34\n414 706 6\n414 730 1\n414 752 40\n414 758 30\n414 761 2\n414 765 5\n414 769 35\n414 783 11\n414 785 32\n414 801 10\n414 824 24\n414 842 6\n414 851 28\n415 76 29\n415 160 28\n415 181 13\n415 206 22\n415 225 23\n415 250 28\n415 254 32\n415 278 25\n415 330 1\n415 353 40\n415 373 5\n415 389 21\n415 391 20\n415 407 35\n415 413 17\n415 449 36\n415 475 5\n415 477 29\n415 485 26\n415 540 30\n415 554 37\n415 569 48\n415 616 29\n415 624 30\n415 678 19\n415 721 19\n415 744 11\n415 752 41\n415 754 17\n415 788 19\n415 799 28\n415 803 10\n415 809 4\n415 813 20\n415 814 16\n415 824 39\n415 825 33\n415 970 13\n415 972 47\n416 17 46\n416 75 38\n416 95 -1\n416 99 31\n416 131 45\n416 161 24\n416 166 42\n416 184 30\n416 193 14\n416 223 24\n416 266 32\n416 287 25\n416 291 23\n416 298 50\n416 309 30\n416 360 14\n416 381 50\n416 419 15\n416 426 32\n416 428 20\n416 464 49\n416 486 37\n416 521 2\n416 528 26\n416 532 21\n416 542 26\n416 548 14\n416 578 12\n416 612 5\n416 630 24\n416 708 46\n416 724 28\n416 737 6\n416 739 28\n416 745 39\n416 749 2\n416 753 6\n416 765 47\n416 832 9\n416 842 -2\n416 882 12\n416 883 29\n416 884 20\n416 970 -1\n416 975 13\n417 42 14\n417 66 40\n417 118 22\n417 130 34\n417 136 -2\n417 168 50\n417 199 37\n417 220 40\n417 245 39\n417 264 25\n417 292 23\n417 323 36\n417 328 38\n417 331 10\n417 393 -2\n417 415 16\n417 424 12\n417 428 22\n417 448 3\n417 489 49\n417 490 12\n417 497 44\n417 521 31\n417 538 18\n417 549 33\n417 559 19\n417 573 47\n417 577 17\n417 608 8\n417 611 5\n417 618 3\n417 685 47\n417 688 22\n417 704 2\n417 706 28\n417 718 36\n417 721 8\n417 772 17\n417 822 0\n417 832 20\n417 869 26\n417 875 28\n417 878 20\n417 881 23\n417 882 36\n417 886 21\n417 920 -2\n417 925 28\n417 950 8\n417 955 25\n417 959 -2\n417 970 0\n417 994 31\n417 998 18\n418 14 8\n418 37 24\n418 51 33\n418 75 43\n418 83 47\n418 94 49\n418 112 48\n418 115 45\n418 130 47\n418 151 38\n418 175 29\n418 192 36\n418 220 48\n418 228 8\n418 269 39\n418 271 19\n418 274 16\n418 275 33\n418 331 28\n418 334 15\n418 343 26\n418 426 43\n418 484 -2\n418 510 1\n418 540 23\n418 552 3\n418 591 20\n418 597 34\n418 598 25\n418 607 35\n418 623 16\n418 701 36\n418 750 27\n418 761 13\n418 768 12\n418 771 43\n418 817 26\n418 819 16\n418 893 33\n418 914 34\n418 925 13\n418 948 27\n418 992 49\n419 24 30\n419 28 26\n419 41 31\n419 49 40\n419 88 35\n419 94 47\n419 104 33\n419 109 2\n419 123 21\n419 174 40\n419 179 32\n419 216 27\n419 222 25\n419 250 47\n419 291 44\n419 324 0\n419 362 47\n419 369 23\n419 372 45\n419 381 48\n419 383 8\n419 396 26\n419 400 31\n419 403 -2\n419 409 38\n419 457 38\n419 466 6\n419 475 35\n419 496 35\n419 522 20\n419 525 34\n419 649 14\n419 701 46\n419 703 19\n419 739 20\n419 749 30\n419 782 46\n419 802 5\n419 832 31\n419 847 28\n419 853 8\n419 865 49\n419 881 16\n419 883 49\n419 908 41\n419 926 29\n419 934 29\n419 937 3\n419 938 8\n419 947 29\n419 959 49\n420 5 14\n420 11 5\n420 55 9\n420 63 8\n420 72 9\n420 108 48\n420 118 44\n420 121 5\n420 282 -1\n420 286 9\n420 300 43\n420 310 7\n420 337 39\n420 339 7\n420 375 9\n420 383 40\n420 426 7\n420 487 31\n420 507 10\n420 515 27\n420 518 22\n420 559 -1\n420 614 28\n420 619 36\n420 664 -1\n420 670 33\n420 673 14\n420 683 4\n420 701 17\n420 721 38\n420 722 33\n420 731 22\n420 776 32\n420 792 34\n420 798 34\n420 815 25\n420 825 -2\n420 861 8\n420 866 38\n420 868 41\n420 878 3\n420 884 43\n420 885 43\n420 894 22\n420 921 9\n420 924 -1\n420 929 35\n420 930 30\n420 937 27\n420 948 26\n421 38 21\n421 47 6\n421 67 45\n421 74 30\n421 77 46\n421 95 14\n421 119 -1\n421 138 7\n421 155 4\n421 178 18\n421 208 8\n421 219 22\n421 231 7\n421 236 5\n421 238 6\n421 251 32\n421 265 6\n421 300 26\n421 317 19\n421 321 37\n421 350 22\n421 353 16\n421 363 25\n421 397 16\n421 408 3\n421 429 8\n421 431 48\n421 433 12\n421 451 21\n421 455 -1\n421 474 44\n421 476 3\n421 507 8\n421 542 33\n421 573 43\n421 587 38\n421 613 17\n421 630 4\n421 644 4\n421 705 45\n421 769 44\n421 778 34\n421 803 7\n421 818 5\n421 837 18\n421 843 31\n421 856 31\n421 858 8\n421 944 32\n421 951 47\n421 955 9\n421 956 49\n421 957 2\n421 965 27\n421 995 13\n422 5 31\n422 14 32\n422 18 27\n422 39 25\n422 42 12\n422 47 45\n422 85 38\n422 109 47\n422 143 46\n422 160 13\n422 177 5\n422 202 34\n422 233 29\n422 246 11\n422 286 10\n422 297 14\n422 298 28\n422 351 18\n422 375 48\n422 411 15\n422 471 47\n422 494 13\n422 534 23\n422 566 50\n422 582 20\n422 646 35\n422 654 21\n422 655 44\n422 671 48\n422 712 26\n422 773 36\n422 802 34\n422 863 32\n422 870 43\n422 877 26\n422 940 47\n422 950 34\n422 952 30\n422 994 3\n423 81 1\n423 101 32\n423 111 7\n423 124 44\n423 142 21\n423 144 16\n423 152 7\n423 159 27\n423 164 31\n423 207 10\n423 240 39\n423 245 40\n423 269 38\n423 326 20\n423 367 43\n423 368 22\n423 388 42\n423 432 10\n423 445 31\n423 453 47\n423 501 27\n423 578 14\n423 606 31\n423 617 2\n423 635 31\n423 645 21\n423 721 16\n423 733 6\n423 736 50\n423 739 18\n423 750 8\n423 776 29\n423 800 50\n423 813 8\n423 872 13\n423 892 36\n423 897 39\n423 926 35\n423 946 29\n423 975 9\n423 984 10\n423 1000 35\n424 25 48\n424 41 45\n424 62 27\n424 70 5\n424 78 19\n424 171 49\n424 180 18\n424 231 31\n424 234 15\n424 246 24\n424 249 33\n424 281 39\n424 337 23\n424 364 20\n424 429 26\n424 500 5\n424 512 31\n424 515 35\n424 554 8\n424 643 50\n424 649 16\n424 664 32\n424 668 29\n424 672 30\n424 708 3\n424 715 6\n424 727 11\n424 753 35\n424 762 40\n424 764 3\n424 773 29\n424 790 32\n424 807 25\n424 825 17\n424 854 8\n424 872 36\n424 902 44\n424 906 34\n424 938 14\n424 961 41\n424 964 41\n425 50 25\n425 52 47\n425 77 -2\n425 89 0\n425 96 47\n425 97 14\n425 98 15\n425 119 23\n425 122 12\n425 148 12\n425 161 44\n425 169 27\n425 171 45\n425 181 50\n425 236 33\n425 318 22\n425 357 -2\n425 364 12\n425 366 20\n425 377 2\n425 383 21\n425 408 13\n425 411 40\n425 415 17\n425 422 27\n425 426 28\n425 427 14\n425 439 6\n425 449 45\n425 462 35\n425 532 6\n425 545 12\n425 555 41\n425 580 24\n425 585 4\n425 644 50\n425 647 15\n425 690 0\n425 733 31\n425 750 50\n425 752 39\n425 753 41\n425 785 36\n425 821 20\n425 837 7\n425 874 48\n425 896 30\n425 906 10\n425 942 10\n425 956 24\n425 958 24\n425 973 5\n426 26 3\n426 35 17\n426 41 12\n426 45 31\n426 78 12\n426 83 30\n426 97 17\n426 98 45\n426 127 2\n426 131 6\n426 138 20\n426 148 11\n426 156 28\n426 184 48\n426 198 31\n426 240 48\n426 291 29\n426 313 13\n426 329 25\n426 335 26\n426 350 37\n426 352 29\n426 371 15\n426 402 14\n426 418 16\n426 439 22\n426 468 19\n426 473 16\n426 474 30\n426 479 17\n426 480 17\n426 486 27\n426 526 5\n426 532 25\n426 536 10\n426 549 40\n426 554 18\n426 566 32\n426 586 42\n426 588 37\n426 607 1\n426 617 11\n426 653 15\n426 665 40\n426 696 9\n426 725 14\n426 737 16\n426 757 28\n426 779 11\n426 804 47\n426 822 5\n426 843 32\n426 858 9\n426 869 35\n426 889 39\n426 907 49\n426 909 21\n426 919 15\n426 996 10\n427 17 18\n427 20 21\n427 35 37\n427 37 0\n427 61 1\n427 68 32\n427 150 41\n427 163 5\n427 166 35\n427 186 12\n427 219 21\n427 227 44\n427 249 8\n427 250 26\n427 251 30\n427 267 24\n427 268 43\n427 334 6\n427 343 44\n427 374 8\n427 399 6\n427 423 46\n427 437 29\n427 454 49\n427 457 -2\n427 476 38\n427 499 9\n427 505 42\n427 561 23\n427 595 35\n427 615 6\n427 624 1\n427 625 28\n427 628 -2\n427 638 34\n427 659 5\n427 697 42\n427 704 22\n427 755 36\n427 765 5\n427 771 9\n427 780 5\n427 800 22\n427 811 -2\n427 850 49\n427 871 25\n427 896 37\n427 945 34\n427 946 8\n427 955 34\n427 983 -2\n428 16 25\n428 76 2\n428 88 12\n428 96 39\n428 108 9\n428 113 50\n428 116 17\n428 127 19\n428 151 40\n428 184 9\n428 202 13\n428 235 15\n428 236 0\n428 248 26\n428 275 38\n428 278 47\n428 334 48\n428 396 6\n428 418 33\n428 425 50\n428 452 37\n428 455 14\n428 494 31\n428 526 42\n428 550 28\n428 552 5\n428 554 33\n428 589 4\n428 595 13\n428 646 46\n428 664 17\n428 672 31\n428 675 28\n428 690 10\n428 693 28\n428 695 14\n428 698 29\n428 719 21\n428 746 39\n428 762 1\n428 775 21\n428 784 28\n428 808 11\n428 853 39\n428 862 42\n428 966 5\n428 973 8\n428 985 2\n429 34 27\n429 58 41\n429 59 41\n429 70 48\n429 90 13\n429 99 18\n429 142 50\n429 193 28\n429 219 29\n429 251 47\n429 284 18\n429 309 50\n429 331 50\n429 347 33\n429 373 15\n429 387 19\n429 396 44\n429 454 21\n429 465 13\n429 499 9\n429 560 14\n429 639 35\n429 662 23\n429 668 25\n429 680 30\n429 684 37\n429 708 36\n429 717 12\n429 725 10\n429 746 30\n429 805 30\n429 833 49\n429 852 37\n429 915 17\n429 925 39\n429 935 16\n429 978 17\n429 991 25\n430 20 21\n430 22 26\n430 44 22\n430 61 3\n430 62 -2\n430 111 11\n430 137 35\n430 138 5\n430 150 31\n430 157 22\n430 173 46\n430 195 34\n430 226 24\n430 233 42\n430 247 7\n430 251 35\n430 252 15\n430 255 46\n430 264 42\n430 265 43\n430 267 49\n430 277 20\n430 300 47\n430 383 17\n430 445 9\n430 481 50\n430 482 6\n430 487 18\n430 489 30\n430 547 14\n430 604 34\n430 611 25\n430 656 39\n430 668 -2\n430 734 31\n430 737 24\n430 756 47\n430 766 34\n430 780 27\n430 790 24\n430 822 13\n430 832 34\n430 838 14\n430 868 9\n430 921 45\n430 963 46\n430 982 8\n431 44 2\n431 53 36\n431 73 42\n431 87 7\n431 102 6\n431 136 -2\n431 140 6\n431 147 4\n431 153 22\n431 204 16\n431 220 22\n431 234 22\n431 249 43\n431 272 40\n431 274 31\n431 279 48\n431 282 8\n431 289 48\n431 317 5\n431 352 6\n431 437 24\n431 447 43\n431 464 42\n431 470 41\n431 476 10\n431 515 15\n431 519 34\n431 588 14\n431 595 33\n431 601 46\n431 621 35\n431 680 35\n431 694 7\n431 698 23\n431 722 -2\n431 741 13\n431 805 16\n431 834 41\n431 849 21\n431 852 32\n431 886 38\n431 901 36\n432 9 20\n432 26 48\n432 43 40\n432 87 13\n432 102 43\n432 113 10\n432 128 14\n432 138 18\n432 146 44\n432 161 17\n432 180 -2\n432 223 -1\n432 230 27\n432 271 24\n432 287 50\n432 346 27\n432 360 12\n432 384 17\n432 408 5\n432 424 15\n432 425 34\n432 493 32\n432 501 18\n432 502 26\n432 520 9\n432 530 20\n432 551 32\n432 594 42\n432 617 31\n432 637 38\n432 674 35\n432 717 27\n432 735 26\n432 749 8\n432 759 20\n432 783 24\n432 793 14\n432 830 28\n432 939 33\n432 985 15\n433 9 45\n433 50 48\n433 52 30\n433 62 22\n433 66 21\n433 80 37\n433 84 18\n433 85 25\n433 137 8\n433 139 19\n433 154 25\n433 167 5\n433 172 45\n433 179 16\n433 248 28\n433 253 33\n433 301 29\n433 370 45\n433 391 37\n433 420 47\n433 421 33\n433 432 35\n433 451 30\n433 471 50\n433 477 14\n433 499 0\n433 531 32\n433 548 48\n433 566 48\n433 581 31\n433 604 11\n433 605 45\n433 606 25\n433 618 7\n433 628 20\n433 642 0\n433 699 2\n433 726 31\n433 742 15\n433 746 12\n433 759 10\n433 760 21\n433 780 41\n433 789 14\n433 791 48\n433 792 36\n433 798 10\n433 801 3\n433 812 33\n433 821 7\n433 900 32\n433 921 19\n433 968 15\n434 19 -1\n434 50 23\n434 107 21\n434 115 38\n434 158 45\n434 212 24\n434 237 11\n434 243 41\n434 258 12\n434 260 46\n434 302 27\n434 369 10\n434 374 44\n434 409 15\n434 463 40\n434 488 43\n434 503 2\n434 526 21\n434 558 29\n434 569 19\n434 577 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49\n448 789 20\n448 794 14\n448 807 28\n448 821 -2\n448 843 -1\n448 848 11\n448 871 48\n448 927 21\n448 942 15\n448 962 9\n449 30 20\n449 70 14\n449 86 12\n449 102 41\n449 108 46\n449 113 -2\n449 124 29\n449 165 3\n449 174 13\n449 184 32\n449 212 1\n449 222 45\n449 234 16\n449 249 21\n449 253 37\n449 263 20\n449 279 20\n449 294 44\n449 295 17\n449 358 27\n449 370 25\n449 378 3\n449 464 36\n449 474 32\n449 494 0\n449 516 48\n449 534 39\n449 556 17\n449 565 11\n449 567 13\n449 586 -2\n449 604 41\n449 659 43\n449 727 28\n449 730 26\n449 738 33\n449 781 40\n449 787 1\n449 794 9\n449 805 -1\n449 827 3\n449 845 38\n449 850 23\n449 861 -2\n449 868 -2\n449 883 18\n449 926 28\n449 984 47\n450 20 29\n450 31 48\n450 74 17\n450 84 37\n450 120 25\n450 140 7\n450 141 20\n450 146 42\n450 172 6\n450 180 48\n450 192 18\n450 193 30\n450 195 38\n450 204 28\n450 206 30\n450 300 12\n450 319 28\n450 322 50\n450 334 9\n450 364 15\n450 370 40\n450 378 28\n450 380 19\n450 384 29\n450 459 26\n450 487 16\n450 535 3\n450 552 4\n450 582 24\n450 597 34\n450 599 10\n450 609 14\n450 657 48\n450 667 7\n450 676 50\n450 726 13\n450 728 50\n450 766 14\n450 768 25\n450 770 15\n450 772 13\n450 811 29\n450 853 26\n450 875 2\n450 909 33\n450 913 49\n450 933 39\n450 962 12\n450 979 44\n450 981 50\n451 7 33\n451 15 12\n451 38 47\n451 93 13\n451 141 40\n451 159 26\n451 166 44\n451 219 19\n451 309 5\n451 341 35\n451 373 34\n451 376 32\n451 394 48\n451 397 35\n451 398 24\n451 418 27\n451 448 2\n451 458 7\n451 469 31\n451 476 44\n451 511 7\n451 513 23\n451 514 4\n451 521 49\n451 551 45\n451 561 11\n451 577 39\n451 612 19\n451 629 47\n451 639 7\n451 656 18\n451 697 49\n451 755 1\n451 787 14\n451 809 20\n451 878 48\n451 879 28\n451 944 37\n451 985 40\n452 5 5\n452 12 21\n452 62 33\n452 67 31\n452 86 24\n452 90 1\n452 99 44\n452 109 7\n452 111 3\n452 118 18\n452 162 4\n452 185 18\n452 195 34\n452 205 36\n452 209 47\n452 227 5\n452 229 40\n452 232 -1\n452 248 10\n452 253 11\n452 273 11\n452 393 48\n452 414 31\n452 432 50\n452 457 45\n452 477 23\n452 479 37\n452 505 27\n452 523 14\n452 541 25\n452 560 25\n452 561 -1\n452 562 38\n452 565 33\n452 586 -1\n452 601 45\n452 622 45\n452 652 32\n452 678 45\n452 703 30\n452 707 12\n452 711 8\n452 738 50\n452 786 25\n452 791 5\n452 792 44\n452 799 39\n452 832 23\n452 842 17\n452 849 27\n452 876 26\n452 929 47\n452 941 6\n452 944 7\n452 981 23\n452 984 38\n453 8 21\n453 16 19\n453 78 50\n453 84 9\n453 108 0\n453 112 6\n453 119 5\n453 133 44\n453 143 45\n453 157 16\n453 165 34\n453 177 6\n453 194 17\n453 226 10\n453 243 41\n453 251 48\n453 290 20\n453 332 34\n453 349 16\n453 371 20\n453 382 2\n453 417 32\n453 441 37\n453 485 6\n453 501 11\n453 503 12\n453 530 35\n453 537 21\n453 548 25\n453 563 49\n453 574 34\n453 579 4\n453 600 43\n453 614 33\n453 644 42\n453 665 50\n453 703 1\n453 728 14\n453 729 22\n453 815 27\n453 827 -1\n453 847 43\n453 856 39\n453 879 0\n453 909 26\n453 945 30\n453 976 44\n454 13 36\n454 15 26\n454 40 34\n454 41 29\n454 116 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565 20\n491 619 44\n491 621 -2\n491 634 28\n491 654 8\n491 668 40\n491 672 25\n491 683 22\n491 700 20\n491 730 28\n491 734 29\n491 752 45\n491 779 23\n491 790 15\n491 810 35\n491 844 25\n491 847 15\n491 849 15\n491 858 43\n491 860 22\n491 914 9\n491 920 23\n491 936 42\n491 946 47\n491 955 45\n492 21 7\n492 22 35\n492 24 6\n492 45 3\n492 60 4\n492 67 12\n492 68 -1\n492 71 0\n492 84 24\n492 106 49\n492 120 43\n492 133 7\n492 140 32\n492 151 13\n492 180 0\n492 186 9\n492 190 31\n492 195 37\n492 211 21\n492 230 10\n492 238 14\n492 253 36\n492 273 33\n492 285 44\n492 325 17\n492 331 7\n492 334 41\n492 368 39\n492 369 26\n492 421 4\n492 493 -2\n492 504 26\n492 508 35\n492 551 36\n492 578 18\n492 585 31\n492 604 19\n492 646 25\n492 647 48\n492 653 19\n492 665 7\n492 687 17\n492 691 41\n492 699 8\n492 703 21\n492 709 27\n492 710 43\n492 711 11\n492 712 2\n492 768 12\n492 788 33\n492 820 -1\n492 835 19\n492 908 34\n492 926 19\n493 5 41\n493 64 9\n493 66 43\n493 95 35\n493 127 45\n493 165 9\n493 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15\n495 100 11\n495 141 1\n495 152 30\n495 164 34\n495 222 23\n495 244 16\n495 286 36\n495 308 4\n495 320 25\n495 353 47\n495 355 33\n495 362 5\n495 371 4\n495 390 39\n495 407 0\n495 440 6\n495 448 11\n495 476 42\n495 510 13\n495 515 48\n495 532 22\n495 536 29\n495 546 -1\n495 570 24\n495 623 21\n495 635 18\n495 636 0\n495 638 16\n495 686 5\n495 693 20\n495 706 7\n495 730 -2\n495 745 15\n495 769 25\n495 783 38\n495 832 28\n495 838 29\n495 839 28\n495 890 24\n495 896 50\n495 899 17\n495 900 46\n495 918 29\n495 927 27\n495 937 13\n495 953 39\n495 967 17\n495 988 9\n496 8 13\n496 14 21\n496 47 47\n496 57 41\n496 71 15\n496 123 36\n496 125 7\n496 126 0\n496 139 16\n496 148 35\n496 169 46\n496 175 6\n496 176 30\n496 179 2\n496 189 34\n496 196 48\n496 219 47\n496 231 24\n496 256 26\n496 257 30\n496 264 5\n496 270 6\n496 273 10\n496 288 50\n496 291 4\n496 301 46\n496 310 8\n496 325 36\n496 328 39\n496 339 13\n496 347 31\n496 349 33\n496 351 27\n496 357 29\n496 384 13\n496 387 22\n496 407 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14\n501 664 1\n501 682 9\n501 716 27\n501 733 0\n501 742 34\n501 749 42\n501 776 6\n501 789 45\n501 795 18\n501 823 38\n501 902 9\n501 975 14\n501 983 20\n502 89 19\n502 95 20\n502 127 11\n502 172 8\n502 178 13\n502 271 10\n502 276 28\n502 295 25\n502 313 21\n502 316 24\n502 332 31\n502 337 44\n502 339 10\n502 367 29\n502 398 15\n502 408 19\n502 433 23\n502 437 31\n502 443 0\n502 505 9\n502 534 4\n502 536 23\n502 583 10\n502 597 46\n502 613 39\n502 652 25\n502 668 46\n502 669 32\n502 671 15\n502 673 40\n502 692 32\n502 702 44\n502 773 1\n502 790 34\n502 804 22\n502 820 28\n502 841 -2\n502 847 35\n502 860 34\n502 883 30\n502 888 12\n502 890 17\n502 892 19\n502 902 39\n502 906 47\n502 945 44\n502 966 19\n502 992 6\n502 997 17\n502 999 5\n503 4 16\n503 35 7\n503 65 32\n503 91 27\n503 102 -2\n503 123 47\n503 135 19\n503 154 11\n503 156 9\n503 252 39\n503 327 48\n503 332 9\n503 373 8\n503 405 30\n503 429 17\n503 452 27\n503 496 34\n503 504 1\n503 512 11\n503 519 41\n503 558 50\n503 574 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25\n508 945 42\n508 964 40\n508 991 42\n508 992 19\n509 11 43\n509 32 9\n509 156 35\n509 195 14\n509 222 48\n509 245 4\n509 255 25\n509 273 20\n509 275 -1\n509 303 22\n509 332 30\n509 357 49\n509 404 10\n509 457 19\n509 463 29\n509 476 31\n509 485 4\n509 518 39\n509 524 33\n509 540 15\n509 549 41\n509 583 28\n509 607 37\n509 664 18\n509 678 11\n509 682 5\n509 693 43\n509 711 6\n509 726 26\n509 742 3\n509 816 48\n509 861 25\n509 869 46\n509 897 31\n509 905 13\n509 927 28\n509 939 3\n509 980 0\n509 983 21\n510 6 39\n510 18 6\n510 19 -1\n510 23 4\n510 27 32\n510 94 33\n510 97 1\n510 110 34\n510 115 42\n510 176 16\n510 185 36\n510 186 22\n510 189 24\n510 203 22\n510 204 30\n510 237 10\n510 268 19\n510 286 14\n510 304 44\n510 305 49\n510 351 14\n510 380 8\n510 382 36\n510 431 25\n510 446 45\n510 453 19\n510 454 29\n510 480 23\n510 490 35\n510 504 3\n510 521 48\n510 535 29\n510 548 44\n510 555 8\n510 562 37\n510 588 20\n510 623 46\n510 625 39\n510 654 1\n510 665 31\n510 746 13\n510 786 47\n510 787 37\n510 817 6\n510 858 47\n510 883 30\n510 934 30\n510 996 20\n511 17 11\n511 28 49\n511 100 18\n511 105 42\n511 109 49\n511 117 35\n511 118 4\n511 170 30\n511 173 44\n511 181 4\n511 193 31\n511 205 34\n511 258 44\n511 282 16\n511 286 35\n511 328 48\n511 348 8\n511 364 49\n511 369 9\n511 372 46\n511 387 0\n511 392 10\n511 414 28\n511 435 4\n511 465 48\n511 490 14\n511 497 46\n511 524 28\n511 563 12\n511 613 31\n511 664 20\n511 687 24\n511 706 45\n511 729 5\n511 763 46\n511 766 49\n511 774 14\n511 783 28\n511 809 31\n511 815 50\n511 816 48\n511 838 17\n511 897 28\n511 920 38\n511 924 37\n511 952 10\n512 24 2\n512 35 31\n512 49 42\n512 118 46\n512 129 17\n512 158 37\n512 165 26\n512 166 42\n512 193 0\n512 212 24\n512 232 28\n512 244 36\n512 306 49\n512 310 15\n512 362 32\n512 382 34\n512 386 41\n512 401 22\n512 412 31\n512 414 27\n512 418 41\n512 458 43\n512 475 25\n512 484 35\n512 501 10\n512 562 19\n512 567 41\n512 579 13\n512 583 42\n512 585 17\n512 596 50\n512 725 32\n512 758 47\n512 768 32\n512 778 42\n512 801 6\n512 826 33\n512 838 11\n512 867 40\n512 869 17\n512 876 44\n512 878 49\n512 908 18\n512 911 5\n512 916 12\n512 950 18\n512 978 43\n512 980 41\n512 990 32\n513 46 35\n513 68 42\n513 121 30\n513 190 11\n513 205 17\n513 212 42\n513 243 17\n513 324 41\n513 344 5\n513 356 22\n513 359 22\n513 381 44\n513 410 9\n513 422 48\n513 438 50\n513 480 37\n513 497 22\n513 512 21\n513 541 39\n513 630 4\n513 640 24\n513 723 16\n513 742 3\n513 749 26\n513 779 24\n513 788 31\n513 827 25\n513 830 47\n513 867 39\n513 893 35\n513 923 18\n513 953 0\n514 1 34\n514 2 22\n514 3 50\n514 35 11\n514 72 38\n514 111 21\n514 116 40\n514 121 10\n514 131 31\n514 140 4\n514 180 18\n514 200 48\n514 233 49\n514 235 45\n514 245 10\n514 248 2\n514 251 40\n514 299 19\n514 311 5\n514 348 50\n514 392 37\n514 393 3\n514 399 13\n514 408 23\n514 425 0\n514 445 9\n514 462 43\n514 496 22\n514 554 37\n514 571 21\n514 572 11\n514 597 26\n514 609 8\n514 675 6\n514 686 22\n514 704 8\n514 705 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37\n516 267 6\n516 297 19\n516 308 26\n516 327 46\n516 328 10\n516 329 44\n516 332 38\n516 351 15\n516 386 19\n516 387 14\n516 395 11\n516 399 14\n516 409 12\n516 454 33\n516 475 19\n516 477 10\n516 495 38\n516 533 17\n516 633 46\n516 652 28\n516 668 26\n516 676 39\n516 708 41\n516 735 21\n516 772 23\n516 785 14\n516 802 32\n516 808 6\n516 854 -2\n516 864 11\n516 886 32\n516 939 3\n516 953 8\n516 996 30\n517 19 29\n517 34 39\n517 36 0\n517 64 16\n517 82 48\n517 83 20\n517 84 -2\n517 92 32\n517 98 34\n517 182 10\n517 193 0\n517 215 41\n517 229 48\n517 254 12\n517 296 4\n517 398 9\n517 464 26\n517 493 28\n517 528 0\n517 529 23\n517 567 16\n517 600 28\n517 602 39\n517 640 47\n517 651 25\n517 676 46\n517 683 45\n517 698 35\n517 713 14\n517 717 10\n517 744 42\n517 770 24\n517 814 35\n517 819 50\n517 855 50\n517 872 15\n517 877 17\n517 904 8\n517 932 4\n517 934 31\n517 939 25\n518 35 12\n518 52 43\n518 54 34\n518 85 41\n518 87 46\n518 117 3\n518 144 35\n518 160 4\n518 184 37\n518 218 6\n518 229 35\n518 240 46\n518 264 19\n518 287 3\n518 307 39\n518 326 44\n518 328 13\n518 339 16\n518 353 42\n518 354 17\n518 355 43\n518 377 47\n518 388 28\n518 401 28\n518 409 39\n518 420 12\n518 445 22\n518 460 6\n518 514 10\n518 549 28\n518 557 21\n518 569 15\n518 590 44\n518 592 10\n518 623 50\n518 638 9\n518 655 32\n518 696 9\n518 704 13\n518 762 40\n518 808 21\n518 847 39\n518 871 29\n518 878 39\n518 904 28\n519 7 -1\n519 11 17\n519 44 4\n519 53 1\n519 78 16\n519 94 3\n519 112 35\n519 136 33\n519 142 7\n519 190 24\n519 199 10\n519 228 38\n519 274 48\n519 319 46\n519 328 13\n519 355 35\n519 357 35\n519 365 13\n519 414 12\n519 421 -1\n519 430 6\n519 460 10\n519 481 33\n519 499 27\n519 522 36\n519 527 32\n519 534 30\n519 585 45\n519 594 29\n519 595 31\n519 604 41\n519 616 20\n519 620 50\n519 624 49\n519 655 6\n519 686 24\n519 691 19\n519 698 16\n519 796 20\n519 800 33\n519 814 26\n519 850 41\n519 857 49\n519 859 12\n519 894 -2\n519 915 49\n519 978 40\n519 980 38\n520 12 7\n520 20 8\n520 49 25\n520 56 13\n520 63 8\n520 73 15\n520 77 35\n520 110 29\n520 119 47\n520 123 41\n520 155 16\n520 174 20\n520 240 33\n520 248 39\n520 254 21\n520 267 8\n520 275 15\n520 287 42\n520 295 46\n520 320 16\n520 406 2\n520 419 35\n520 421 50\n520 424 12\n520 468 26\n520 514 32\n520 517 8\n520 552 34\n520 557 13\n520 586 -2\n520 593 44\n520 616 9\n520 618 22\n520 637 13\n520 642 10\n520 650 42\n520 673 11\n520 683 11\n520 697 45\n520 707 45\n520 723 18\n520 728 17\n520 758 23\n520 759 30\n520 772 23\n520 782 25\n520 791 14\n520 840 12\n520 874 16\n520 917 50\n520 942 16\n520 953 28\n520 976 30\n520 995 15\n521 13 1\n521 32 23\n521 49 10\n521 72 10\n521 84 44\n521 163 28\n521 168 4\n521 171 21\n521 193 16\n521 228 7\n521 256 41\n521 259 9\n521 322 22\n521 343 30\n521 346 42\n521 349 12\n521 350 42\n521 385 23\n521 389 50\n521 457 10\n521 482 42\n521 492 8\n521 584 35\n521 613 31\n521 626 11\n521 641 2\n521 654 47\n521 686 11\n521 706 21\n521 737 28\n521 745 26\n521 778 44\n521 796 31\n521 909 33\n521 931 34\n521 944 10\n521 977 19\n521 981 14\n521 992 7\n522 38 42\n522 39 0\n522 49 47\n522 63 4\n522 77 30\n522 80 24\n522 86 29\n522 88 2\n522 124 13\n522 125 23\n522 203 6\n522 270 0\n522 287 36\n522 300 29\n522 329 49\n522 350 19\n522 426 38\n522 435 41\n522 500 31\n522 502 16\n522 512 32\n522 517 29\n522 562 39\n522 564 44\n522 587 39\n522 593 14\n522 601 9\n522 621 32\n522 626 40\n522 630 37\n522 668 42\n522 671 21\n522 686 43\n522 706 18\n522 726 33\n522 733 42\n522 769 -1\n522 794 45\n522 906 45\n522 928 23\n522 958 40\n523 28 19\n523 42 13\n523 59 18\n523 90 34\n523 123 24\n523 132 22\n523 154 44\n523 157 29\n523 160 22\n523 170 43\n523 212 37\n523 230 43\n523 256 31\n523 282 32\n523 297 9\n523 310 9\n523 335 21\n523 383 46\n523 416 7\n523 417 34\n523 478 6\n523 482 30\n523 492 3\n523 505 31\n523 557 22\n523 572 43\n523 614 40\n523 691 40\n523 699 22\n523 733 37\n523 741 31\n523 742 45\n523 764 23\n523 776 30\n523 800 15\n523 813 17\n523 815 37\n523 838 9\n523 842 10\n523 879 48\n523 919 1\n523 922 44\n523 928 17\n523 929 21\n523 941 50\n523 953 10\n523 985 5\n523 994 20\n524 5 21\n524 23 42\n524 58 18\n524 66 47\n524 67 3\n524 79 45\n524 81 12\n524 114 42\n524 136 14\n524 194 0\n524 214 4\n524 216 12\n524 233 32\n524 242 3\n524 290 21\n524 319 32\n524 336 20\n524 345 39\n524 369 45\n524 412 37\n524 413 41\n524 418 28\n524 419 18\n524 432 2\n524 477 10\n524 542 0\n524 574 32\n524 585 16\n524 586 29\n524 625 15\n524 637 28\n524 657 34\n524 719 3\n524 728 23\n524 729 25\n524 753 44\n524 754 3\n524 782 42\n524 838 -1\n524 839 44\n524 846 4\n524 854 42\n524 859 44\n524 863 7\n524 894 3\n524 895 36\n524 932 2\n524 974 -1\n525 56 11\n525 57 50\n525 65 15\n525 66 19\n525 75 47\n525 97 1\n525 113 20\n525 129 23\n525 139 5\n525 157 32\n525 172 17\n525 228 -1\n525 241 9\n525 298 23\n525 303 45\n525 308 2\n525 321 42\n525 418 21\n525 451 19\n525 473 20\n525 526 35\n525 530 16\n525 553 31\n525 555 26\n525 559 45\n525 589 18\n525 594 15\n525 600 3\n525 624 45\n525 677 26\n525 693 7\n525 702 17\n525 715 6\n525 732 2\n525 741 36\n525 749 36\n525 760 16\n525 790 24\n525 850 -1\n525 855 0\n525 892 34\n525 902 0\n525 979 16\n526 13 3\n526 42 24\n526 47 40\n526 57 3\n526 68 33\n526 71 21\n526 156 22\n526 172 8\n526 182 30\n526 207 5\n526 209 32\n526 235 39\n526 262 34\n526 271 39\n526 284 20\n526 290 17\n526 308 7\n526 309 41\n526 321 47\n526 335 45\n526 339 30\n526 343 2\n526 381 49\n526 387 20\n526 480 17\n526 501 47\n526 502 32\n526 540 26\n526 567 -1\n526 568 39\n526 581 28\n526 622 23\n526 626 39\n526 650 40\n526 701 17\n526 728 33\n526 737 14\n526 745 21\n526 800 44\n526 814 28\n526 818 28\n526 827 13\n526 834 38\n526 866 42\n526 882 9\n526 957 2\n526 1000 33\n527 3 24\n527 32 8\n527 46 17\n527 83 48\n527 111 10\n527 143 30\n527 146 15\n527 158 32\n527 239 39\n527 255 31\n527 265 16\n527 291 32\n527 307 48\n527 316 -1\n527 331 5\n527 336 50\n527 339 39\n527 350 12\n527 356 18\n527 391 30\n527 453 3\n527 460 6\n527 466 37\n527 518 20\n527 540 7\n527 568 47\n527 585 38\n527 609 42\n527 626 1\n527 630 38\n527 677 12\n527 683 37\n527 686 46\n527 743 24\n527 744 29\n527 755 4\n527 763 31\n527 795 -1\n527 821 25\n527 865 39\n527 868 19\n527 901 16\n527 933 35\n527 990 31\n528 10 25\n528 46 3\n528 78 10\n528 90 1\n528 108 11\n528 113 38\n528 123 48\n528 178 50\n528 184 13\n528 194 45\n528 196 44\n528 202 28\n528 228 33\n528 265 11\n528 281 15\n528 288 27\n528 299 44\n528 317 30\n528 320 25\n528 346 16\n528 349 14\n528 354 50\n528 356 50\n528 376 19\n528 423 38\n528 424 -2\n528 440 32\n528 479 42\n528 499 5\n528 502 4\n528 582 8\n528 606 9\n528 687 35\n528 704 22\n528 707 26\n528 723 33\n528 729 1\n528 739 48\n528 745 32\n528 778 10\n528 781 2\n528 807 33\n528 808 32\n528 821 2\n528 824 44\n528 835 18\n528 836 34\n528 857 35\n528 859 39\n528 872 44\n528 893 45\n528 926 4\n528 927 47\n528 945 6\n528 987 26\n529 23 8\n529 55 15\n529 58 42\n529 60 49\n529 70 11\n529 119 45\n529 145 4\n529 157 47\n529 164 48\n529 169 36\n529 204 42\n529 211 17\n529 233 15\n529 236 29\n529 241 48\n529 283 17\n529 289 39\n529 337 50\n529 372 16\n529 383 41\n529 389 38\n529 396 4\n529 427 20\n529 434 16\n529 460 37\n529 462 11\n529 467 35\n529 509 45\n529 513 7\n529 566 4\n529 573 42\n529 576 10\n529 589 32\n529 600 38\n529 606 36\n529 629 2\n529 645 2\n529 666 11\n529 676 9\n529 680 46\n529 684 9\n529 710 21\n529 712 5\n529 760 46\n529 780 45\n529 821 0\n529 829 33\n529 849 48\n529 856 -2\n529 860 18\n529 868 39\n529 872 27\n529 901 1\n529 911 30\n529 948 40\n529 979 22\n530 27 6\n530 82 21\n530 86 23\n530 96 12\n530 110 42\n530 116 36\n530 125 23\n530 150 14\n530 155 -2\n530 172 34\n530 180 22\n530 206 20\n530 218 22\n530 226 7\n530 232 18\n530 265 32\n530 267 5\n530 289 7\n530 319 1\n530 337 10\n530 344 31\n530 420 25\n530 433 0\n530 439 49\n530 469 27\n530 489 15\n530 505 8\n530 522 10\n530 546 18\n530 580 30\n530 593 6\n530 636 48\n530 643 41\n530 655 3\n530 664 11\n530 716 44\n530 747 50\n530 753 19\n530 775 45\n530 787 36\n530 798 50\n530 825 48\n530 853 17\n530 886 37\n530 912 50\n530 913 11\n530 935 22\n530 941 40\n530 951 49\n530 957 36\n531 12 41\n531 15 21\n531 16 3\n531 26 26\n531 51 6\n531 54 6\n531 56 34\n531 91 22\n531 164 7\n531 173 25\n531 180 -1\n531 198 4\n531 203 22\n531 208 -2\n531 221 25\n531 241 30\n531 258 24\n531 263 25\n531 286 33\n531 344 27\n531 347 36\n531 354 15\n531 355 18\n531 356 49\n531 357 4\n531 360 36\n531 393 40\n531 400 42\n531 417 42\n531 450 39\n531 459 8\n531 466 17\n531 490 0\n531 495 33\n531 526 27\n531 527 16\n531 534 21\n531 598 30\n531 615 41\n531 649 48\n531 667 29\n531 680 10\n531 695 49\n531 700 9\n531 730 5\n531 731 13\n531 749 31\n531 752 36\n531 757 20\n531 764 24\n531 766 4\n531 796 5\n531 824 49\n531 859 34\n531 867 49\n531 877 5\n531 891 34\n531 911 9\n531 918 27\n531 929 48\n531 932 12\n531 986 2\n532 13 36\n532 26 10\n532 60 13\n532 96 -2\n532 101 11\n532 120 38\n532 122 5\n532 149 5\n532 158 12\n532 201 44\n532 206 29\n532 212 7\n532 258 7\n532 265 1\n532 272 8\n532 273 19\n532 276 6\n532 282 35\n532 284 36\n532 303 1\n532 324 9\n532 347 43\n532 353 26\n532 365 33\n532 397 27\n532 421 40\n532 430 39\n532 453 9\n532 473 13\n532 478 11\n532 484 2\n532 494 19\n532 506 34\n532 517 11\n532 558 5\n532 572 34\n532 584 1\n532 628 14\n532 631 31\n532 649 12\n532 670 24\n532 750 14\n532 760 30\n532 798 14\n532 833 47\n532 858 29\n532 879 12\n532 900 20\n532 907 39\n532 985 19\n533 41 23\n533 77 14\n533 80 32\n533 104 4\n533 111 -1\n533 125 13\n533 132 43\n533 191 10\n533 195 43\n533 230 26\n533 244 6\n533 254 6\n533 256 34\n533 266 43\n533 269 4\n533 296 39\n533 301 17\n533 307 24\n533 309 13\n533 323 24\n533 395 -1\n533 404 11\n533 438 6\n533 474 12\n533 480 24\n533 535 38\n533 537 18\n533 558 43\n533 586 32\n533 595 21\n533 620 46\n533 692 5\n533 817 8\n533 820 6\n533 824 46\n533 834 47\n533 838 22\n533 847 30\n533 876 22\n533 928 49\n533 941 36\n533 951 30\n533 976 3\n534 9 10\n534 23 18\n534 53 6\n534 67 39\n534 95 30\n534 123 40\n534 221 38\n534 222 38\n534 227 12\n534 259 37\n534 277 47\n534 317 34\n534 400 5\n534 421 27\n534 426 48\n534 438 28\n534 445 36\n534 472 18\n534 475 39\n534 482 47\n534 489 36\n534 509 33\n534 512 -1\n534 546 42\n534 604 25\n534 613 14\n534 631 31\n534 660 26\n534 662 1\n534 664 30\n534 669 42\n534 676 39\n534 680 1\n534 682 47\n534 692 20\n534 710 3\n534 726 17\n534 765 49\n534 788 18\n534 796 40\n534 816 34\n534 854 2\n534 885 37\n534 886 34\n534 896 35\n534 907 19\n534 990 34\n535 1 -2\n535 21 9\n535 59 37\n535 78 44\n535 95 11\n535 110 47\n535 114 19\n535 157 26\n535 159 35\n535 167 47\n535 168 18\n535 175 7\n535 207 6\n535 212 13\n535 236 47\n535 259 29\n535 261 18\n535 268 20\n535 279 47\n535 302 41\n535 315 19\n535 323 43\n535 359 45\n535 374 35\n535 378 47\n535 397 15\n535 416 40\n535 443 7\n535 451 50\n535 525 35\n535 538 1\n535 582 17\n535 629 31\n535 665 19\n535 684 -1\n535 692 2\n535 713 24\n535 729 37\n535 734 29\n535 755 40\n535 757 9\n535 774 -2\n535 786 40\n535 804 10\n535 872 28\n535 887 16\n535 888 11\n535 905 28\n535 937 5\n535 942 35\n535 945 39\n535 988 28\n535 992 9\n536 30 17\n536 49 14\n536 51 17\n536 72 37\n536 85 31\n536 98 41\n536 106 11\n536 117 21\n536 158 14\n536 200 35\n536 209 10\n536 212 49\n536 237 14\n536 275 36\n536 291 6\n536 308 42\n536 375 25\n536 398 4\n536 414 21\n536 422 5\n536 438 28\n536 442 17\n536 453 10\n536 459 29\n536 460 36\n536 466 15\n536 471 0\n536 472 50\n536 485 15\n536 534 16\n536 543 0\n536 577 50\n536 586 11\n536 600 1\n536 607 17\n536 629 18\n536 637 18\n536 667 39\n536 693 13\n536 722 30\n536 723 3\n536 781 25\n536 821 22\n536 836 5\n536 848 30\n536 880 41\n536 921 15\n536 937 49\n536 981 28\n537 42 41\n537 66 0\n537 117 37\n537 136 5\n537 153 36\n537 166 20\n537 184 42\n537 213 22\n537 218 26\n537 223 41\n537 237 17\n537 247 46\n537 266 46\n537 284 -2\n537 294 25\n537 344 38\n537 383 25\n537 433 10\n537 442 33\n537 446 4\n537 487 29\n537 493 27\n537 560 29\n537 561 37\n537 617 32\n537 618 26\n537 649 14\n537 706 -1\n537 774 31\n537 779 4\n537 790 4\n537 802 21\n537 838 3\n537 877 34\n537 892 46\n537 940 27\n537 968 28\n537 977 47\n538 2 31\n538 15 40\n538 16 18\n538 36 11\n538 57 15\n538 68 38\n538 93 8\n538 109 6\n538 119 47\n538 151 9\n538 170 15\n538 182 24\n538 183 27\n538 196 41\n538 245 40\n538 259 46\n538 281 50\n538 294 43\n538 336 9\n538 339 30\n538 344 8\n538 358 23\n538 361 22\n538 373 43\n538 374 14\n538 382 13\n538 413 1\n538 415 40\n538 473 24\n538 503 10\n538 513 38\n538 563 1\n538 566 2\n538 590 3\n538 591 16\n538 639 35\n538 649 37\n538 652 28\n538 679 33\n538 717 30\n538 718 11\n538 719 27\n538 732 16\n538 744 7\n538 760 2\n538 773 50\n538 780 18\n538 781 12\n538 822 38\n538 837 9\n538 855 47\n538 866 20\n538 874 2\n538 902 30\n538 971 1\n538 987 2\n538 990 48\n539 45 30\n539 76 49\n539 92 -1\n539 112 16\n539 160 50\n539 194 45\n539 224 29\n539 256 46\n539 283 23\n539 286 5\n539 325 48\n539 379 11\n539 384 0\n539 430 15\n539 515 29\n539 528 24\n539 545 42\n539 551 38\n539 561 48\n539 609 32\n539 631 45\n539 635 33\n539 655 29\n539 661 39\n539 663 45\n539 697 23\n539 734 34\n539 832 16\n539 927 41\n539 935 27\n539 961 17\n539 983 38\n539 997 21\n540 11 17\n540 111 13\n540 119 9\n540 195 6\n540 246 31\n540 269 38\n540 291 31\n540 307 48\n540 339 23\n540 344 16\n540 357 16\n540 406 26\n540 407 7\n540 426 48\n540 428 42\n540 444 15\n540 477 33\n540 487 36\n540 511 25\n540 586 16\n540 589 29\n540 624 43\n540 644 44\n540 661 35\n540 662 31\n540 686 27\n540 702 26\n540 705 26\n540 719 18\n540 724 48\n540 733 28\n540 735 35\n540 766 28\n540 798 13\n540 803 42\n540 821 27\n540 864 41\n540 902 10\n540 907 0\n540 926 14\n540 953 4\n540 956 40\n540 961 17\n541 30 1\n541 102 35\n541 106 38\n541 111 13\n541 133 29\n541 146 9\n541 199 19\n541 229 9\n541 252 31\n541 298 48\n541 323 23\n541 343 43\n541 348 27\n541 360 6\n541 421 23\n541 434 45\n541 445 39\n541 456 42\n541 495 46\n541 504 36\n541 505 23\n541 526 41\n541 542 29\n541 554 29\n541 584 43\n541 588 2\n541 629 38\n541 669 0\n541 702 19\n541 705 39\n541 717 46\n541 720 42\n541 731 48\n541 752 -1\n541 771 37\n541 814 22\n541 879 11\n541 893 43\n541 909 41\n541 955 22\n541 963 10\n541 996 32\n542 27 28\n542 94 5\n542 113 7\n542 126 6\n542 132 48\n542 140 27\n542 143 44\n542 149 27\n542 204 29\n542 216 7\n542 256 33\n542 301 17\n542 334 19\n542 377 42\n542 383 41\n542 393 18\n542 402 32\n542 406 33\n542 427 1\n542 447 39\n542 451 29\n542 457 13\n542 469 30\n542 484 45\n542 491 29\n542 508 25\n542 537 47\n542 602 47\n542 629 11\n542 638 41\n542 639 48\n542 650 44\n542 679 24\n542 696 27\n542 701 43\n542 707 3\n542 716 9\n542 758 9\n542 767 14\n542 769 40\n542 787 -2\n542 788 41\n542 808 4\n542 810 45\n542 824 6\n542 836 27\n542 849 18\n542 912 20\n542 937 44\n542 972 -1\n542 978 6\n543 1 17\n543 12 47\n543 49 11\n543 50 41\n543 73 28\n543 84 16\n543 119 26\n543 146 10\n543 232 16\n543 246 38\n543 297 12\n543 321 28\n543 343 28\n543 351 43\n543 362 36\n543 373 21\n543 384 24\n543 436 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182 12\n626 193 30\n626 194 39\n626 227 20\n626 235 32\n626 240 25\n626 286 38\n626 291 16\n626 334 46\n626 344 27\n626 350 3\n626 354 11\n626 367 13\n626 381 13\n626 413 15\n626 420 19\n626 432 1\n626 438 49\n626 470 29\n626 478 38\n626 515 21\n626 547 2\n626 555 39\n626 576 39\n626 630 26\n626 632 18\n626 642 44\n626 684 23\n626 705 9\n626 718 20\n626 740 36\n626 741 23\n626 750 36\n626 763 49\n626 764 39\n626 789 9\n626 838 6\n626 855 44\n626 902 39\n626 934 29\n626 990 39\n626 993 40\n626 996 31\n627 92 9\n627 118 46\n627 131 3\n627 144 37\n627 149 50\n627 208 18\n627 233 2\n627 241 3\n627 279 39\n627 294 23\n627 315 29\n627 318 49\n627 327 21\n627 337 30\n627 338 5\n627 358 28\n627 361 27\n627 405 23\n627 407 4\n627 462 10\n627 464 44\n627 478 50\n627 499 3\n627 521 10\n627 530 38\n627 533 10\n627 537 8\n627 541 38\n627 564 39\n627 568 41\n627 570 22\n627 573 30\n627 581 1\n627 582 2\n627 592 12\n627 599 47\n627 602 17\n627 640 42\n627 657 19\n627 660 36\n627 670 8\n627 695 23\n627 696 29\n627 700 4\n627 706 32\n627 741 4\n627 754 13\n627 761 7\n627 775 21\n627 790 1\n627 807 50\n627 817 26\n627 861 46\n627 863 25\n627 879 11\n627 901 20\n627 907 46\n627 909 32\n627 943 15\n627 946 49\n627 998 23\n628 24 35\n628 112 28\n628 140 17\n628 170 37\n628 171 50\n628 177 6\n628 198 47\n628 212 16\n628 243 8\n628 286 24\n628 301 29\n628 336 1\n628 346 47\n628 357 30\n628 361 23\n628 363 47\n628 406 0\n628 415 16\n628 427 37\n628 433 37\n628 436 19\n628 519 33\n628 523 50\n628 554 22\n628 561 45\n628 612 7\n628 624 41\n628 631 3\n628 674 35\n628 679 49\n628 687 38\n628 698 35\n628 754 31\n628 761 0\n628 763 28\n628 772 34\n628 774 7\n628 782 42\n628 786 9\n628 806 37\n628 817 12\n628 821 13\n628 824 3\n628 837 46\n628 854 25\n628 856 40\n628 858 6\n628 928 30\n628 994 26\n629 21 13\n629 29 8\n629 36 17\n629 50 35\n629 69 11\n629 79 14\n629 94 49\n629 140 33\n629 164 17\n629 167 41\n629 170 15\n629 204 35\n629 208 45\n629 245 31\n629 247 6\n629 250 35\n629 298 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43\n650 717 44\n650 727 23\n650 732 25\n650 785 50\n650 811 35\n650 818 8\n650 821 31\n650 829 22\n650 846 41\n650 913 45\n650 924 35\n650 927 17\n650 947 17\n650 948 35\n650 976 2\n650 990 13\n651 3 12\n651 35 14\n651 61 32\n651 83 9\n651 91 20\n651 98 32\n651 100 12\n651 111 33\n651 119 10\n651 120 5\n651 137 48\n651 139 35\n651 150 41\n651 169 34\n651 170 20\n651 173 26\n651 185 28\n651 190 49\n651 264 18\n651 267 35\n651 322 34\n651 351 12\n651 387 46\n651 395 31\n651 434 6\n651 446 19\n651 450 28\n651 451 24\n651 477 39\n651 608 49\n651 627 1\n651 631 29\n651 662 8\n651 667 40\n651 669 42\n651 672 38\n651 682 27\n651 692 34\n651 736 6\n651 825 49\n651 828 49\n651 834 42\n651 838 47\n651 850 32\n651 867 44\n651 889 36\n651 896 11\n651 902 24\n651 921 24\n651 948 19\n651 967 18\n651 969 21\n651 998 43\n652 100 24\n652 114 24\n652 147 4\n652 192 35\n652 247 8\n652 268 43\n652 289 6\n652 331 27\n652 347 20\n652 349 43\n652 377 50\n652 399 37\n652 421 24\n652 422 -1\n652 424 34\n652 426 5\n652 446 13\n652 453 47\n652 462 45\n652 466 20\n652 481 13\n652 483 49\n652 521 39\n652 550 6\n652 559 26\n652 651 19\n652 694 44\n652 700 38\n652 723 -1\n652 784 8\n652 788 36\n652 797 48\n652 808 43\n652 827 36\n652 847 24\n652 864 9\n652 949 16\n652 963 5\n652 970 35\n652 982 31\n653 41 36\n653 42 37\n653 51 25\n653 73 21\n653 130 28\n653 174 50\n653 209 39\n653 228 6\n653 261 21\n653 266 10\n653 274 33\n653 323 17\n653 339 41\n653 368 10\n653 379 48\n653 392 27\n653 433 34\n653 445 7\n653 519 15\n653 521 28\n653 527 46\n653 548 41\n653 558 41\n653 570 4\n653 592 37\n653 595 32\n653 605 24\n653 620 17\n653 632 28\n653 666 9\n653 715 32\n653 728 43\n653 736 -1\n653 738 -2\n653 749 10\n653 753 48\n653 763 3\n653 799 11\n653 803 24\n653 810 22\n653 837 50\n653 838 36\n653 868 16\n653 887 25\n653 909 49\n653 927 33\n653 930 45\n653 940 33\n653 959 2\n653 992 50\n653 995 26\n654 11 38\n654 141 8\n654 180 46\n654 182 20\n654 209 27\n654 249 13\n654 264 37\n654 272 6\n654 309 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10\n655 892 8\n655 909 40\n655 923 44\n655 935 15\n655 966 20\n655 989 36\n656 11 2\n656 18 34\n656 34 41\n656 78 1\n656 104 5\n656 137 27\n656 175 10\n656 176 10\n656 191 3\n656 193 9\n656 195 33\n656 200 50\n656 216 50\n656 307 43\n656 333 33\n656 390 1\n656 398 16\n656 402 5\n656 403 46\n656 413 3\n656 426 44\n656 473 20\n656 480 9\n656 481 36\n656 490 44\n656 492 17\n656 507 22\n656 551 31\n656 569 44\n656 609 31\n656 624 50\n656 634 45\n656 680 17\n656 681 4\n656 688 -2\n656 697 20\n656 698 46\n656 732 29\n656 748 48\n656 759 4\n656 766 0\n656 780 7\n656 811 26\n656 838 39\n656 849 23\n656 873 48\n656 874 24\n656 917 26\n656 925 40\n656 953 31\n657 10 10\n657 51 14\n657 64 49\n657 93 32\n657 114 20\n657 128 37\n657 165 -1\n657 173 31\n657 184 5\n657 216 33\n657 282 26\n657 284 22\n657 289 10\n657 300 24\n657 320 29\n657 331 22\n657 364 0\n657 440 30\n657 476 32\n657 491 -2\n657 493 44\n657 496 7\n657 507 32\n657 525 27\n657 549 18\n657 573 11\n657 580 39\n657 584 7\n657 587 41\n657 588 41\n657 589 2\n657 613 0\n657 627 21\n657 648 16\n657 659 40\n657 663 46\n657 664 41\n657 665 23\n657 680 8\n657 742 27\n657 765 17\n657 767 7\n657 769 31\n657 783 40\n657 795 18\n657 799 49\n657 817 44\n657 820 13\n657 833 36\n657 850 13\n657 852 45\n657 857 1\n657 906 15\n657 960 25\n657 962 22\n657 967 48\n657 972 34\n657 976 16\n657 991 32\n658 28 19\n658 31 48\n658 55 18\n658 77 45\n658 84 -1\n658 98 13\n658 119 20\n658 149 26\n658 167 27\n658 201 28\n658 209 8\n658 210 36\n658 213 32\n658 232 8\n658 269 21\n658 286 28\n658 287 21\n658 303 46\n658 312 -2\n658 376 49\n658 391 13\n658 433 46\n658 441 40\n658 496 42\n658 497 12\n658 504 39\n658 540 46\n658 567 6\n658 576 16\n658 595 40\n658 597 26\n658 605 46\n658 615 24\n658 627 9\n658 639 34\n658 648 41\n658 650 17\n658 654 4\n658 690 28\n658 706 8\n658 708 34\n658 709 48\n658 734 -2\n658 792 31\n658 828 16\n658 839 1\n658 905 44\n658 910 16\n658 912 42\n658 924 13\n658 928 7\n658 938 17\n658 975 28\n659 64 46\n659 94 43\n659 105 31\n659 146 22\n659 156 12\n659 157 27\n659 163 18\n659 166 24\n659 190 35\n659 206 8\n659 220 33\n659 325 43\n659 344 10\n659 366 20\n659 373 -2\n659 433 11\n659 438 50\n659 445 45\n659 459 50\n659 473 17\n659 490 32\n659 497 20\n659 506 17\n659 533 7\n659 546 42\n659 567 20\n659 574 16\n659 579 17\n659 585 19\n659 597 33\n659 600 50\n659 607 16\n659 640 43\n659 643 1\n659 655 50\n659 673 37\n659 686 35\n659 698 28\n659 711 45\n659 762 37\n659 769 4\n659 771 37\n659 785 12\n659 815 27\n659 831 43\n659 892 25\n659 926 17\n659 942 4\n659 950 32\n659 969 7\n659 978 43\n660 28 42\n660 130 24\n660 138 11\n660 146 5\n660 150 16\n660 170 4\n660 217 17\n660 220 42\n660 267 13\n660 331 10\n660 359 22\n660 364 21\n660 370 37\n660 386 42\n660 393 36\n660 410 13\n660 422 34\n660 456 4\n660 489 34\n660 506 6\n660 581 33\n660 632 36\n660 657 23\n660 691 38\n660 712 41\n660 732 1\n660 735 49\n660 741 23\n660 743 24\n660 748 23\n660 760 34\n660 763 15\n660 779 28\n660 794 25\n660 797 2\n660 826 1\n660 844 1\n660 846 24\n660 867 46\n660 875 10\n660 912 38\n660 915 4\n660 922 23\n660 969 23\n660 977 15\n660 997 12\n661 25 11\n661 31 24\n661 46 46\n661 107 40\n661 132 18\n661 149 43\n661 151 27\n661 162 25\n661 175 8\n661 179 37\n661 198 13\n661 200 23\n661 217 33\n661 224 15\n661 234 12\n661 271 38\n661 293 3\n661 320 40\n661 340 9\n661 388 2\n661 389 32\n661 417 33\n661 425 36\n661 439 33\n661 469 27\n661 493 12\n661 524 12\n661 528 18\n661 596 21\n661 624 34\n661 715 12\n661 744 -1\n661 752 48\n661 796 46\n661 821 29\n661 865 36\n661 883 9\n661 884 26\n661 892 45\n661 914 8\n661 935 12\n661 936 7\n661 949 18\n661 976 29\n661 996 1\n662 24 30\n662 41 19\n662 45 38\n662 48 43\n662 79 19\n662 109 42\n662 192 17\n662 280 17\n662 308 24\n662 328 48\n662 334 22\n662 344 27\n662 420 10\n662 462 29\n662 495 48\n662 525 23\n662 557 14\n662 585 24\n662 600 24\n662 670 20\n662 713 11\n662 718 47\n662 721 21\n662 732 35\n662 780 41\n662 790 38\n662 791 39\n662 810 34\n662 811 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5\n664 767 34\n664 783 15\n664 787 10\n664 805 39\n664 844 -1\n664 852 38\n664 858 15\n664 866 20\n664 887 20\n664 911 0\n664 912 38\n664 914 33\n664 960 7\n665 20 31\n665 36 33\n665 42 24\n665 43 35\n665 92 9\n665 96 12\n665 99 47\n665 112 22\n665 125 41\n665 136 8\n665 155 5\n665 156 45\n665 177 16\n665 191 24\n665 217 40\n665 252 31\n665 254 40\n665 263 44\n665 274 15\n665 282 49\n665 291 18\n665 297 22\n665 310 27\n665 331 10\n665 362 7\n665 451 3\n665 480 50\n665 487 42\n665 522 8\n665 537 28\n665 543 25\n665 546 40\n665 565 12\n665 577 11\n665 581 32\n665 612 23\n665 630 13\n665 639 47\n665 643 22\n665 646 0\n665 704 23\n665 724 27\n665 735 39\n665 804 43\n665 811 15\n665 822 3\n665 837 5\n665 841 6\n665 864 21\n665 891 42\n665 900 16\n665 913 2\n665 963 18\n665 966 5\n665 995 -1\n666 5 3\n666 33 21\n666 44 35\n666 49 21\n666 96 9\n666 103 12\n666 138 5\n666 153 16\n666 237 36\n666 241 37\n666 270 35\n666 276 42\n666 298 38\n666 311 32\n666 393 34\n666 403 29\n666 412 18\n666 469 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321 14\n704 347 22\n704 354 -2\n704 359 10\n704 385 49\n704 398 10\n704 426 42\n704 481 28\n704 501 16\n704 511 41\n704 637 18\n704 640 23\n704 649 39\n704 684 34\n704 690 0\n704 761 45\n704 770 28\n704 775 20\n704 799 21\n704 802 24\n704 807 4\n704 814 10\n704 841 22\n704 864 11\n704 870 24\n704 874 14\n704 952 46\n704 958 25\n704 963 39\n704 970 15\n704 981 43\n704 987 20\n704 991 16\n705 7 44\n705 17 25\n705 51 26\n705 85 26\n705 102 13\n705 105 19\n705 111 39\n705 135 17\n705 138 42\n705 167 31\n705 177 48\n705 222 24\n705 234 9\n705 236 47\n705 244 20\n705 254 48\n705 255 45\n705 377 4\n705 410 43\n705 413 3\n705 419 29\n705 468 19\n705 516 28\n705 520 44\n705 541 31\n705 575 11\n705 590 9\n705 609 5\n705 610 31\n705 626 33\n705 639 11\n705 656 8\n705 679 6\n705 708 37\n705 758 16\n705 762 30\n705 822 27\n705 827 9\n705 834 47\n705 886 1\n705 986 30\n706 13 3\n706 39 32\n706 94 7\n706 97 46\n706 125 30\n706 137 36\n706 142 2\n706 147 40\n706 148 3\n706 272 27\n706 283 13\n706 292 20\n706 308 10\n706 311 28\n706 323 47\n706 328 42\n706 338 15\n706 341 10\n706 402 47\n706 420 13\n706 435 8\n706 452 10\n706 463 34\n706 482 16\n706 487 30\n706 529 30\n706 597 48\n706 616 18\n706 623 20\n706 649 20\n706 657 11\n706 667 37\n706 727 43\n706 768 31\n706 769 50\n706 784 31\n706 791 40\n706 810 28\n706 862 23\n706 887 24\n706 898 30\n706 959 31\n707 1 45\n707 7 38\n707 36 25\n707 49 45\n707 62 19\n707 70 7\n707 73 13\n707 109 18\n707 139 32\n707 167 9\n707 173 35\n707 190 5\n707 219 25\n707 224 28\n707 259 44\n707 267 19\n707 268 29\n707 276 22\n707 283 38\n707 289 17\n707 330 22\n707 345 8\n707 347 24\n707 374 14\n707 439 25\n707 440 39\n707 456 27\n707 517 18\n707 537 39\n707 555 18\n707 574 50\n707 649 38\n707 658 39\n707 664 49\n707 673 20\n707 681 10\n707 694 24\n707 742 16\n707 750 37\n707 834 44\n707 840 22\n707 851 42\n707 858 37\n707 863 44\n707 935 16\n707 984 22\n707 1000 26\n708 8 26\n708 15 19\n708 32 4\n708 46 39\n708 56 35\n708 62 14\n708 71 6\n708 76 16\n708 78 39\n708 86 39\n708 99 20\n708 107 39\n708 115 26\n708 128 8\n708 142 20\n708 152 27\n708 161 42\n708 193 31\n708 201 34\n708 225 29\n708 298 22\n708 302 33\n708 349 24\n708 384 34\n708 388 41\n708 405 46\n708 409 30\n708 443 18\n708 480 2\n708 488 43\n708 534 4\n708 599 44\n708 652 5\n708 684 43\n708 751 19\n708 787 2\n708 795 22\n708 799 31\n708 833 26\n708 877 37\n708 881 46\n708 889 12\n708 890 48\n708 900 0\n708 901 42\n708 919 34\n708 932 10\n708 996 39\n709 46 13\n709 55 44\n709 113 34\n709 119 40\n709 199 10\n709 204 35\n709 205 45\n709 232 10\n709 249 38\n709 284 30\n709 294 8\n709 303 26\n709 324 29\n709 346 39\n709 417 31\n709 445 37\n709 501 7\n709 534 45\n709 564 32\n709 570 36\n709 670 20\n709 680 38\n709 755 32\n709 775 18\n709 834 18\n709 869 26\n709 880 34\n709 897 20\n709 922 30\n709 934 6\n709 937 6\n709 978 3\n709 990 28\n709 996 23\n710 2 3\n710 16 33\n710 43 11\n710 73 35\n710 87 21\n710 102 30\n710 126 46\n710 132 39\n710 167 32\n710 194 32\n710 203 24\n710 211 11\n710 257 17\n710 350 26\n710 370 20\n710 409 7\n710 425 43\n710 439 20\n710 458 48\n710 485 24\n710 494 34\n710 501 20\n710 536 43\n710 539 33\n710 546 45\n710 550 39\n710 570 10\n710 586 27\n710 588 49\n710 639 50\n710 666 42\n710 669 46\n710 718 22\n710 727 26\n710 737 48\n710 776 48\n710 809 22\n710 818 6\n710 833 19\n710 843 34\n710 856 48\n710 859 30\n710 883 16\n710 886 45\n710 889 10\n710 907 48\n710 919 47\n710 927 31\n710 931 50\n710 935 48\n710 947 10\n710 959 22\n710 980 36\n710 986 15\n710 991 3\n711 26 2\n711 52 27\n711 81 28\n711 110 12\n711 127 9\n711 147 50\n711 153 22\n711 154 49\n711 171 10\n711 172 44\n711 179 30\n711 184 36\n711 211 48\n711 248 4\n711 250 3\n711 271 20\n711 282 22\n711 320 49\n711 323 44\n711 360 33\n711 380 28\n711 429 -2\n711 431 50\n711 444 2\n711 459 -1\n711 468 45\n711 489 2\n711 508 3\n711 516 4\n711 546 0\n711 563 0\n711 579 48\n711 595 19\n711 645 48\n711 648 23\n711 651 48\n711 687 9\n711 771 38\n711 792 40\n711 850 44\n711 865 25\n711 867 45\n711 893 17\n711 903 40\n711 919 23\n711 924 9\n711 927 7\n711 935 50\n711 963 33\n712 4 9\n712 17 49\n712 18 40\n712 20 21\n712 29 40\n712 50 23\n712 86 16\n712 89 16\n712 91 24\n712 108 47\n712 133 42\n712 142 11\n712 143 14\n712 152 29\n712 210 9\n712 219 29\n712 253 49\n712 276 10\n712 358 26\n712 379 9\n712 405 29\n712 443 21\n712 497 43\n712 529 47\n712 541 11\n712 593 12\n712 608 9\n712 612 33\n712 614 39\n712 621 10\n712 634 8\n712 694 39\n712 750 6\n712 788 0\n712 822 45\n712 840 44\n712 970 3\n713 2 33\n713 28 3\n713 82 40\n713 85 13\n713 95 28\n713 110 32\n713 144 0\n713 158 37\n713 167 50\n713 175 7\n713 182 17\n713 184 20\n713 188 28\n713 228 -2\n713 301 14\n713 327 36\n713 358 6\n713 418 24\n713 479 32\n713 520 23\n713 565 20\n713 603 19\n713 660 13\n713 669 -2\n713 671 0\n713 687 31\n713 690 15\n713 698 50\n713 736 50\n713 760 30\n713 777 44\n713 825 37\n713 847 4\n713 850 21\n713 876 29\n713 879 6\n713 880 9\n713 897 7\n713 963 40\n713 967 9\n713 979 37\n713 985 0\n714 28 14\n714 95 22\n714 100 26\n714 122 16\n714 127 16\n714 144 38\n714 148 18\n714 156 25\n714 171 40\n714 181 27\n714 203 2\n714 230 22\n714 266 26\n714 270 21\n714 296 24\n714 309 38\n714 316 22\n714 333 16\n714 347 43\n714 358 46\n714 361 17\n714 365 41\n714 375 36\n714 433 25\n714 436 33\n714 523 22\n714 548 45\n714 559 17\n714 615 30\n714 620 32\n714 670 19\n714 688 36\n714 730 13\n714 828 8\n714 834 42\n714 839 48\n714 846 46\n714 847 40\n714 871 13\n714 883 19\n714 900 22\n714 936 38\n714 944 23\n714 946 15\n714 1000 24\n715 21 42\n715 62 23\n715 78 47\n715 81 37\n715 99 18\n715 135 2\n715 165 26\n715 227 7\n715 258 49\n715 278 22\n715 293 24\n715 323 47\n715 347 42\n715 351 16\n715 384 13\n715 385 20\n715 404 -2\n715 410 46\n715 420 38\n715 430 14\n715 440 -2\n715 501 43\n715 507 5\n715 544 9\n715 549 49\n715 573 42\n715 578 37\n715 663 3\n715 689 37\n715 755 15\n715 779 13\n715 786 10\n715 835 7\n715 864 -1\n715 867 6\n715 870 -1\n715 890 40\n715 906 23\n715 915 37\n715 922 11\n715 960 5\n715 972 44\n715 981 2\n715 993 15\n716 1 7\n716 35 15\n716 37 8\n716 38 16\n716 67 40\n716 75 16\n716 80 10\n716 86 12\n716 96 30\n716 106 33\n716 109 38\n716 129 28\n716 185 22\n716 228 44\n716 255 13\n716 276 5\n716 339 -2\n716 348 20\n716 361 33\n716 366 24\n716 385 6\n716 396 1\n716 457 3\n716 459 28\n716 504 7\n716 515 8\n716 519 4\n716 529 31\n716 534 40\n716 563 5\n716 565 13\n716 567 22\n716 587 2\n716 591 7\n716 628 -2\n716 637 44\n716 646 48\n716 664 12\n716 672 42\n716 675 36\n716 677 18\n716 694 0\n716 714 18\n716 736 8\n716 766 28\n716 783 19\n716 788 35\n716 791 -1\n716 807 13\n716 843 48\n716 845 45\n716 873 29\n716 876 36\n716 904 9\n716 940 17\n716 959 2\n716 1000 48\n717 2 30\n717 8 33\n717 18 32\n717 89 46\n717 101 11\n717 131 16\n717 145 12\n717 165 6\n717 167 20\n717 200 -1\n717 262 2\n717 276 2\n717 286 21\n717 289 45\n717 316 14\n717 330 24\n717 343 32\n717 367 48\n717 386 42\n717 391 17\n717 405 5\n717 466 13\n717 469 13\n717 510 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44\n721 91 44\n721 115 29\n721 121 15\n721 163 25\n721 173 40\n721 229 41\n721 267 -1\n721 295 36\n721 336 9\n721 361 9\n721 399 31\n721 416 0\n721 420 9\n721 434 24\n721 479 34\n721 487 21\n721 522 22\n721 566 33\n721 593 6\n721 617 45\n721 623 18\n721 652 6\n721 686 34\n721 690 22\n721 702 46\n721 707 39\n721 716 45\n721 748 46\n721 768 32\n721 787 -1\n721 819 1\n721 820 50\n721 839 37\n721 843 21\n721 844 25\n721 855 37\n721 863 43\n721 872 27\n721 884 6\n721 893 49\n721 895 37\n721 924 10\n721 952 46\n721 958 4\n721 959 31\n721 982 30\n721 997 35\n722 12 21\n722 28 38\n722 42 43\n722 78 50\n722 79 5\n722 85 26\n722 101 14\n722 175 49\n722 176 27\n722 209 46\n722 217 33\n722 226 41\n722 228 41\n722 232 9\n722 267 30\n722 306 3\n722 311 25\n722 325 38\n722 339 44\n722 344 12\n722 353 33\n722 383 -1\n722 417 23\n722 463 18\n722 474 7\n722 500 22\n722 539 8\n722 612 10\n722 621 30\n722 631 20\n722 639 10\n722 649 47\n722 651 30\n722 661 26\n722 686 27\n722 707 11\n722 725 28\n722 776 31\n722 787 23\n722 823 26\n722 824 29\n722 863 24\n722 868 41\n722 909 37\n722 915 18\n722 928 22\n722 936 38\n722 944 27\n722 981 11\n723 6 26\n723 41 39\n723 55 21\n723 81 37\n723 90 50\n723 108 18\n723 170 11\n723 209 31\n723 228 47\n723 236 18\n723 239 29\n723 269 14\n723 285 24\n723 289 24\n723 316 49\n723 333 23\n723 335 48\n723 343 31\n723 379 27\n723 420 29\n723 432 17\n723 442 7\n723 458 45\n723 464 42\n723 475 44\n723 576 14\n723 588 46\n723 632 19\n723 638 8\n723 682 12\n723 698 36\n723 720 29\n723 750 34\n723 751 45\n723 766 30\n723 772 35\n723 847 39\n723 864 28\n723 885 29\n723 896 19\n723 921 31\n723 934 38\n723 963 0\n724 9 41\n724 61 6\n724 89 40\n724 101 13\n724 109 21\n724 123 3\n724 129 18\n724 178 24\n724 188 27\n724 236 12\n724 246 33\n724 249 34\n724 258 36\n724 260 31\n724 267 1\n724 339 41\n724 347 10\n724 374 32\n724 375 42\n724 392 13\n724 393 16\n724 397 4\n724 424 31\n724 449 18\n724 450 -1\n724 470 5\n724 476 16\n724 493 35\n724 494 18\n724 502 24\n724 507 3\n724 547 26\n724 549 41\n724 563 28\n724 572 22\n724 574 1\n724 598 -2\n724 628 0\n724 663 30\n724 688 45\n724 725 3\n724 730 13\n724 762 18\n724 770 12\n724 794 19\n724 834 12\n724 859 50\n724 883 21\n724 905 28\n724 932 37\n724 933 18\n724 937 28\n724 945 16\n724 972 12\n725 61 31\n725 64 40\n725 75 35\n725 88 46\n725 94 13\n725 117 11\n725 130 47\n725 132 19\n725 174 12\n725 186 10\n725 228 33\n725 255 14\n725 258 16\n725 343 12\n725 351 15\n725 397 30\n725 429 33\n725 443 35\n725 490 19\n725 495 11\n725 515 46\n725 532 42\n725 541 46\n725 553 40\n725 564 7\n725 570 43\n725 593 8\n725 612 37\n725 617 18\n725 620 36\n725 635 4\n725 640 10\n725 651 43\n725 673 20\n725 678 15\n725 697 26\n725 744 37\n725 745 45\n725 767 20\n725 777 44\n725 794 24\n725 827 29\n725 829 8\n725 855 33\n725 861 23\n725 869 16\n725 894 45\n725 915 10\n725 917 44\n725 955 42\n725 960 17\n725 991 3\n725 993 37\n725 996 22\n725 997 13\n725 998 9\n726 1 45\n726 10 33\n726 18 21\n726 54 25\n726 65 14\n726 83 31\n726 87 31\n726 153 27\n726 194 23\n726 207 0\n726 415 31\n726 451 32\n726 492 37\n726 545 12\n726 560 4\n726 569 39\n726 571 39\n726 598 8\n726 605 40\n726 607 37\n726 626 21\n726 634 23\n726 649 39\n726 672 23\n726 687 42\n726 709 45\n726 764 4\n726 803 33\n726 838 44\n726 874 15\n727 5 35\n727 8 32\n727 17 32\n727 30 37\n727 35 8\n727 41 1\n727 53 26\n727 61 0\n727 95 26\n727 97 37\n727 102 1\n727 111 31\n727 117 26\n727 127 42\n727 128 16\n727 132 18\n727 201 9\n727 206 23\n727 223 46\n727 238 5\n727 256 42\n727 292 19\n727 305 39\n727 310 47\n727 354 19\n727 412 47\n727 442 28\n727 505 0\n727 536 22\n727 560 15\n727 563 19\n727 564 29\n727 593 47\n727 601 14\n727 629 35\n727 643 46\n727 644 26\n727 645 47\n727 707 40\n727 718 8\n727 782 9\n727 812 4\n727 822 -2\n727 853 31\n727 868 6\n727 870 17\n727 912 49\n727 928 28\n727 930 43\n727 934 22\n727 949 2\n727 954 49\n727 955 33\n727 965 49\n727 966 41\n727 985 21\n727 997 50\n728 34 44\n728 39 28\n728 47 11\n728 205 28\n728 216 44\n728 219 21\n728 239 44\n728 247 50\n728 271 43\n728 273 47\n728 303 26\n728 310 19\n728 337 15\n728 350 9\n728 368 25\n728 382 27\n728 383 12\n728 403 9\n728 432 9\n728 457 9\n728 480 14\n728 559 2\n728 581 30\n728 583 32\n728 592 1\n728 597 48\n728 602 27\n728 603 10\n728 608 46\n728 650 37\n728 718 25\n728 787 38\n728 793 5\n728 824 50\n728 830 -2\n728 859 10\n728 881 38\n728 921 13\n728 950 7\n728 957 44\n728 964 -2\n728 982 35\n728 983 35\n729 6 42\n729 13 26\n729 41 37\n729 74 25\n729 79 41\n729 92 38\n729 111 10\n729 166 11\n729 189 6\n729 196 25\n729 238 -2\n729 245 32\n729 246 14\n729 275 20\n729 286 29\n729 319 29\n729 338 28\n729 405 23\n729 413 39\n729 439 7\n729 515 33\n729 544 31\n729 573 2\n729 585 28\n729 588 16\n729 627 21\n729 634 3\n729 654 -1\n729 665 4\n729 670 21\n729 672 6\n729 696 29\n729 731 49\n729 767 37\n729 802 24\n729 820 11\n729 826 15\n729 836 4\n729 851 16\n729 874 26\n729 913 33\n729 915 11\n729 940 5\n729 971 4\n729 975 1\n729 996 15\n730 4 41\n730 19 31\n730 36 17\n730 45 42\n730 65 29\n730 90 49\n730 119 27\n730 143 23\n730 189 45\n730 227 24\n730 276 26\n730 278 22\n730 282 21\n730 298 20\n730 323 8\n730 355 47\n730 398 49\n730 422 2\n730 437 19\n730 446 32\n730 457 39\n730 469 47\n730 504 42\n730 513 42\n730 525 32\n730 544 10\n730 561 -2\n730 637 -2\n730 647 39\n730 666 44\n730 698 36\n730 702 25\n730 753 12\n730 771 18\n730 793 25\n730 800 36\n730 810 13\n730 853 28\n730 867 30\n730 901 30\n730 939 43\n730 989 24\n731 15 36\n731 30 49\n731 44 27\n731 65 31\n731 75 46\n731 119 27\n731 151 17\n731 162 20\n731 170 47\n731 175 48\n731 189 7\n731 243 36\n731 264 23\n731 297 13\n731 314 8\n731 315 24\n731 332 9\n731 340 37\n731 370 13\n731 374 40\n731 376 19\n731 404 8\n731 409 40\n731 427 20\n731 473 33\n731 491 50\n731 500 34\n731 566 17\n731 568 47\n731 608 45\n731 610 42\n731 615 29\n731 620 42\n731 628 9\n731 639 16\n731 660 42\n731 690 39\n731 694 30\n731 700 7\n731 704 23\n731 719 24\n731 736 16\n731 737 19\n731 739 3\n731 758 10\n731 784 48\n731 802 46\n731 826 27\n731 836 27\n731 854 45\n731 889 14\n731 891 36\n731 909 47\n731 954 23\n731 964 7\n732 6 48\n732 19 34\n732 46 18\n732 76 48\n732 108 39\n732 135 15\n732 137 47\n732 154 14\n732 217 22\n732 266 21\n732 292 34\n732 341 49\n732 346 38\n732 371 34\n732 386 12\n732 392 29\n732 398 1\n732 399 28\n732 416 13\n732 449 49\n732 451 29\n732 467 50\n732 484 50\n732 503 31\n732 557 30\n732 560 1\n732 564 24\n732 570 30\n732 599 47\n732 624 23\n732 656 42\n732 710 38\n732 867 25\n732 909 14\n732 922 35\n732 923 45\n732 947 11\n732 955 46\n732 960 49\n732 963 19\n732 983 20\n732 991 9\n733 12 35\n733 39 22\n733 67 15\n733 78 3\n733 80 38\n733 102 20\n733 129 21\n733 133 31\n733 152 8\n733 154 17\n733 162 42\n733 232 15\n733 233 33\n733 244 46\n733 260 47\n733 273 39\n733 324 46\n733 343 10\n733 352 46\n733 365 31\n733 371 3\n733 380 32\n733 423 48\n733 459 23\n733 483 18\n733 528 19\n733 551 36\n733 588 10\n733 592 47\n733 600 20\n733 634 24\n733 636 31\n733 660 38\n733 676 33\n733 677 49\n733 682 22\n733 701 34\n733 706 3\n733 719 -1\n733 727 23\n733 751 39\n733 809 42\n733 843 23\n733 886 22\n733 901 15\n733 924 5\n733 930 4\n733 935 23\n733 960 45\n733 970 33\n733 985 17\n734 1 22\n734 7 24\n734 13 15\n734 14 32\n734 49 19\n734 63 4\n734 64 2\n734 97 27\n734 99 34\n734 123 3\n734 124 31\n734 129 20\n734 153 34\n734 162 46\n734 191 1\n734 257 21\n734 258 41\n734 267 16\n734 280 27\n734 311 50\n734 321 13\n734 337 27\n734 349 10\n734 354 11\n734 357 35\n734 358 12\n734 359 18\n734 394 41\n734 412 10\n734 427 27\n734 444 12\n734 492 30\n734 526 37\n734 561 15\n734 580 36\n734 596 30\n734 617 20\n734 629 14\n734 636 23\n734 658 45\n734 662 33\n734 683 28\n734 702 28\n734 719 33\n734 722 39\n734 724 5\n734 726 25\n734 743 26\n734 760 45\n734 802 6\n734 804 50\n734 827 33\n734 837 23\n734 840 44\n734 851 46\n734 881 14\n734 921 10\n734 932 21\n734 953 30\n734 972 5\n734 976 1\n734 977 35\n734 995 28\n735 38 39\n735 50 25\n735 52 13\n735 64 47\n735 67 42\n735 98 48\n735 169 19\n735 186 42\n735 203 27\n735 207 2\n735 222 43\n735 225 49\n735 351 3\n735 371 7\n735 410 1\n735 460 1\n735 483 20\n735 506 17\n735 551 32\n735 584 15\n735 610 10\n735 702 33\n735 709 6\n735 732 13\n735 773 43\n735 775 18\n735 798 15\n735 815 41\n735 832 43\n735 850 46\n735 880 30\n735 887 45\n735 889 -2\n735 891 10\n735 900 32\n735 944 49\n735 989 37\n736 12 24\n736 38 23\n736 39 37\n736 60 14\n736 86 42\n736 95 12\n736 97 20\n736 136 50\n736 153 16\n736 164 9\n736 203 27\n736 207 7\n736 210 33\n736 224 47\n736 239 7\n736 241 5\n736 277 25\n736 292 24\n736 320 4\n736 363 4\n736 414 37\n736 420 26\n736 457 48\n736 536 39\n736 577 42\n736 578 7\n736 606 44\n736 613 28\n736 621 42\n736 643 44\n736 657 4\n736 660 19\n736 669 31\n736 677 29\n736 687 41\n736 707 46\n736 719 9\n736 783 49\n736 817 43\n736 837 13\n736 860 37\n736 892 19\n736 906 21\n736 949 50\n736 951 9\n736 986 26\n736 989 40\n737 13 48\n737 19 40\n737 64 39\n737 88 29\n737 106 26\n737 125 19\n737 130 22\n737 201 8\n737 202 13\n737 212 43\n737 234 24\n737 267 40\n737 288 18\n737 302 2\n737 315 20\n737 322 4\n737 323 35\n737 368 50\n737 370 24\n737 377 4\n737 387 47\n737 391 36\n737 411 3\n737 430 48\n737 444 50\n737 446 15\n737 495 9\n737 511 45\n737 538 8\n737 544 43\n737 557 35\n737 602 12\n737 619 33\n737 623 17\n737 630 -1\n737 636 31\n737 650 23\n737 667 37\n737 693 0\n737 703 39\n737 732 15\n737 739 38\n737 789 37\n737 816 32\n737 841 32\n737 858 42\n737 880 24\n737 900 48\n737 929 22\n737 932 25\n737 949 20\n737 950 43\n738 21 29\n738 72 13\n738 73 16\n738 82 7\n738 93 39\n738 111 25\n738 114 34\n738 136 17\n738 176 18\n738 200 43\n738 306 18\n738 336 3\n738 353 9\n738 370 40\n738 443 47\n738 528 0\n738 530 29\n738 599 13\n738 611 -1\n738 632 23\n738 674 -2\n738 688 36\n738 703 15\n738 725 40\n738 742 11\n738 788 28\n738 792 32\n738 837 8\n738 912 35\n738 938 43\n738 947 27\n738 955 22\n738 957 40\n738 973 28\n738 975 5\n739 3 21\n739 8 33\n739 57 27\n739 79 45\n739 105 28\n739 108 39\n739 111 40\n739 133 18\n739 177 23\n739 221 28\n739 234 37\n739 257 33\n739 285 19\n739 301 36\n739 337 23\n739 349 20\n739 386 4\n739 388 15\n739 389 26\n739 402 34\n739 403 36\n739 442 21\n739 475 42\n739 484 33\n739 504 12\n739 530 41\n739 538 48\n739 544 48\n739 574 36\n739 580 26\n739 582 26\n739 583 24\n739 599 29\n739 609 7\n739 620 40\n739 631 32\n739 653 33\n739 703 44\n739 704 29\n739 711 32\n739 715 21\n739 717 22\n739 740 20\n739 751 7\n739 752 28\n739 759 48\n739 790 10\n739 836 42\n739 849 39\n739 870 19\n739 871 40\n739 884 24\n739 888 2\n739 901 14\n739 913 49\n739 931 19\n739 942 24\n739 960 14\n739 965 44\n739 974 21\n739 983 37\n740 3 47\n740 28 47\n740 44 34\n740 46 35\n740 48 16\n740 58 20\n740 73 1\n740 98 22\n740 101 15\n740 114 38\n740 139 18\n740 162 14\n740 171 13\n740 189 28\n740 195 11\n740 217 34\n740 273 41\n740 314 31\n740 322 36\n740 356 18\n740 368 46\n740 494 33\n740 501 34\n740 505 37\n740 514 33\n740 521 16\n740 534 38\n740 556 17\n740 575 6\n740 632 7\n740 680 5\n740 682 42\n740 729 43\n740 761 43\n740 771 45\n740 787 47\n740 792 12\n740 823 5\n740 851 37\n740 916 29\n740 951 36\n740 986 45\n740 997 7\n741 23 24\n741 41 20\n741 112 18\n741 114 48\n741 135 50\n741 174 43\n741 188 35\n741 212 9\n741 225 50\n741 287 9\n741 298 18\n741 311 9\n741 320 39\n741 322 39\n741 353 16\n741 354 25\n741 380 13\n741 396 16\n741 425 49\n741 431 41\n741 464 24\n741 491 3\n741 520 5\n741 569 27\n741 581 22\n741 592 38\n741 637 9\n741 654 17\n741 712 4\n741 720 22\n741 733 7\n741 745 45\n741 781 11\n741 787 24\n741 801 40\n741 809 40\n741 812 43\n741 830 36\n741 852 41\n741 856 22\n741 873 39\n741 874 48\n741 944 26\n741 986 48\n741 998 44\n742 8 3\n742 13 25\n742 14 5\n742 51 16\n742 56 20\n742 89 42\n742 97 -1\n742 130 1\n742 195 47\n742 198 48\n742 217 40\n742 220 21\n742 222 0\n742 244 22\n742 246 7\n742 299 36\n742 323 26\n742 331 9\n742 347 44\n742 374 43\n742 384 14\n742 430 1\n742 481 35\n742 487 27\n742 531 39\n742 539 44\n742 549 19\n742 560 22\n742 568 41\n742 576 30\n742 582 1\n742 606 24\n742 652 37\n742 681 17\n742 703 12\n742 720 5\n742 728 27\n742 735 1\n742 736 20\n742 804 34\n742 806 25\n742 814 10\n742 852 49\n742 855 23\n742 868 7\n742 885 4\n742 895 43\n742 922 47\n742 928 43\n742 930 21\n742 958 11\n742 961 50\n743 19 5\n743 70 -1\n743 81 20\n743 112 19\n743 147 11\n743 161 38\n743 163 23\n743 167 48\n743 178 13\n743 253 45\n743 278 25\n743 302 4\n743 309 8\n743 336 36\n743 359 22\n743 366 44\n743 377 30\n743 380 5\n743 439 9\n743 445 38\n743 465 35\n743 479 3\n743 490 43\n743 493 39\n743 506 16\n743 532 34\n743 542 17\n743 554 46\n743 561 40\n743 562 10\n743 590 40\n743 606 49\n743 625 44\n743 627 47\n743 675 8\n743 683 40\n743 685 29\n743 688 37\n743 695 14\n743 710 20\n743 748 47\n743 761 48\n743 771 38\n743 808 43\n743 842 24\n743 879 20\n743 907 21\n743 921 49\n743 924 40\n744 25 7\n744 104 21\n744 109 49\n744 117 4\n744 144 50\n744 166 45\n744 190 22\n744 207 39\n744 219 33\n744 234 46\n744 269 11\n744 273 30\n744 282 50\n744 283 43\n744 286 40\n744 296 16\n744 298 43\n744 413 13\n744 422 13\n744 452 48\n744 458 49\n744 465 6\n744 468 34\n744 470 50\n744 476 39\n744 482 21\n744 487 39\n744 505 14\n744 527 4\n744 548 36\n744 561 19\n744 572 28\n744 602 42\n744 615 37\n744 665 38\n744 667 19\n744 679 41\n744 684 5\n744 695 32\n744 716 36\n744 718 20\n744 735 39\n744 739 29\n744 786 35\n744 796 8\n744 826 35\n744 832 41\n744 840 18\n744 923 12\n744 945 11\n744 951 28\n744 953 35\n744 962 20\n744 991 14\n744 996 30\n744 997 42\n745 22 30\n745 29 34\n745 32 23\n745 35 29\n745 47 21\n745 74 40\n745 102 25\n745 110 21\n745 115 6\n745 170 6\n745 186 29\n745 216 17\n745 217 41\n745 240 13\n745 246 16\n745 277 37\n745 278 29\n745 333 48\n745 355 48\n745 363 4\n745 368 37\n745 389 38\n745 456 31\n745 457 35\n745 516 39\n745 517 31\n745 525 6\n745 558 38\n745 588 21\n745 599 37\n745 607 16\n745 617 43\n745 665 49\n745 692 45\n745 718 30\n745 719 24\n745 730 30\n745 737 19\n745 755 26\n745 789 34\n745 834 47\n745 908 21\n745 932 38\n745 956 16\n746 15 9\n746 16 6\n746 44 41\n746 115 45\n746 150 37\n746 229 46\n746 231 2\n746 236 37\n746 309 25\n746 340 23\n746 348 31\n746 424 3\n746 488 26\n746 538 50\n746 575 43\n746 609 10\n746 613 18\n746 622 24\n746 651 40\n746 657 34\n746 659 40\n746 685 41\n746 690 32\n746 749 2\n746 850 8\n746 904 23\n746 923 13\n746 928 19\n746 936 -1\n746 939 34\n746 951 43\n746 962 43\n746 980 43\n746 989 1\n747 23 9\n747 25 8\n747 39 -1\n747 73 1\n747 93 42\n747 105 1\n747 154 24\n747 201 25\n747 214 40\n747 215 40\n747 269 25\n747 283 35\n747 300 38\n747 322 35\n747 338 34\n747 365 0\n747 410 38\n747 440 35\n747 442 5\n747 446 34\n747 453 4\n747 463 17\n747 485 37\n747 574 15\n747 579 23\n747 588 41\n747 606 33\n747 611 50\n747 624 25\n747 642 41\n747 644 38\n747 670 16\n747 711 14\n747 746 32\n747 764 34\n747 776 4\n747 786 21\n747 808 23\n747 820 14\n747 881 12\n747 891 39\n747 908 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20\n749 943 10\n749 964 43\n750 72 10\n750 120 15\n750 125 26\n750 158 30\n750 173 6\n750 177 18\n750 190 12\n750 204 23\n750 231 31\n750 242 4\n750 254 3\n750 257 36\n750 282 33\n750 334 42\n750 365 48\n750 370 41\n750 372 38\n750 389 19\n750 408 24\n750 431 1\n750 437 1\n750 445 9\n750 484 24\n750 499 35\n750 519 19\n750 536 10\n750 538 11\n750 587 17\n750 622 39\n750 626 39\n750 628 23\n750 638 18\n750 658 43\n750 681 31\n750 684 9\n750 714 7\n750 762 18\n750 775 3\n750 791 36\n750 800 14\n750 810 7\n750 811 20\n750 818 9\n750 822 19\n750 823 40\n750 829 28\n750 836 20\n750 839 6\n750 842 48\n750 860 31\n750 884 4\n750 902 23\n750 913 42\n750 930 10\n750 949 27\n750 974 6\n750 988 39\n750 993 30\n751 4 35\n751 37 32\n751 125 18\n751 130 32\n751 135 0\n751 150 47\n751 168 33\n751 176 30\n751 224 9\n751 262 6\n751 307 37\n751 310 9\n751 333 40\n751 336 2\n751 340 37\n751 369 4\n751 397 24\n751 421 20\n751 450 28\n751 451 43\n751 466 11\n751 477 37\n751 525 37\n751 534 7\n751 549 3\n751 567 26\n751 670 40\n751 672 14\n751 673 19\n751 689 37\n751 762 49\n751 768 32\n751 770 34\n751 787 50\n751 805 23\n751 825 17\n751 834 27\n751 857 7\n751 866 18\n751 871 35\n751 886 38\n751 902 16\n751 904 8\n751 915 34\n751 928 50\n751 939 50\n751 940 26\n751 941 14\n751 951 32\n751 967 27\n751 978 0\n752 45 20\n752 69 21\n752 92 33\n752 102 34\n752 161 49\n752 167 21\n752 172 39\n752 182 12\n752 194 13\n752 217 42\n752 245 25\n752 295 49\n752 318 6\n752 363 8\n752 380 20\n752 400 27\n752 405 -2\n752 412 19\n752 425 25\n752 487 24\n752 499 20\n752 510 10\n752 539 41\n752 554 5\n752 559 14\n752 588 28\n752 599 6\n752 602 4\n752 616 11\n752 655 44\n752 674 28\n752 675 22\n752 686 26\n752 704 22\n752 705 41\n752 790 34\n752 798 5\n752 807 3\n752 828 16\n752 836 35\n752 839 -1\n752 842 32\n752 848 2\n752 849 3\n752 898 3\n752 903 41\n752 909 38\n752 936 46\n752 948 32\n752 966 33\n752 981 39\n752 984 25\n753 4 32\n753 80 24\n753 83 13\n753 96 23\n753 137 6\n753 147 9\n753 161 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54 8\n808 101 5\n808 108 26\n808 113 50\n808 119 -2\n808 146 0\n808 149 35\n808 159 6\n808 181 14\n808 294 21\n808 335 50\n808 361 15\n808 394 23\n808 415 42\n808 439 30\n808 440 5\n808 443 41\n808 478 18\n808 504 39\n808 508 50\n808 559 23\n808 576 39\n808 605 39\n808 608 28\n808 637 1\n808 719 24\n808 736 13\n808 787 32\n808 792 27\n808 807 26\n808 809 29\n808 822 37\n808 829 11\n808 833 47\n808 841 21\n808 856 32\n808 858 4\n808 862 7\n808 891 8\n808 892 19\n808 924 46\n808 935 42\n808 966 38\n809 67 39\n809 77 17\n809 87 25\n809 162 13\n809 188 4\n809 220 47\n809 248 13\n809 252 20\n809 275 33\n809 303 34\n809 318 50\n809 325 24\n809 329 38\n809 359 5\n809 360 33\n809 369 43\n809 371 21\n809 420 24\n809 433 15\n809 487 32\n809 494 0\n809 506 17\n809 507 31\n809 523 38\n809 545 21\n809 548 7\n809 560 17\n809 564 7\n809 566 41\n809 578 34\n809 626 37\n809 632 48\n809 655 5\n809 690 21\n809 726 -1\n809 756 4\n809 762 -2\n809 784 16\n809 797 24\n809 832 17\n809 849 23\n809 891 17\n809 903 26\n809 928 28\n809 964 20\n809 970 22\n809 982 33\n809 988 41\n810 5 23\n810 18 4\n810 25 37\n810 30 14\n810 34 10\n810 55 18\n810 78 2\n810 87 24\n810 88 -1\n810 99 27\n810 109 32\n810 113 7\n810 133 49\n810 153 11\n810 192 5\n810 206 3\n810 307 49\n810 311 39\n810 317 41\n810 344 16\n810 372 37\n810 402 -1\n810 408 7\n810 411 29\n810 412 39\n810 422 8\n810 452 20\n810 468 40\n810 543 33\n810 544 43\n810 546 35\n810 566 50\n810 571 16\n810 576 2\n810 601 42\n810 610 39\n810 614 27\n810 690 39\n810 698 41\n810 710 29\n810 795 43\n810 823 25\n810 853 33\n810 854 24\n810 861 32\n810 863 0\n810 877 41\n810 883 12\n810 906 32\n810 908 2\n810 941 4\n810 972 32\n810 975 27\n810 979 1\n810 985 50\n810 992 44\n811 27 24\n811 32 38\n811 68 10\n811 78 19\n811 119 10\n811 139 32\n811 183 40\n811 190 34\n811 216 5\n811 219 0\n811 276 44\n811 282 13\n811 284 13\n811 295 22\n811 367 38\n811 376 35\n811 392 44\n811 406 16\n811 413 15\n811 444 3\n811 511 21\n811 527 32\n811 599 47\n811 624 46\n811 635 47\n811 643 45\n811 653 36\n811 718 48\n811 719 46\n811 752 42\n811 753 31\n811 757 21\n811 760 25\n811 777 29\n811 924 26\n811 941 14\n811 955 31\n811 957 13\n811 986 0\n811 987 29\n812 13 46\n812 32 22\n812 58 18\n812 76 8\n812 91 2\n812 92 45\n812 94 7\n812 119 50\n812 128 19\n812 150 11\n812 205 44\n812 218 32\n812 219 14\n812 228 49\n812 229 50\n812 238 30\n812 270 50\n812 282 15\n812 315 33\n812 322 46\n812 346 24\n812 380 8\n812 390 29\n812 428 15\n812 434 29\n812 449 2\n812 450 18\n812 453 17\n812 481 20\n812 497 49\n812 520 16\n812 522 26\n812 525 24\n812 551 27\n812 569 13\n812 643 44\n812 667 43\n812 673 15\n812 685 6\n812 749 36\n812 758 28\n812 763 12\n812 826 1\n812 852 32\n812 859 16\n812 893 26\n812 946 23\n812 948 47\n812 990 -2\n812 993 50\n813 63 3\n813 94 -2\n813 126 24\n813 139 9\n813 172 22\n813 204 6\n813 224 31\n813 259 7\n813 290 36\n813 294 36\n813 300 11\n813 309 27\n813 310 19\n813 321 30\n813 345 45\n813 370 50\n813 396 41\n813 403 31\n813 429 7\n813 433 32\n813 439 33\n813 455 23\n813 484 4\n813 501 7\n813 518 0\n813 540 44\n813 552 34\n813 580 46\n813 583 46\n813 593 0\n813 599 35\n813 642 24\n813 644 37\n813 662 33\n813 683 39\n813 700 29\n813 728 26\n813 734 48\n813 789 24\n813 794 29\n813 802 4\n813 811 23\n813 839 38\n813 844 49\n813 849 17\n813 859 49\n813 861 0\n813 913 6\n813 914 41\n813 916 22\n813 952 4\n813 953 9\n813 955 14\n813 959 34\n813 962 41\n813 971 11\n813 991 6\n814 12 10\n814 13 34\n814 28 8\n814 71 19\n814 82 16\n814 98 18\n814 108 25\n814 200 38\n814 228 35\n814 249 5\n814 264 8\n814 282 19\n814 308 45\n814 311 22\n814 314 48\n814 322 2\n814 332 6\n814 374 18\n814 400 37\n814 413 23\n814 458 14\n814 480 32\n814 498 35\n814 502 25\n814 543 6\n814 563 7\n814 579 26\n814 582 28\n814 677 40\n814 691 9\n814 707 14\n814 731 45\n814 774 45\n814 787 50\n814 799 38\n814 802 41\n814 839 7\n814 914 26\n814 929 38\n814 954 27\n814 962 4\n814 981 25\n814 991 33\n814 1000 42\n815 7 0\n815 26 24\n815 83 21\n815 87 42\n815 127 33\n815 145 28\n815 167 14\n815 176 50\n815 184 26\n815 187 46\n815 210 24\n815 226 18\n815 228 29\n815 231 41\n815 235 30\n815 253 48\n815 302 38\n815 343 30\n815 348 50\n815 375 39\n815 382 30\n815 421 2\n815 437 41\n815 484 -2\n815 488 40\n815 492 20\n815 507 20\n815 514 23\n815 533 14\n815 583 48\n815 596 18\n815 618 40\n815 636 31\n815 656 13\n815 681 24\n815 686 31\n815 695 38\n815 708 23\n815 712 14\n815 739 26\n815 764 30\n815 771 20\n815 787 42\n815 811 20\n815 926 32\n815 928 0\n815 951 15\n815 969 7\n815 990 31\n816 4 16\n816 10 31\n816 13 1\n816 31 24\n816 44 30\n816 46 6\n816 56 26\n816 60 46\n816 128 22\n816 145 27\n816 160 27\n816 205 22\n816 225 21\n816 259 46\n816 281 1\n816 282 49\n816 297 21\n816 311 13\n816 314 9\n816 316 43\n816 357 8\n816 364 9\n816 377 50\n816 381 11\n816 389 37\n816 406 41\n816 419 7\n816 443 12\n816 466 37\n816 473 43\n816 478 23\n816 490 36\n816 544 8\n816 547 33\n816 556 5\n816 576 44\n816 582 28\n816 599 31\n816 612 36\n816 617 13\n816 636 10\n816 641 45\n816 689 22\n816 702 -2\n816 765 -1\n816 778 41\n816 784 25\n816 807 28\n816 848 13\n816 861 10\n816 868 50\n816 893 26\n816 913 16\n816 934 16\n816 996 39\n817 4 21\n817 67 31\n817 69 21\n817 105 35\n817 120 12\n817 133 29\n817 146 23\n817 150 35\n817 162 19\n817 186 46\n817 211 44\n817 301 38\n817 305 26\n817 308 24\n817 331 49\n817 366 7\n817 376 11\n817 393 34\n817 404 11\n817 406 44\n817 431 7\n817 441 14\n817 448 9\n817 504 28\n817 526 16\n817 539 17\n817 549 20\n817 563 14\n817 569 3\n817 606 49\n817 609 17\n817 639 18\n817 686 49\n817 802 46\n817 805 42\n817 812 35\n817 828 46\n817 877 16\n817 905 38\n817 951 46\n817 974 31\n817 987 18\n818 14 9\n818 20 -2\n818 74 36\n818 103 5\n818 110 36\n818 122 46\n818 125 49\n818 157 32\n818 159 33\n818 170 4\n818 191 30\n818 204 22\n818 220 9\n818 222 8\n818 248 27\n818 250 38\n818 254 14\n818 276 20\n818 294 4\n818 303 18\n818 356 6\n818 362 12\n818 366 18\n818 367 26\n818 382 40\n818 396 16\n818 453 18\n818 469 10\n818 518 49\n818 528 2\n818 535 3\n818 580 26\n818 582 40\n818 605 0\n818 665 31\n818 667 29\n818 676 32\n818 679 12\n818 691 9\n818 703 46\n818 782 33\n818 787 45\n818 795 25\n818 826 -1\n818 849 43\n818 854 36\n818 865 8\n818 898 9\n818 903 45\n818 907 5\n818 916 48\n818 924 28\n818 964 43\n818 966 -1\n818 980 25\n819 58 48\n819 65 48\n819 85 29\n819 110 39\n819 117 41\n819 157 41\n819 162 10\n819 198 50\n819 201 10\n819 224 43\n819 237 40\n819 266 4\n819 317 -1\n819 401 8\n819 434 41\n819 456 5\n819 499 21\n819 506 23\n819 676 33\n819 682 5\n819 691 24\n819 696 39\n819 702 13\n819 708 21\n819 716 30\n819 717 28\n819 719 14\n819 746 49\n819 752 22\n819 784 48\n819 811 17\n819 839 42\n819 847 6\n819 868 -1\n819 877 46\n819 883 14\n819 910 12\n819 952 15\n819 973 46\n819 980 38\n819 996 34\n820 28 23\n820 42 16\n820 62 37\n820 94 7\n820 116 25\n820 117 14\n820 157 21\n820 168 38\n820 170 15\n820 177 16\n820 180 49\n820 183 25\n820 187 3\n820 213 17\n820 221 2\n820 236 23\n820 255 28\n820 313 18\n820 323 26\n820 328 48\n820 336 26\n820 376 48\n820 388 -1\n820 403 11\n820 418 36\n820 425 27\n820 436 11\n820 468 47\n820 476 49\n820 489 17\n820 506 4\n820 547 22\n820 557 7\n820 572 1\n820 599 33\n820 623 50\n820 624 29\n820 632 8\n820 651 46\n820 668 19\n820 686 23\n820 723 22\n820 757 8\n820 758 0\n820 776 26\n820 826 46\n820 878 4\n820 879 49\n820 902 34\n820 907 0\n820 919 40\n820 932 50\n820 940 40\n820 965 9\n820 993 4\n820 999 28\n821 8 39\n821 14 19\n821 15 29\n821 35 45\n821 46 43\n821 71 41\n821 94 31\n821 128 17\n821 169 5\n821 197 3\n821 199 25\n821 210 47\n821 220 20\n821 235 38\n821 237 39\n821 270 31\n821 354 37\n821 359 15\n821 364 20\n821 370 5\n821 385 12\n821 404 36\n821 420 20\n821 425 18\n821 431 4\n821 452 46\n821 487 30\n821 509 10\n821 513 17\n821 555 9\n821 675 -2\n821 687 11\n821 689 17\n821 704 39\n821 709 14\n821 725 41\n821 786 32\n821 794 43\n821 796 48\n821 839 1\n821 843 32\n821 852 43\n821 870 21\n821 891 4\n821 928 36\n821 944 42\n821 957 46\n821 958 17\n821 961 8\n821 962 34\n821 995 29\n822 62 22\n822 85 30\n822 91 30\n822 115 13\n822 136 24\n822 145 19\n822 146 30\n822 236 48\n822 257 32\n822 315 19\n822 382 29\n822 397 49\n822 417 50\n822 423 26\n822 475 43\n822 477 49\n822 495 47\n822 564 30\n822 576 22\n822 596 41\n822 614 32\n822 634 12\n822 649 35\n822 659 20\n822 671 41\n822 738 14\n822 792 28\n822 803 50\n822 818 3\n822 821 11\n822 823 46\n822 862 18\n822 868 15\n822 918 38\n822 924 23\n822 951 12\n822 958 24\n822 959 45\n822 961 29\n822 998 24\n823 4 44\n823 7 33\n823 68 -2\n823 71 46\n823 83 3\n823 116 29\n823 128 17\n823 184 25\n823 209 49\n823 213 5\n823 215 50\n823 226 22\n823 272 27\n823 280 -2\n823 346 30\n823 396 24\n823 422 34\n823 450 39\n823 459 14\n823 460 44\n823 517 33\n823 530 30\n823 592 49\n823 630 29\n823 650 27\n823 653 1\n823 656 37\n823 659 35\n823 712 37\n823 722 29\n823 765 17\n823 780 28\n823 782 23\n823 806 34\n823 818 20\n823 844 42\n823 891 23\n823 919 18\n823 935 42\n823 946 16\n823 983 17\n823 990 43\n823 992 29\n824 11 25\n824 16 20\n824 34 22\n824 35 0\n824 41 33\n824 46 9\n824 60 48\n824 78 23\n824 96 44\n824 103 41\n824 190 45\n824 198 48\n824 215 26\n824 220 8\n824 221 42\n824 229 4\n824 234 44\n824 263 29\n824 267 12\n824 273 35\n824 303 23\n824 308 39\n824 334 12\n824 369 5\n824 372 47\n824 386 5\n824 391 19\n824 398 49\n824 413 36\n824 421 43\n824 423 -1\n824 424 2\n824 458 13\n824 493 -1\n824 496 11\n824 509 23\n824 523 32\n824 537 43\n824 608 24\n824 638 9\n824 643 10\n824 648 31\n824 662 11\n824 670 10\n824 681 11\n824 694 22\n824 711 34\n824 719 22\n824 755 24\n824 764 8\n824 785 26\n824 791 36\n824 796 42\n824 806 42\n824 830 14\n824 836 11\n824 912 28\n824 916 -1\n824 952 41\n824 968 36\n824 982 36\n824 987 45\n824 988 45\n825 9 27\n825 21 40\n825 74 31\n825 81 11\n825 90 18\n825 129 39\n825 131 34\n825 132 29\n825 171 28\n825 187 20\n825 213 0\n825 217 49\n825 230 42\n825 235 43\n825 240 14\n825 252 3\n825 291 8\n825 300 33\n825 353 47\n825 382 28\n825 390 39\n825 392 39\n825 396 38\n825 413 39\n825 435 5\n825 449 8\n825 466 25\n825 494 37\n825 524 40\n825 533 28\n825 567 13\n825 579 11\n825 585 33\n825 645 19\n825 665 39\n825 666 32\n825 734 41\n825 739 31\n825 754 6\n825 766 36\n825 773 48\n825 775 26\n825 801 14\n825 826 35\n825 836 47\n825 839 1\n825 866 26\n825 869 0\n825 931 30\n825 934 49\n825 951 50\n825 954 27\n825 959 1\n825 964 -1\n825 998 8\n826 2 20\n826 43 48\n826 90 2\n826 122 5\n826 128 28\n826 129 34\n826 130 0\n826 132 42\n826 147 25\n826 152 5\n826 159 -2\n826 160 28\n826 219 22\n826 232 47\n826 240 18\n826 280 35\n826 306 12\n826 384 39\n826 388 16\n826 417 21\n826 444 30\n826 463 39\n826 468 33\n826 473 39\n826 480 7\n826 493 25\n826 512 23\n826 519 12\n826 539 12\n826 586 14\n826 594 43\n826 625 2\n826 649 6\n826 656 25\n826 669 34\n826 680 0\n826 701 17\n826 702 17\n826 706 46\n826 708 13\n826 857 45\n826 889 45\n826 917 25\n826 962 30\n826 972 10\n827 1 11\n827 28 17\n827 34 43\n827 48 30\n827 88 -1\n827 101 12\n827 164 50\n827 185 11\n827 196 21\n827 223 45\n827 244 34\n827 270 15\n827 272 6\n827 277 49\n827 283 8\n827 293 36\n827 299 -1\n827 334 50\n827 360 42\n827 407 46\n827 455 18\n827 475 39\n827 484 10\n827 502 19\n827 506 5\n827 510 4\n827 519 37\n827 525 47\n827 530 30\n827 577 27\n827 705 39\n827 758 0\n827 787 38\n827 814 15\n827 851 16\n827 870 45\n827 892 30\n827 905 7\n827 966 11\n827 997 32\n828 3 39\n828 15 18\n828 29 43\n828 35 37\n828 50 23\n828 74 16\n828 77 30\n828 98 27\n828 181 49\n828 187 27\n828 192 1\n828 232 29\n828 246 44\n828 255 15\n828 286 26\n828 305 30\n828 323 18\n828 363 0\n828 364 20\n828 396 21\n828 442 34\n828 508 9\n828 516 27\n828 529 13\n828 549 45\n828 552 -1\n828 556 35\n828 578 42\n828 611 36\n828 620 50\n828 658 10\n828 686 44\n828 693 18\n828 726 17\n828 743 41\n828 749 22\n828 771 20\n828 777 44\n828 792 -2\n828 809 5\n828 850 25\n828 851 18\n828 873 34\n828 894 7\n828 911 28\n828 934 36\n828 961 34\n829 87 23\n829 119 22\n829 124 47\n829 145 4\n829 156 21\n829 164 24\n829 209 38\n829 217 39\n829 264 15\n829 273 42\n829 323 19\n829 350 49\n829 361 13\n829 395 50\n829 425 35\n829 448 45\n829 462 23\n829 478 35\n829 480 12\n829 501 34\n829 517 29\n829 541 5\n829 582 27\n829 592 47\n829 609 27\n829 611 18\n829 735 23\n829 742 25\n829 767 10\n829 771 12\n829 772 19\n829 779 32\n829 865 15\n829 945 44\n829 985 30\n830 4 21\n830 7 37\n830 13 0\n830 28 49\n830 42 7\n830 62 36\n830 68 31\n830 79 9\n830 103 7\n830 111 17\n830 251 22\n830 286 14\n830 322 8\n830 328 37\n830 330 42\n830 345 37\n830 348 3\n830 420 37\n830 461 30\n830 462 46\n830 492 49\n830 507 7\n830 508 22\n830 513 46\n830 587 33\n830 594 1\n830 596 50\n830 600 16\n830 604 47\n830 617 5\n830 647 48\n830 653 7\n830 672 34\n830 677 14\n830 686 11\n830 690 21\n830 696 10\n830 708 48\n830 732 29\n830 740 7\n830 742 24\n830 769 18\n830 778 9\n830 784 2\n830 820 18\n830 821 12\n830 840 32\n830 844 50\n830 891 44\n830 899 41\n830 906 12\n830 917 38\n830 926 46\n830 958 28\n830 961 34\n830 966 13\n830 974 24\n830 988 41\n830 994 47\n831 9 25\n831 46 29\n831 50 17\n831 95 24\n831 99 9\n831 115 31\n831 116 11\n831 127 29\n831 141 33\n831 191 33\n831 214 37\n831 228 10\n831 279 41\n831 286 15\n831 297 32\n831 352 3\n831 365 17\n831 373 27\n831 382 46\n831 384 19\n831 436 47\n831 466 36\n831 477 35\n831 485 16\n831 511 36\n831 521 32\n831 522 12\n831 539 14\n831 564 0\n831 602 15\n831 620 35\n831 658 28\n831 672 28\n831 674 32\n831 683 12\n831 702 8\n831 725 49\n831 742 1\n831 819 3\n831 821 31\n831 833 6\n831 838 43\n831 879 19\n831 880 20\n831 909 12\n831 925 13\n831 926 38\n831 933 8\n831 940 30\n831 944 44\n831 947 28\n831 949 33\n831 970 18\n831 988 45\n832 21 14\n832 49 43\n832 53 36\n832 56 35\n832 60 33\n832 62 46\n832 81 38\n832 117 2\n832 138 23\n832 163 17\n832 172 36\n832 184 7\n832 194 21\n832 196 5\n832 206 25\n832 223 50\n832 228 30\n832 229 30\n832 236 40\n832 241 41\n832 245 7\n832 258 10\n832 272 32\n832 292 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5\n846 823 18\n846 831 12\n846 886 48\n846 891 18\n846 894 19\n846 933 45\n846 948 4\n846 974 35\n846 990 24\n847 7 6\n847 36 17\n847 42 47\n847 49 34\n847 84 47\n847 137 40\n847 143 9\n847 178 48\n847 184 38\n847 194 35\n847 207 15\n847 212 33\n847 220 35\n847 225 19\n847 230 28\n847 272 20\n847 282 17\n847 317 13\n847 328 3\n847 369 27\n847 394 8\n847 415 0\n847 456 13\n847 476 29\n847 520 47\n847 549 35\n847 556 21\n847 589 1\n847 635 18\n847 642 5\n847 645 42\n847 651 29\n847 662 31\n847 666 38\n847 667 25\n847 693 21\n847 700 12\n847 709 38\n847 711 37\n847 724 34\n847 752 2\n847 758 40\n847 764 34\n847 769 37\n847 794 7\n847 818 29\n847 819 45\n847 850 34\n847 910 9\n847 913 44\n847 931 39\n847 942 -2\n847 953 34\n848 33 35\n848 49 33\n848 69 25\n848 77 6\n848 129 46\n848 139 11\n848 208 37\n848 216 13\n848 248 29\n848 327 26\n848 341 26\n848 347 40\n848 348 23\n848 373 -2\n848 386 -2\n848 410 20\n848 433 28\n848 477 49\n848 506 5\n848 508 27\n848 540 10\n848 635 15\n848 670 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40\n928 4 48\n928 37 33\n928 39 4\n928 44 10\n928 48 21\n928 80 6\n928 109 8\n928 126 9\n928 144 48\n928 153 39\n928 169 38\n928 185 32\n928 188 4\n928 230 31\n928 237 27\n928 250 43\n928 259 5\n928 296 20\n928 301 36\n928 333 30\n928 368 2\n928 378 32\n928 430 12\n928 432 35\n928 444 24\n928 478 49\n928 491 20\n928 502 1\n928 534 47\n928 563 23\n928 585 38\n928 593 25\n928 610 34\n928 633 48\n928 676 9\n928 686 50\n928 699 6\n928 706 13\n928 714 47\n928 722 45\n928 746 49\n928 763 26\n928 798 16\n928 803 41\n928 831 1\n928 860 19\n928 861 49\n928 868 50\n928 933 32\n928 942 20\n928 968 24\n928 970 19\n928 983 15\n928 987 40\n928 988 16\n928 1000 38\n929 27 13\n929 37 18\n929 40 1\n929 55 47\n929 59 43\n929 72 13\n929 92 9\n929 102 31\n929 106 37\n929 124 45\n929 130 14\n929 191 19\n929 214 50\n929 277 2\n929 313 6\n929 318 31\n929 330 17\n929 391 21\n929 420 48\n929 426 25\n929 429 33\n929 435 3\n929 462 3\n929 465 16\n929 486 29\n929 519 36\n929 554 14\n929 588 48\n929 594 3\n929 662 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4\n984 404 9\n984 412 8\n984 418 40\n984 423 32\n984 442 1\n984 455 40\n984 481 16\n984 490 41\n984 492 14\n984 509 6\n984 511 36\n984 527 32\n984 531 30\n984 552 19\n984 615 26\n984 622 29\n984 668 3\n984 677 42\n984 686 19\n984 713 6\n984 733 24\n984 770 36\n984 790 42\n984 796 38\n984 803 44\n984 846 -2\n984 860 10\n984 873 43\n984 901 27\n984 916 43\n984 917 49\n984 951 7\n984 952 42\n984 964 50\n984 965 8\n984 983 13\n985 17 25\n985 31 6\n985 52 19\n985 62 11\n985 64 44\n985 152 33\n985 175 15\n985 231 22\n985 269 17\n985 292 35\n985 327 48\n985 395 5\n985 448 6\n985 451 35\n985 465 15\n985 474 19\n985 494 24\n985 501 1\n985 589 17\n985 610 23\n985 652 6\n985 654 26\n985 668 39\n985 692 19\n985 712 2\n985 727 50\n985 729 2\n985 730 28\n985 803 47\n985 831 20\n985 893 48\n985 928 26\n985 978 29\n985 996 44\n986 30 22\n986 47 20\n986 63 30\n986 67 10\n986 162 35\n986 177 48\n986 197 47\n986 227 44\n986 234 17\n986 253 3\n986 271 47\n986 279 4\n986 308 22\n986 309 37\n986 340 8\n986 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5\n988 521 7\n988 524 47\n988 569 27\n988 624 33\n988 656 29\n988 658 12\n988 684 37\n988 685 6\n988 745 23\n988 754 27\n988 779 31\n988 785 12\n988 787 3\n988 821 47\n988 833 8\n988 842 43\n988 858 19\n988 881 9\n988 965 4\n988 971 50\n988 975 40\n988 983 32\n988 996 32\n989 23 -2\n989 137 -2\n989 140 46\n989 144 3\n989 156 32\n989 157 32\n989 184 30\n989 204 2\n989 216 20\n989 227 27\n989 262 34\n989 270 11\n989 276 14\n989 284 4\n989 340 11\n989 341 38\n989 344 41\n989 382 38\n989 388 11\n989 397 41\n989 403 36\n989 405 46\n989 408 5\n989 413 6\n989 423 31\n989 435 2\n989 439 24\n989 481 39\n989 512 0\n989 518 28\n989 557 44\n989 563 36\n989 567 46\n989 583 6\n989 616 10\n989 622 38\n989 624 27\n989 644 47\n989 645 7\n989 646 46\n989 650 40\n989 657 41\n989 668 7\n989 674 11\n989 779 21\n989 784 34\n989 796 14\n989 834 43\n989 840 12\n989 842 41\n989 880 11\n989 886 47\n989 913 26\n989 916 44\n989 933 9\n989 934 19\n989 951 43\n989 957 38\n989 971 15\n989 978 30\n989 988 22\n989 991 7\n990 2 8\n990 18 49\n990 66 22\n990 84 39\n990 117 21\n990 136 49\n990 143 34\n990 185 7\n990 200 12\n990 209 12\n990 214 27\n990 238 14\n990 242 13\n990 251 45\n990 255 49\n990 264 9\n990 265 22\n990 281 24\n990 314 27\n990 318 21\n990 355 9\n990 374 5\n990 384 34\n990 420 31\n990 424 0\n990 448 14\n990 452 24\n990 465 3\n990 475 8\n990 479 46\n990 482 12\n990 500 31\n990 525 25\n990 528 6\n990 567 2\n990 573 27\n990 589 34\n990 601 39\n990 607 8\n990 624 9\n990 687 11\n990 738 19\n990 771 31\n990 780 43\n990 783 17\n990 786 9\n990 808 40\n990 810 34\n990 813 36\n990 835 34\n990 853 17\n990 867 32\n990 879 26\n990 911 27\n990 944 10\n990 992 5\n990 994 46\n991 65 30\n991 89 12\n991 106 48\n991 130 5\n991 131 -2\n991 132 16\n991 164 5\n991 179 48\n991 185 30\n991 228 27\n991 230 11\n991 262 17\n991 289 24\n991 315 1\n991 317 36\n991 338 48\n991 432 17\n991 438 13\n991 440 40\n991 448 44\n991 477 35\n991 512 43\n991 528 7\n991 563 21\n991 569 49\n991 587 3\n991 646 25\n991 666 39\n991 725 33\n991 744 23\n991 768 20\n991 813 0\n991 823 22\n991 839 16\n991 850 35\n991 857 45\n991 921 49\n991 999 38\n992 2 23\n992 65 4\n992 93 1\n992 125 46\n992 130 42\n992 160 18\n992 164 45\n992 183 33\n992 213 1\n992 230 16\n992 294 25\n992 381 8\n992 395 27\n992 410 50\n992 413 11\n992 418 50\n992 425 47\n992 469 39\n992 480 11\n992 492 8\n992 496 41\n992 514 31\n992 517 37\n992 551 23\n992 561 27\n992 574 0\n992 642 14\n992 671 22\n992 683 28\n992 725 8\n992 768 8\n992 804 37\n992 825 38\n992 832 49\n992 867 33\n992 869 46\n992 870 40\n992 929 43\n992 953 30\n992 969 19\n992 972 22\n992 977 14\n992 988 34\n993 3 5\n993 13 -2\n993 45 42\n993 71 26\n993 135 11\n993 163 13\n993 188 12\n993 195 4\n993 225 22\n993 249 11\n993 250 33\n993 252 45\n993 279 14\n993 302 28\n993 306 20\n993 315 21\n993 326 39\n993 388 0\n993 426 47\n993 427 48\n993 449 34\n993 459 45\n993 475 7\n993 493 11\n993 501 5\n993 514 7\n993 541 6\n993 562 23\n993 577 48\n993 629 27\n993 630 40\n993 684 9\n993 686 30\n993 691 46\n993 751 16\n993 758 20\n993 764 33\n993 826 21\n993 837 19\n993 860 30\n993 872 41\n993 875 39\n993 878 39\n993 958 45\n993 988 13\n993 995 25\n994 7 41\n994 34 5\n994 67 47\n994 68 2\n994 111 4\n994 127 22\n994 129 36\n994 152 44\n994 167 13\n994 184 1\n994 213 24\n994 252 38\n994 270 47\n994 291 49\n994 295 34\n994 312 6\n994 324 32\n994 334 28\n994 348 0\n994 363 31\n994 398 2\n994 417 44\n994 440 30\n994 448 41\n994 449 30\n994 455 3\n994 489 18\n994 509 20\n994 548 33\n994 567 -1\n994 583 18\n994 626 43\n994 631 8\n994 641 4\n994 645 29\n994 652 40\n994 671 34\n994 712 0\n994 724 49\n994 749 24\n994 767 15\n994 795 3\n994 821 13\n994 823 50\n994 827 4\n994 828 40\n994 838 49\n994 859 1\n994 872 35\n994 885 38\n994 906 47\n994 927 29\n994 928 49\n994 938 46\n994 963 37\n994 979 18\n994 984 47\n994 985 49\n995 8 11\n995 12 7\n995 18 26\n995 21 7\n995 25 46\n995 27 15\n995 34 22\n995 53 12\n995 92 13\n995 97 7\n995 116 20\n995 139 41\n995 152 33\n995 209 32\n995 212 25\n995 238 6\n995 246 27\n995 261 7\n995 267 37\n995 271 17\n995 282 5\n995 296 34\n995 340 21\n995 358 19\n995 425 37\n995 430 44\n995 445 15\n995 479 24\n995 505 29\n995 526 22\n995 528 29\n995 545 49\n995 547 41\n995 550 14\n995 570 49\n995 579 36\n995 669 11\n995 682 28\n995 687 6\n995 763 24\n995 811 11\n995 815 9\n995 827 46\n995 881 30\n995 905 38\n995 907 28\n995 932 33\n995 939 36\n995 960 29\n995 985 26\n995 990 33\n996 12 47\n996 19 21\n996 33 4\n996 34 29\n996 40 22\n996 78 24\n996 90 20\n996 133 2\n996 135 5\n996 147 7\n996 175 35\n996 258 2\n996 275 7\n996 352 49\n996 369 20\n996 382 15\n996 387 4\n996 400 41\n996 438 25\n996 459 27\n996 461 34\n996 480 29\n996 495 22\n996 502 38\n996 523 43\n996 568 19\n996 576 50\n996 584 1\n996 600 36\n996 604 34\n996 653 10\n996 667 45\n996 689 37\n996 707 35\n996 731 38\n996 736 46\n996 740 28\n996 767 41\n996 774 30\n996 785 21\n996 801 41\n996 863 24\n996 884 12\n996 910 43\n996 912 30\n996 928 19\n996 931 16\n996 944 33\n997 20 13\n997 26 2\n997 48 -1\n997 85 44\n997 112 1\n997 225 31\n997 266 48\n997 270 17\n997 291 12\n997 308 30\n997 322 38\n997 335 47\n997 337 27\n997 371 46\n997 373 40\n997 438 14\n997 451 16\n997 470 20\n997 526 35\n997 553 21\n997 599 35\n997 606 43\n997 627 42\n997 634 32\n997 660 43\n997 662 12\n997 663 42\n997 668 5\n997 671 6\n997 686 12\n997 691 48\n997 712 0\n997 729 18\n997 742 19\n997 755 16\n997 813 48\n997 828 44\n997 849 30\n997 852 46\n997 856 45\n997 860 24\n997 871 16\n997 897 11\n997 901 47\n997 917 31\n997 943 -1\n997 979 28\n997 980 26\n998 54 -2\n998 55 26\n998 58 10\n998 90 30\n998 95 14\n998 111 -2\n998 132 29\n998 159 -1\n998 175 38\n998 192 -2\n998 201 9\n998 204 49\n998 225 23\n998 270 8\n998 315 21\n998 335 14\n998 393 1\n998 401 13\n998 420 31\n998 438 7\n998 440 -2\n998 446 6\n998 450 13\n998 481 8\n998 485 15\n998 550 1\n998 595 1\n998 600 2\n998 607 -2\n998 609 3\n998 628 43\n998 639 1\n998 649 -1\n998 682 22\n998 736 6\n998 741 21\n998 776 15\n998 831 5\n998 833 49\n998 870 41\n998 925 4\n998 931 5\n998 932 2\n998 952 44\n998 961 31\n998 992 34\n999 22 32\n999 49 38\n999 68 19\n999 76 17\n999 94 12\n999 104 26\n999 132 21\n999 136 47\n999 137 40\n999 145 17\n999 159 10\n999 172 37\n999 177 16\n999 180 32\n999 192 31\n999 252 13\n999 254 29\n999 285 5\n999 307 47\n999 337 46\n999 367 13\n999 416 43\n999 447 45\n999 462 36\n999 493 34\n999 550 20\n999 561 17\n999 576 41\n999 588 42\n999 597 5\n999 611 39\n999 617 26\n999 623 49\n999 630 31\n999 649 16\n999 665 25\n999 678 32\n999 690 21\n999 705 36\n999 777 47\n999 797 49\n999 801 8\n999 831 28\n999 840 26\n999 860 3\n999 873 15\n999 882 12\n999 890 13\n999 901 29\n999 919 31\n999 951 28\n999 997 15\n1000 23 38\n1000 42 19\n1000 113 46\n1000 145 49\n1000 154 1\n1000 183 32\n1000 214 1\n1000 219 27\n1000 232 21\n1000 242 43\n1000 248 13\n1000 259 19\n1000 270 35\n1000 305 49\n1000 323 47\n1000 327 33\n1000 339 33\n1000 408 22\n1000 414 24\n1000 421 28\n1000 448 34\n1000 449 1\n1000 452 36\n1000 458 12\n1000 459 27\n1000 494 38\n1000 528 28\n1000 546 37\n1000 558 19\n1000 576 39\n1000 583 29\n1000 592 25\n1000 632 23\n1000 650 15\n1000 656 22\n1000 683 23\n1000 709 3\n1000 749 42\n1000 757 47\n1000 761 7\n1000 769 22\n1000 782 16\n1000 789 2\n1000 814 8\n1000 816 16\n1000 840 1\n1000 846 28\n1000 855 49\n1000 858 50\n1000 859 4\n1000 873 23\n1000 899 31\n1000 902 21\n1000 909 42\n1000 914 25\n1000 984 12\n1000 988 3\n"
  },
  {
    "path": "floyd_warshall/problem18.8file2.txt",
    "content": "1000 47978\n1 2 2\n1 26 28\n1 68 -2\n1 123 48\n1 139 28\n1 147 2\n1 182 41\n1 187 7\n1 215 15\n1 227 27\n1 229 17\n1 246 45\n1 254 3\n1 290 10\n1 307 6\n1 339 24\n1 344 -1\n1 389 4\n1 403 14\n1 416 30\n1 431 20\n1 449 4\n1 543 26\n1 545 39\n1 547 1\n1 583 50\n1 584 29\n1 591 31\n1 603 25\n1 611 0\n1 614 39\n1 621 31\n1 659 0\n1 711 34\n1 737 30\n1 841 40\n1 846 41\n1 849 36\n1 852 0\n1 864 24\n1 868 28\n1 886 42\n1 890 15\n1 892 25\n1 896 19\n1 898 14\n1 903 37\n1 910 27\n1 913 21\n1 920 49\n1 938 35\n1 946 5\n1 984 -2\n1 985 31\n2 16 41\n2 26 38\n2 36 37\n2 43 8\n2 46 39\n2 48 17\n2 59 1\n2 61 14\n2 68 0\n2 88 2\n2 96 17\n2 106 45\n2 115 37\n2 214 10\n2 217 45\n2 225 6\n2 245 40\n2 288 46\n2 307 8\n2 315 20\n2 340 35\n2 382 6\n2 384 19\n2 389 36\n2 391 31\n2 452 31\n2 496 47\n2 498 23\n2 517 39\n2 560 50\n2 569 15\n2 577 43\n2 582 6\n2 617 49\n2 656 35\n2 660 6\n2 678 -1\n2 692 43\n2 728 48\n2 756 5\n2 822 14\n2 832 16\n2 854 20\n2 865 9\n2 873 45\n2 923 17\n2 970 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238 18\n9 243 37\n9 313 13\n9 375 5\n9 383 10\n9 425 25\n9 491 7\n9 513 37\n9 519 26\n9 544 9\n9 549 37\n9 551 6\n9 611 20\n9 625 41\n9 650 40\n9 670 37\n9 681 23\n9 739 7\n9 793 28\n9 801 38\n9 814 5\n9 821 10\n9 833 46\n9 867 4\n9 909 10\n9 910 23\n9 939 0\n9 972 1\n9 974 46\n9 984 48\n9 989 49\n9 999 36\n10 28 21\n10 30 0\n10 37 -2\n10 59 46\n10 60 24\n10 62 0\n10 64 27\n10 92 25\n10 95 44\n10 143 29\n10 191 33\n10 208 42\n10 241 44\n10 254 33\n10 302 42\n10 317 20\n10 343 21\n10 399 1\n10 449 33\n10 450 32\n10 491 23\n10 518 1\n10 529 16\n10 570 7\n10 574 21\n10 578 6\n10 655 45\n10 685 3\n10 687 20\n10 767 -2\n10 775 34\n10 799 13\n10 802 36\n10 810 11\n10 814 19\n10 820 30\n10 823 3\n10 848 36\n10 852 31\n10 873 47\n10 876 18\n10 897 17\n10 967 8\n10 973 44\n10 996 39\n11 13 36\n11 35 20\n11 107 21\n11 113 1\n11 125 16\n11 127 19\n11 138 27\n11 168 1\n11 178 19\n11 186 17\n11 201 14\n11 237 29\n11 245 29\n11 266 48\n11 337 34\n11 371 39\n11 374 6\n11 440 44\n11 480 4\n11 482 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780 14\n21 787 50\n21 806 49\n21 846 11\n21 864 3\n21 895 47\n21 897 26\n21 911 35\n21 912 16\n21 915 17\n21 943 19\n21 947 37\n21 959 4\n21 971 45\n21 979 45\n21 991 9\n22 3 18\n22 5 22\n22 15 42\n22 35 31\n22 97 35\n22 99 -1\n22 113 16\n22 151 29\n22 165 23\n22 166 8\n22 211 44\n22 214 28\n22 215 23\n22 289 19\n22 295 8\n22 304 19\n22 311 12\n22 369 46\n22 386 41\n22 429 0\n22 431 40\n22 452 33\n22 471 47\n22 494 48\n22 523 -1\n22 543 21\n22 560 33\n22 572 13\n22 630 5\n22 655 34\n22 669 3\n22 704 -2\n22 717 50\n22 728 46\n22 757 47\n22 763 27\n22 774 11\n22 787 37\n22 797 25\n22 799 25\n22 811 1\n22 817 21\n22 843 26\n22 844 22\n22 910 25\n22 921 16\n22 927 39\n22 930 48\n22 933 33\n22 941 45\n23 26 9\n23 27 -1\n23 36 23\n23 47 19\n23 84 47\n23 89 20\n23 104 49\n23 123 10\n23 141 28\n23 170 13\n23 187 36\n23 229 44\n23 245 24\n23 253 47\n23 257 39\n23 287 14\n23 295 -2\n23 298 43\n23 299 49\n23 324 33\n23 351 26\n23 384 19\n23 423 29\n23 432 28\n23 485 29\n23 505 12\n23 514 33\n23 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37\n27 457 26\n27 466 11\n27 477 11\n27 503 25\n27 523 47\n27 550 3\n27 560 25\n27 568 11\n27 575 28\n27 588 35\n27 646 47\n27 651 38\n27 670 22\n27 679 40\n27 680 27\n27 681 35\n27 706 45\n27 724 35\n27 732 15\n27 733 29\n27 745 29\n27 751 30\n27 775 -2\n27 782 6\n27 786 41\n27 787 36\n27 802 32\n27 809 45\n27 828 47\n27 834 0\n27 860 37\n27 911 -2\n27 927 5\n27 945 41\n27 962 14\n27 985 12\n28 2 33\n28 13 39\n28 14 40\n28 17 13\n28 101 33\n28 130 -2\n28 133 -2\n28 140 14\n28 146 20\n28 164 43\n28 190 39\n28 225 11\n28 229 22\n28 244 40\n28 249 11\n28 284 5\n28 342 13\n28 343 34\n28 385 27\n28 398 29\n28 404 45\n28 406 8\n28 450 38\n28 455 10\n28 458 45\n28 466 33\n28 473 47\n28 493 0\n28 521 33\n28 576 48\n28 593 2\n28 598 13\n28 647 37\n28 670 6\n28 742 19\n28 757 27\n28 770 12\n28 820 50\n28 837 -2\n28 857 5\n28 878 40\n28 887 40\n28 936 13\n28 940 19\n28 945 33\n28 972 32\n28 973 46\n28 977 38\n28 979 35\n28 985 39\n28 996 18\n29 56 12\n29 89 35\n29 108 6\n29 162 20\n29 185 41\n29 187 36\n29 195 45\n29 203 31\n29 213 31\n29 214 35\n29 321 21\n29 379 30\n29 380 37\n29 401 14\n29 421 0\n29 437 34\n29 471 13\n29 474 5\n29 518 50\n29 563 0\n29 564 32\n29 598 43\n29 605 50\n29 612 -1\n29 613 41\n29 625 44\n29 687 24\n29 689 25\n29 698 17\n29 718 31\n29 751 46\n29 778 48\n29 820 43\n29 827 12\n29 838 40\n29 855 37\n29 876 50\n29 883 5\n29 888 25\n29 909 35\n29 955 13\n29 975 32\n29 991 32\n30 19 50\n30 34 23\n30 37 23\n30 61 37\n30 115 43\n30 116 2\n30 131 12\n30 138 49\n30 158 49\n30 172 12\n30 194 33\n30 203 -2\n30 210 36\n30 247 18\n30 252 10\n30 285 22\n30 290 37\n30 304 45\n30 310 37\n30 318 1\n30 336 34\n30 348 19\n30 393 18\n30 448 4\n30 471 45\n30 475 40\n30 505 37\n30 553 9\n30 558 33\n30 570 19\n30 602 15\n30 641 35\n30 644 40\n30 664 14\n30 683 32\n30 701 38\n30 726 14\n30 736 42\n30 753 22\n30 762 47\n30 763 25\n30 782 11\n30 785 22\n30 816 50\n30 823 29\n30 840 12\n30 896 11\n30 932 34\n30 937 4\n30 981 49\n30 995 46\n31 64 46\n31 70 33\n31 92 4\n31 115 13\n31 116 36\n31 140 24\n31 164 8\n31 166 43\n31 188 1\n31 217 24\n31 247 11\n31 281 3\n31 321 9\n31 329 40\n31 330 3\n31 340 14\n31 367 17\n31 390 13\n31 399 42\n31 419 28\n31 447 25\n31 453 35\n31 476 22\n31 537 36\n31 596 41\n31 602 36\n31 617 -2\n31 645 43\n31 663 40\n31 677 18\n31 680 21\n31 727 42\n31 741 2\n31 764 48\n31 773 2\n31 790 40\n31 816 -2\n31 824 28\n31 844 18\n31 849 50\n31 853 10\n31 862 40\n31 872 12\n31 879 7\n31 888 21\n31 892 43\n31 897 27\n31 915 39\n31 933 16\n31 934 18\n31 938 50\n31 949 23\n31 952 11\n31 993 15\n32 24 6\n32 27 14\n32 98 14\n32 123 25\n32 132 19\n32 155 44\n32 188 21\n32 189 37\n32 200 43\n32 230 23\n32 236 18\n32 248 32\n32 259 2\n32 291 4\n32 341 27\n32 381 32\n32 419 43\n32 423 10\n32 439 0\n32 468 24\n32 527 9\n32 553 14\n32 561 19\n32 565 -2\n32 575 21\n32 590 37\n32 592 24\n32 594 41\n32 623 21\n32 674 18\n32 738 0\n32 755 27\n32 774 25\n32 804 21\n32 810 20\n32 853 5\n32 870 27\n32 878 17\n32 881 50\n32 894 -2\n32 917 46\n32 950 -1\n32 990 7\n33 19 7\n33 74 41\n33 101 8\n33 104 25\n33 111 41\n33 128 20\n33 134 42\n33 185 28\n33 220 45\n33 229 39\n33 239 32\n33 257 25\n33 269 37\n33 276 26\n33 279 41\n33 293 8\n33 337 37\n33 340 10\n33 345 18\n33 346 1\n33 379 22\n33 412 33\n33 417 10\n33 441 34\n33 481 28\n33 499 19\n33 554 29\n33 555 7\n33 570 35\n33 605 48\n33 614 38\n33 618 30\n33 641 24\n33 644 40\n33 661 42\n33 683 8\n33 698 15\n33 720 32\n33 732 13\n33 744 49\n33 745 17\n33 751 18\n33 801 14\n33 802 30\n33 835 40\n33 843 14\n33 877 24\n33 881 11\n33 883 26\n33 906 46\n33 967 16\n34 2 0\n34 24 43\n34 26 29\n34 47 24\n34 56 40\n34 107 13\n34 168 32\n34 180 3\n34 188 27\n34 190 49\n34 197 21\n34 208 30\n34 218 50\n34 227 8\n34 238 16\n34 251 29\n34 264 28\n34 268 35\n34 284 46\n34 299 22\n34 304 20\n34 308 41\n34 314 5\n34 317 29\n34 345 42\n34 359 47\n34 369 36\n34 374 18\n34 418 35\n34 449 16\n34 460 17\n34 475 17\n34 490 26\n34 493 37\n34 507 2\n34 512 29\n34 528 4\n34 626 11\n34 647 17\n34 664 33\n34 680 30\n34 681 -1\n34 698 3\n34 705 0\n34 720 33\n34 733 38\n34 738 37\n34 765 39\n34 775 -2\n34 782 23\n34 853 44\n34 937 8\n34 979 11\n34 992 11\n35 8 9\n35 26 39\n35 37 47\n35 61 20\n35 65 7\n35 66 45\n35 133 28\n35 270 49\n35 294 12\n35 310 42\n35 352 47\n35 375 40\n35 437 32\n35 456 20\n35 497 4\n35 503 44\n35 513 35\n35 521 6\n35 523 44\n35 533 46\n35 545 34\n35 566 42\n35 572 10\n35 607 39\n35 626 9\n35 642 18\n35 663 21\n35 685 16\n35 696 38\n35 712 14\n35 713 17\n35 729 30\n35 743 18\n35 766 7\n35 782 16\n35 793 27\n35 795 12\n35 801 44\n35 809 38\n35 829 37\n35 841 1\n35 851 26\n35 858 46\n35 860 50\n35 884 7\n35 890 50\n35 956 16\n35 957 40\n35 987 36\n36 29 19\n36 47 23\n36 55 48\n36 98 4\n36 116 0\n36 126 7\n36 137 25\n36 164 21\n36 168 16\n36 190 35\n36 198 16\n36 202 33\n36 203 21\n36 205 21\n36 218 44\n36 233 21\n36 270 4\n36 291 1\n36 295 39\n36 304 28\n36 306 15\n36 315 -2\n36 317 9\n36 347 30\n36 352 42\n36 353 3\n36 356 27\n36 360 8\n36 367 40\n36 376 34\n36 402 48\n36 424 27\n36 426 6\n36 437 2\n36 438 4\n36 459 23\n36 487 14\n36 494 29\n36 535 34\n36 573 31\n36 575 14\n36 578 37\n36 598 46\n36 610 6\n36 629 -2\n36 635 8\n36 663 47\n36 667 2\n36 675 42\n36 679 20\n36 716 11\n36 828 17\n36 830 9\n36 832 -1\n36 892 16\n36 899 31\n36 919 45\n36 928 29\n36 958 19\n36 962 31\n36 987 50\n37 16 30\n37 50 17\n37 58 44\n37 63 34\n37 82 34\n37 87 27\n37 94 22\n37 96 6\n37 147 38\n37 176 27\n37 192 43\n37 205 11\n37 225 38\n37 266 29\n37 287 48\n37 301 18\n37 319 21\n37 358 23\n37 377 33\n37 378 35\n37 423 49\n37 463 11\n37 466 36\n37 491 7\n37 594 37\n37 609 29\n37 619 0\n37 631 46\n37 640 49\n37 648 2\n37 652 41\n37 653 35\n37 660 25\n37 674 12\n37 691 37\n37 723 17\n37 743 12\n37 749 22\n37 782 26\n37 786 29\n37 813 6\n37 816 21\n37 830 14\n37 850 13\n37 865 26\n37 876 38\n37 915 35\n37 930 49\n37 933 16\n37 985 42\n37 1000 18\n38 7 -2\n38 36 46\n38 45 35\n38 53 41\n38 54 14\n38 67 14\n38 100 44\n38 116 19\n38 117 -2\n38 141 33\n38 153 47\n38 192 25\n38 225 31\n38 244 49\n38 296 33\n38 298 46\n38 305 9\n38 314 10\n38 340 16\n38 380 17\n38 389 15\n38 405 37\n38 451 18\n38 478 40\n38 487 33\n38 517 42\n38 549 25\n38 572 15\n38 619 35\n38 696 39\n38 700 5\n38 708 8\n38 722 5\n38 725 17\n38 811 43\n38 822 41\n38 935 16\n38 954 27\n38 983 23\n38 992 27\n38 996 30\n38 998 40\n39 101 34\n39 109 36\n39 114 24\n39 122 25\n39 158 39\n39 165 36\n39 198 28\n39 207 16\n39 293 18\n39 327 10\n39 399 25\n39 402 22\n39 425 28\n39 429 13\n39 471 43\n39 485 29\n39 486 39\n39 501 9\n39 513 16\n39 542 16\n39 557 10\n39 626 7\n39 667 18\n39 700 2\n39 712 26\n39 714 41\n39 726 29\n39 727 27\n39 770 9\n39 776 40\n39 802 45\n39 822 49\n39 836 30\n39 837 3\n39 841 36\n39 849 24\n39 877 32\n39 951 8\n39 968 25\n39 975 48\n39 980 21\n40 11 7\n40 17 6\n40 34 14\n40 44 24\n40 120 47\n40 177 40\n40 201 29\n40 221 20\n40 273 6\n40 280 30\n40 294 21\n40 371 -2\n40 374 18\n40 382 -2\n40 448 33\n40 481 8\n40 484 44\n40 517 34\n40 531 27\n40 613 4\n40 619 29\n40 621 32\n40 655 39\n40 663 1\n40 670 34\n40 680 11\n40 699 13\n40 782 18\n40 816 16\n40 845 24\n40 901 37\n40 927 28\n40 972 21\n40 986 16\n40 990 35\n41 30 33\n41 51 26\n41 74 34\n41 89 17\n41 109 49\n41 176 28\n41 200 29\n41 203 24\n41 204 21\n41 219 45\n41 224 45\n41 256 19\n41 257 28\n41 271 10\n41 346 36\n41 356 9\n41 371 20\n41 379 2\n41 402 0\n41 403 13\n41 404 10\n41 436 18\n41 437 33\n41 446 39\n41 514 13\n41 516 47\n41 530 21\n41 551 30\n41 566 34\n41 583 29\n41 638 0\n41 644 47\n41 651 5\n41 669 24\n41 701 4\n41 717 45\n41 726 49\n41 732 49\n41 735 18\n41 740 35\n41 753 15\n41 759 16\n41 801 2\n41 813 19\n41 838 27\n41 901 39\n41 976 11\n41 986 27\n42 59 14\n42 71 15\n42 72 49\n42 74 5\n42 87 41\n42 100 46\n42 101 11\n42 147 28\n42 169 41\n42 179 43\n42 186 34\n42 275 -2\n42 290 19\n42 293 29\n42 294 17\n42 308 35\n42 334 19\n42 343 24\n42 398 16\n42 400 21\n42 429 27\n42 441 13\n42 456 11\n42 460 12\n42 496 23\n42 513 26\n42 532 13\n42 535 11\n42 577 40\n42 579 25\n42 583 40\n42 590 43\n42 603 35\n42 608 12\n42 628 4\n42 637 39\n42 640 15\n42 666 44\n42 670 40\n42 685 31\n42 699 33\n42 700 43\n42 704 31\n42 706 16\n42 707 10\n42 738 21\n42 739 47\n42 748 2\n42 750 43\n42 762 18\n42 787 32\n42 890 45\n42 901 32\n42 925 37\n42 961 13\n42 963 50\n42 977 30\n42 983 17\n42 986 28\n42 998 49\n43 6 20\n43 64 38\n43 101 11\n43 109 35\n43 112 28\n43 120 49\n43 156 29\n43 163 3\n43 171 28\n43 175 21\n43 184 37\n43 199 18\n43 238 15\n43 261 3\n43 266 17\n43 274 19\n43 280 41\n43 332 30\n43 358 38\n43 388 44\n43 417 42\n43 423 32\n43 456 21\n43 494 11\n43 544 22\n43 570 25\n43 589 11\n43 636 3\n43 637 23\n43 698 17\n43 700 25\n43 775 22\n43 781 32\n43 804 13\n43 806 46\n43 809 7\n43 823 33\n43 856 44\n43 862 13\n43 865 4\n43 899 31\n43 901 18\n43 963 15\n43 965 10\n43 984 11\n44 29 36\n44 40 28\n44 64 46\n44 66 32\n44 87 26\n44 97 36\n44 125 39\n44 139 -1\n44 165 13\n44 256 17\n44 258 42\n44 278 19\n44 295 37\n44 315 18\n44 369 29\n44 382 17\n44 390 16\n44 391 40\n44 392 22\n44 476 17\n44 526 40\n44 527 8\n44 536 40\n44 657 34\n44 675 48\n44 744 47\n44 806 37\n44 846 47\n44 851 44\n44 920 41\n44 956 35\n45 4 27\n45 11 26\n45 85 -2\n45 110 27\n45 112 7\n45 155 16\n45 159 50\n45 164 12\n45 190 39\n45 207 48\n45 213 -2\n45 224 -1\n45 259 19\n45 279 2\n45 294 -1\n45 320 10\n45 349 17\n45 366 43\n45 403 38\n45 441 18\n45 534 16\n45 548 24\n45 569 15\n45 575 19\n45 596 44\n45 620 0\n45 676 22\n45 702 38\n45 745 9\n45 764 33\n45 780 10\n45 792 40\n45 836 23\n45 917 1\n45 922 6\n45 965 39\n45 980 37\n46 3 35\n46 60 25\n46 61 26\n46 98 25\n46 117 31\n46 133 25\n46 146 41\n46 181 23\n46 245 19\n46 260 10\n46 295 26\n46 302 28\n46 310 31\n46 335 24\n46 341 13\n46 351 39\n46 359 19\n46 361 30\n46 367 42\n46 383 26\n46 423 33\n46 444 26\n46 448 3\n46 462 45\n46 469 29\n46 470 18\n46 521 19\n46 573 34\n46 574 0\n46 602 15\n46 608 35\n46 632 3\n46 658 15\n46 662 20\n46 669 37\n46 689 0\n46 696 39\n46 700 22\n46 709 9\n46 773 7\n46 776 38\n46 780 36\n46 788 19\n46 796 29\n46 798 17\n46 818 8\n46 828 1\n46 832 33\n46 845 12\n46 858 19\n46 878 8\n46 882 26\n46 889 22\n46 893 27\n46 903 33\n46 981 12\n46 987 9\n47 1 19\n47 16 12\n47 33 49\n47 86 16\n47 103 8\n47 122 46\n47 137 38\n47 171 20\n47 191 39\n47 202 42\n47 267 18\n47 268 43\n47 291 14\n47 308 43\n47 321 38\n47 332 39\n47 428 33\n47 506 48\n47 509 11\n47 553 39\n47 577 20\n47 605 18\n47 651 7\n47 781 42\n47 848 3\n47 859 49\n47 887 39\n47 910 28\n47 913 18\n47 936 16\n47 942 15\n47 945 5\n47 995 35\n47 997 29\n48 20 4\n48 104 17\n48 155 18\n48 159 16\n48 177 34\n48 200 33\n48 216 17\n48 236 18\n48 289 25\n48 325 44\n48 326 19\n48 330 43\n48 334 24\n48 364 39\n48 370 48\n48 422 29\n48 442 15\n48 518 23\n48 544 22\n48 557 29\n48 571 26\n48 586 44\n48 592 50\n48 628 38\n48 635 25\n48 649 19\n48 670 41\n48 709 3\n48 726 26\n48 739 26\n48 755 32\n48 787 44\n48 809 18\n48 843 34\n48 849 20\n48 865 31\n48 876 20\n48 928 16\n48 933 14\n48 952 37\n48 974 12\n48 984 44\n49 1 46\n49 9 13\n49 13 28\n49 46 23\n49 50 13\n49 75 35\n49 127 20\n49 157 48\n49 158 -2\n49 160 9\n49 176 35\n49 205 21\n49 304 8\n49 315 36\n49 325 -2\n49 346 47\n49 372 17\n49 399 10\n49 414 7\n49 417 36\n49 421 38\n49 425 34\n49 446 39\n49 447 40\n49 450 7\n49 474 25\n49 483 12\n49 495 -2\n49 521 33\n49 642 43\n49 650 22\n49 658 16\n49 670 19\n49 689 45\n49 702 15\n49 712 43\n49 724 47\n49 731 -2\n49 789 39\n49 868 13\n49 884 25\n49 904 16\n49 918 48\n49 932 30\n49 962 26\n49 975 50\n49 978 8\n49 990 16\n49 1000 49\n50 8 38\n50 40 29\n50 67 42\n50 68 33\n50 95 24\n50 146 5\n50 177 33\n50 195 6\n50 198 5\n50 234 22\n50 236 17\n50 272 35\n50 284 17\n50 303 48\n50 310 45\n50 325 43\n50 331 45\n50 333 10\n50 337 33\n50 368 0\n50 373 37\n50 381 12\n50 407 21\n50 411 7\n50 423 25\n50 466 22\n50 486 32\n50 535 19\n50 557 33\n50 558 26\n50 566 46\n50 580 0\n50 588 40\n50 591 -1\n50 618 8\n50 623 16\n50 624 14\n50 634 5\n50 652 35\n50 681 7\n50 700 12\n50 714 29\n50 716 21\n50 733 12\n50 779 7\n50 815 7\n50 822 29\n50 823 30\n50 824 16\n50 829 24\n50 854 10\n50 877 22\n50 888 22\n50 937 29\n50 948 25\n50 973 42\n51 10 36\n51 105 8\n51 110 25\n51 146 12\n51 172 7\n51 248 11\n51 266 6\n51 284 6\n51 293 31\n51 304 18\n51 329 38\n51 441 7\n51 448 46\n51 463 31\n51 465 35\n51 466 19\n51 501 4\n51 534 28\n51 556 38\n51 574 25\n51 650 -2\n51 715 49\n51 737 45\n51 739 33\n51 767 42\n51 864 22\n51 905 19\n51 938 16\n51 967 18\n52 19 27\n52 35 46\n52 42 10\n52 72 40\n52 84 39\n52 85 21\n52 89 44\n52 117 50\n52 123 46\n52 140 36\n52 229 21\n52 246 23\n52 265 29\n52 270 37\n52 342 29\n52 356 45\n52 411 17\n52 412 44\n52 431 40\n52 469 25\n52 513 8\n52 548 34\n52 550 50\n52 581 19\n52 590 12\n52 593 41\n52 634 37\n52 695 45\n52 697 49\n52 699 49\n52 735 22\n52 757 31\n52 763 21\n52 790 6\n52 793 3\n52 818 13\n52 821 44\n52 835 17\n52 884 16\n52 897 12\n52 898 38\n52 904 9\n52 906 19\n52 932 32\n53 1 9\n53 17 16\n53 29 39\n53 39 4\n53 60 20\n53 85 38\n53 117 15\n53 157 21\n53 181 44\n53 202 18\n53 212 50\n53 220 23\n53 242 10\n53 272 41\n53 274 12\n53 275 28\n53 288 23\n53 313 10\n53 323 28\n53 335 18\n53 347 23\n53 368 9\n53 383 11\n53 438 40\n53 480 13\n53 508 18\n53 572 18\n53 640 36\n53 646 40\n53 651 41\n53 683 43\n53 686 -2\n53 690 42\n53 753 28\n53 768 6\n53 795 41\n53 803 11\n53 818 26\n53 827 39\n53 907 18\n53 943 39\n53 970 33\n53 996 15\n54 39 32\n54 214 17\n54 277 9\n54 314 0\n54 323 10\n54 377 31\n54 397 44\n54 412 4\n54 425 3\n54 441 38\n54 445 48\n54 477 31\n54 482 25\n54 483 23\n54 509 11\n54 530 2\n54 537 37\n54 555 7\n54 570 5\n54 572 48\n54 584 14\n54 585 2\n54 598 22\n54 648 37\n54 653 45\n54 654 20\n54 716 14\n54 728 24\n54 730 23\n54 742 41\n54 772 4\n54 778 35\n54 783 42\n54 817 36\n54 864 12\n54 895 21\n54 917 23\n54 927 -2\n54 970 19\n55 13 21\n55 67 15\n55 122 -1\n55 133 7\n55 136 31\n55 141 37\n55 143 0\n55 145 16\n55 171 42\n55 196 19\n55 243 -2\n55 268 46\n55 291 14\n55 329 2\n55 337 4\n55 340 25\n55 349 25\n55 375 50\n55 382 23\n55 404 27\n55 431 18\n55 460 24\n55 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892 46\n113 924 48\n113 931 39\n113 969 17\n113 977 25\n114 36 46\n114 39 -1\n114 55 12\n114 65 -1\n114 68 11\n114 78 8\n114 85 29\n114 101 39\n114 175 4\n114 184 29\n114 189 25\n114 191 5\n114 213 12\n114 283 3\n114 285 50\n114 293 50\n114 296 5\n114 297 16\n114 299 -2\n114 317 6\n114 326 40\n114 366 5\n114 367 41\n114 387 25\n114 407 18\n114 419 17\n114 445 -2\n114 497 49\n114 531 6\n114 542 16\n114 546 7\n114 547 -1\n114 560 33\n114 590 8\n114 613 39\n114 636 24\n114 649 7\n114 669 44\n114 688 13\n114 697 25\n114 749 -2\n114 769 49\n114 853 14\n114 868 13\n114 906 34\n114 932 18\n114 942 0\n114 972 -2\n115 3 -1\n115 7 34\n115 20 43\n115 47 17\n115 116 20\n115 135 22\n115 168 22\n115 175 24\n115 212 27\n115 248 0\n115 281 45\n115 293 41\n115 298 50\n115 300 26\n115 307 42\n115 335 18\n115 347 5\n115 387 38\n115 390 6\n115 442 33\n115 509 38\n115 515 31\n115 521 24\n115 524 4\n115 558 16\n115 564 20\n115 656 13\n115 666 15\n115 681 29\n115 683 27\n115 691 21\n115 705 35\n115 708 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18\n119 653 8\n119 760 43\n119 767 41\n119 775 8\n119 820 22\n119 823 5\n119 830 13\n119 889 13\n119 958 6\n120 15 28\n120 38 12\n120 45 5\n120 83 38\n120 99 16\n120 119 10\n120 149 14\n120 185 17\n120 198 14\n120 235 37\n120 340 35\n120 347 34\n120 387 20\n120 404 25\n120 437 9\n120 475 29\n120 500 33\n120 524 34\n120 535 21\n120 554 34\n120 559 37\n120 567 48\n120 576 49\n120 584 -1\n120 590 20\n120 601 35\n120 613 39\n120 640 45\n120 653 46\n120 670 10\n120 674 0\n120 678 6\n120 707 12\n120 708 15\n120 728 23\n120 735 16\n120 736 23\n120 757 20\n120 777 50\n120 782 39\n120 796 8\n120 835 19\n120 873 33\n120 902 6\n120 979 47\n120 986 32\n121 4 26\n121 12 38\n121 23 32\n121 30 11\n121 85 48\n121 162 37\n121 193 26\n121 209 5\n121 239 29\n121 251 4\n121 264 16\n121 275 40\n121 298 12\n121 300 30\n121 333 28\n121 335 47\n121 346 23\n121 347 -1\n121 392 10\n121 396 21\n121 476 20\n121 554 21\n121 563 30\n121 571 23\n121 592 3\n121 616 23\n121 619 19\n121 643 31\n121 649 37\n121 672 37\n121 679 28\n121 680 41\n121 698 50\n121 774 5\n121 788 50\n121 801 20\n121 858 34\n121 881 27\n121 910 7\n121 915 43\n121 918 38\n121 946 24\n121 955 -2\n121 961 33\n121 982 2\n121 995 30\n122 30 25\n122 33 4\n122 48 43\n122 66 38\n122 71 27\n122 87 47\n122 89 13\n122 119 15\n122 147 13\n122 176 42\n122 180 49\n122 182 50\n122 187 21\n122 218 30\n122 249 12\n122 255 34\n122 314 50\n122 316 43\n122 373 15\n122 382 33\n122 387 38\n122 392 0\n122 411 2\n122 416 37\n122 426 0\n122 475 2\n122 488 41\n122 501 12\n122 536 4\n122 541 3\n122 554 -2\n122 584 27\n122 597 42\n122 620 8\n122 668 34\n122 671 15\n122 679 11\n122 707 18\n122 722 49\n122 728 12\n122 757 37\n122 792 11\n122 816 12\n122 842 8\n122 850 25\n122 852 10\n122 867 33\n122 875 33\n122 895 3\n122 903 22\n122 907 29\n122 915 47\n122 923 15\n122 956 12\n122 959 12\n122 981 4\n122 992 50\n122 999 7\n123 39 49\n123 63 0\n123 68 26\n123 70 36\n123 85 20\n123 98 7\n123 164 20\n123 226 38\n123 232 30\n123 251 34\n123 264 9\n123 282 33\n123 298 37\n123 305 -2\n123 333 10\n123 400 25\n123 408 8\n123 409 40\n123 420 35\n123 440 49\n123 459 32\n123 471 16\n123 538 23\n123 574 2\n123 586 43\n123 587 44\n123 617 28\n123 622 39\n123 635 0\n123 643 18\n123 661 37\n123 720 46\n123 734 37\n123 735 28\n123 745 -2\n123 763 39\n123 772 13\n123 783 39\n123 793 36\n123 824 9\n123 826 29\n123 831 24\n123 860 17\n123 937 15\n123 942 34\n123 965 1\n123 973 11\n123 979 33\n123 990 50\n123 992 7\n124 2 27\n124 35 3\n124 53 40\n124 86 18\n124 108 10\n124 120 33\n124 139 6\n124 177 12\n124 187 45\n124 203 30\n124 204 44\n124 219 47\n124 276 28\n124 312 41\n124 325 12\n124 356 48\n124 360 31\n124 369 27\n124 378 31\n124 390 16\n124 409 -2\n124 462 10\n124 488 29\n124 489 22\n124 510 12\n124 535 34\n124 560 9\n124 586 28\n124 589 35\n124 591 46\n124 600 35\n124 630 37\n124 645 32\n124 659 20\n124 689 28\n124 714 9\n124 719 28\n124 724 46\n124 727 13\n124 746 -1\n124 757 39\n124 785 43\n124 821 49\n124 846 41\n124 872 9\n124 877 0\n124 904 22\n124 913 9\n124 924 13\n124 936 5\n124 999 10\n125 50 17\n125 134 13\n125 140 2\n125 196 31\n125 215 29\n125 247 47\n125 266 2\n125 270 50\n125 288 16\n125 291 39\n125 326 2\n125 335 28\n125 344 40\n125 345 12\n125 346 6\n125 352 15\n125 362 -2\n125 418 28\n125 434 15\n125 448 50\n125 456 12\n125 462 9\n125 463 13\n125 520 14\n125 538 31\n125 542 29\n125 561 2\n125 573 38\n125 645 11\n125 659 35\n125 677 42\n125 681 39\n125 698 2\n125 702 45\n125 725 5\n125 768 31\n125 770 13\n125 792 18\n125 794 23\n125 865 3\n125 868 47\n125 930 34\n125 943 0\n125 945 3\n125 994 9\n126 3 15\n126 8 17\n126 9 49\n126 16 22\n126 18 24\n126 68 1\n126 82 0\n126 99 13\n126 107 0\n126 120 38\n126 145 45\n126 150 48\n126 177 14\n126 186 35\n126 207 29\n126 266 27\n126 278 27\n126 286 50\n126 305 50\n126 335 11\n126 339 14\n126 368 8\n126 384 37\n126 417 36\n126 440 9\n126 447 45\n126 451 24\n126 453 18\n126 491 37\n126 495 48\n126 581 12\n126 598 0\n126 601 22\n126 605 25\n126 608 9\n126 639 49\n126 656 42\n126 663 33\n126 667 50\n126 674 40\n126 690 36\n126 723 4\n126 725 16\n126 779 5\n126 781 21\n126 795 0\n126 831 13\n126 834 38\n126 841 46\n126 842 2\n126 847 7\n126 851 11\n126 856 19\n126 864 40\n126 924 22\n126 930 15\n126 942 26\n126 995 38\n127 61 20\n127 65 5\n127 84 48\n127 89 -1\n127 108 0\n127 137 5\n127 138 0\n127 152 42\n127 188 26\n127 198 44\n127 212 15\n127 213 30\n127 242 -2\n127 318 32\n127 322 30\n127 352 10\n127 404 -2\n127 408 21\n127 448 32\n127 450 34\n127 463 23\n127 500 4\n127 508 28\n127 526 4\n127 574 11\n127 597 44\n127 615 46\n127 620 16\n127 624 2\n127 630 32\n127 637 26\n127 661 39\n127 662 36\n127 675 19\n127 690 39\n127 729 19\n127 759 17\n127 777 -2\n127 791 30\n127 792 48\n127 862 -2\n127 871 41\n127 874 33\n127 888 49\n127 943 25\n127 964 41\n127 969 49\n127 974 43\n128 29 29\n128 32 16\n128 34 36\n128 105 8\n128 123 34\n128 143 15\n128 192 18\n128 195 36\n128 206 33\n128 218 41\n128 234 48\n128 252 -1\n128 287 36\n128 306 29\n128 313 9\n128 325 35\n128 437 14\n128 443 33\n128 455 1\n128 502 13\n128 549 26\n128 584 31\n128 594 7\n128 638 20\n128 647 38\n128 672 39\n128 681 44\n128 734 8\n128 740 7\n128 748 4\n128 753 46\n128 760 39\n128 767 19\n128 778 23\n128 824 19\n128 837 13\n128 845 46\n128 908 27\n128 911 40\n128 928 9\n129 17 22\n129 94 34\n129 111 5\n129 115 37\n129 175 22\n129 221 7\n129 249 44\n129 280 12\n129 315 43\n129 327 23\n129 341 17\n129 358 48\n129 364 44\n129 365 49\n129 372 16\n129 395 41\n129 397 36\n129 410 11\n129 458 40\n129 479 19\n129 542 8\n129 544 23\n129 546 3\n129 552 17\n129 579 36\n129 592 4\n129 625 27\n129 709 23\n129 710 9\n129 716 12\n129 730 26\n129 752 5\n129 756 40\n129 778 19\n129 793 -1\n129 810 21\n129 826 34\n129 836 47\n129 843 5\n129 857 25\n129 871 38\n129 917 17\n129 996 8\n130 55 26\n130 115 44\n130 117 15\n130 149 46\n130 151 35\n130 171 10\n130 184 5\n130 257 37\n130 258 42\n130 269 18\n130 284 19\n130 299 24\n130 353 11\n130 356 31\n130 359 14\n130 381 17\n130 552 35\n130 567 27\n130 583 49\n130 621 35\n130 626 21\n130 651 13\n130 666 22\n130 678 26\n130 689 15\n130 695 -1\n130 702 27\n130 738 1\n130 740 38\n130 764 49\n130 785 17\n130 792 47\n130 795 13\n130 824 49\n130 865 29\n130 871 42\n130 879 32\n130 884 0\n130 907 7\n131 14 23\n131 36 33\n131 87 48\n131 128 8\n131 175 30\n131 191 16\n131 218 30\n131 245 28\n131 286 42\n131 306 10\n131 330 45\n131 409 49\n131 414 0\n131 432 16\n131 458 20\n131 465 24\n131 471 26\n131 510 13\n131 521 16\n131 535 6\n131 587 11\n131 600 49\n131 604 30\n131 623 19\n131 662 50\n131 713 18\n131 773 -1\n131 804 16\n131 810 14\n131 845 40\n131 861 20\n131 871 25\n131 896 47\n131 956 39\n131 960 40\n131 971 48\n131 988 41\n132 13 16\n132 68 13\n132 92 23\n132 107 47\n132 194 31\n132 210 44\n132 243 8\n132 250 11\n132 257 15\n132 284 29\n132 290 26\n132 306 40\n132 308 46\n132 311 33\n132 324 5\n132 353 45\n132 364 10\n132 369 13\n132 385 26\n132 388 30\n132 395 47\n132 403 6\n132 405 15\n132 438 38\n132 450 42\n132 452 23\n132 454 22\n132 458 43\n132 477 7\n132 479 7\n132 492 46\n132 521 2\n132 530 37\n132 544 21\n132 566 2\n132 581 37\n132 594 5\n132 606 47\n132 611 24\n132 615 6\n132 616 29\n132 640 26\n132 650 49\n132 663 15\n132 682 2\n132 691 9\n132 717 3\n132 746 14\n132 764 35\n132 765 16\n132 775 31\n132 805 10\n132 825 41\n132 832 34\n132 871 40\n132 896 33\n132 911 10\n132 912 41\n132 928 47\n132 937 33\n132 962 25\n133 46 23\n133 75 41\n133 99 32\n133 136 16\n133 160 48\n133 164 31\n133 209 32\n133 213 14\n133 224 49\n133 263 11\n133 282 20\n133 291 47\n133 315 36\n133 323 14\n133 343 33\n133 344 43\n133 352 17\n133 361 36\n133 379 6\n133 400 1\n133 410 45\n133 418 21\n133 436 40\n133 454 43\n133 518 15\n133 554 38\n133 557 48\n133 564 7\n133 579 11\n133 584 5\n133 622 37\n133 634 5\n133 638 11\n133 850 10\n133 852 8\n133 860 15\n133 866 13\n133 871 38\n133 879 34\n133 898 21\n133 980 24\n134 24 32\n134 31 41\n134 35 33\n134 39 8\n134 45 21\n134 53 15\n134 63 5\n134 70 41\n134 77 44\n134 121 38\n134 127 10\n134 137 9\n134 145 37\n134 149 13\n134 158 20\n134 170 23\n134 220 40\n134 242 4\n134 290 26\n134 291 24\n134 299 16\n134 303 39\n134 312 34\n134 330 12\n134 348 50\n134 354 20\n134 360 30\n134 387 14\n134 407 23\n134 418 22\n134 440 25\n134 459 25\n134 487 35\n134 494 20\n134 540 25\n134 561 27\n134 563 39\n134 567 30\n134 594 27\n134 624 13\n134 654 10\n134 720 47\n134 730 31\n134 732 6\n134 774 37\n134 779 36\n134 790 43\n134 829 8\n134 922 6\n134 923 9\n134 930 28\n134 948 34\n134 971 45\n134 975 39\n134 985 18\n135 5 47\n135 59 -1\n135 99 45\n135 100 45\n135 120 16\n135 139 42\n135 166 50\n135 170 21\n135 189 40\n135 201 23\n135 234 34\n135 252 26\n135 271 29\n135 303 22\n135 322 44\n135 339 11\n135 341 41\n135 351 6\n135 374 10\n135 408 33\n135 415 47\n135 432 13\n135 456 1\n135 457 23\n135 463 14\n135 464 34\n135 482 46\n135 486 14\n135 506 19\n135 507 37\n135 533 6\n135 542 33\n135 579 50\n135 597 33\n135 633 17\n135 649 17\n135 681 39\n135 700 26\n135 710 14\n135 718 11\n135 767 14\n135 835 10\n135 867 44\n135 895 5\n135 969 46\n135 987 7\n136 11 29\n136 31 33\n136 37 6\n136 38 20\n136 58 49\n136 78 32\n136 97 41\n136 99 14\n136 108 28\n136 128 20\n136 167 12\n136 177 32\n136 190 23\n136 217 43\n136 219 38\n136 257 48\n136 268 32\n136 269 35\n136 276 41\n136 315 29\n136 340 22\n136 389 36\n136 424 42\n136 529 46\n136 548 8\n136 610 37\n136 619 29\n136 624 -2\n136 663 14\n136 724 16\n136 793 48\n136 837 32\n136 846 29\n136 858 4\n136 885 46\n136 895 48\n136 897 40\n136 903 21\n136 909 32\n136 921 36\n136 927 39\n136 936 46\n136 971 13\n136 978 48\n136 985 23\n137 44 6\n137 88 38\n137 89 6\n137 216 43\n137 225 35\n137 230 24\n137 233 39\n137 263 48\n137 264 9\n137 303 38\n137 309 36\n137 310 39\n137 389 -1\n137 416 29\n137 442 30\n137 444 48\n137 463 49\n137 518 5\n137 555 39\n137 580 8\n137 582 37\n137 597 21\n137 600 44\n137 624 9\n137 663 49\n137 710 1\n137 716 30\n137 783 46\n137 803 6\n137 814 33\n137 816 47\n137 842 31\n137 885 7\n137 947 47\n137 948 36\n137 949 28\n137 963 16\n137 980 19\n137 999 43\n138 17 37\n138 51 23\n138 89 33\n138 100 24\n138 121 24\n138 126 40\n138 240 2\n138 246 49\n138 250 13\n138 253 37\n138 264 36\n138 265 23\n138 275 42\n138 279 4\n138 361 -1\n138 385 39\n138 393 25\n138 399 11\n138 403 32\n138 414 27\n138 525 21\n138 577 14\n138 596 43\n138 633 7\n138 664 18\n138 673 3\n138 679 27\n138 696 26\n138 723 7\n138 741 25\n138 784 8\n138 801 44\n138 805 12\n138 828 18\n138 848 4\n138 889 8\n138 981 0\n138 985 35\n139 7 38\n139 23 27\n139 34 41\n139 72 30\n139 113 25\n139 126 43\n139 135 32\n139 169 13\n139 190 42\n139 252 45\n139 279 43\n139 368 8\n139 372 44\n139 373 7\n139 422 32\n139 423 27\n139 452 24\n139 456 15\n139 470 18\n139 516 17\n139 537 32\n139 539 28\n139 547 34\n139 566 39\n139 575 44\n139 614 11\n139 662 6\n139 719 45\n139 724 17\n139 746 46\n139 749 26\n139 754 20\n139 794 5\n139 797 26\n139 814 14\n139 864 20\n139 876 4\n139 882 27\n139 904 35\n139 964 30\n139 965 3\n139 980 30\n140 1 49\n140 16 36\n140 28 21\n140 29 36\n140 95 28\n140 115 25\n140 133 9\n140 155 34\n140 199 32\n140 214 24\n140 245 11\n140 292 43\n140 354 41\n140 436 36\n140 441 18\n140 483 40\n140 503 34\n140 515 23\n140 528 49\n140 531 15\n140 535 12\n140 540 22\n140 570 40\n140 580 31\n140 663 44\n140 666 9\n140 670 6\n140 690 40\n140 710 36\n140 711 26\n140 716 16\n140 754 31\n140 790 40\n140 794 43\n140 832 14\n140 848 30\n140 872 35\n140 889 31\n140 943 43\n140 955 27\n140 999 45\n141 7 33\n141 35 13\n141 39 41\n141 82 7\n141 102 -2\n141 115 38\n141 122 31\n141 166 20\n141 178 42\n141 188 42\n141 244 28\n141 258 18\n141 263 0\n141 316 32\n141 317 20\n141 346 31\n141 370 24\n141 377 10\n141 385 36\n141 410 31\n141 434 21\n141 445 7\n141 495 20\n141 510 4\n141 534 47\n141 536 44\n141 537 35\n141 588 38\n141 593 31\n141 605 37\n141 646 14\n141 651 31\n141 677 28\n141 697 45\n141 778 18\n141 781 8\n141 825 23\n141 832 27\n141 838 39\n141 839 43\n141 869 37\n141 885 50\n141 922 11\n142 15 43\n142 16 45\n142 30 19\n142 55 47\n142 75 27\n142 79 17\n142 123 41\n142 158 47\n142 175 13\n142 184 24\n142 220 17\n142 241 0\n142 263 17\n142 289 -2\n142 290 47\n142 346 35\n142 352 12\n142 360 6\n142 367 48\n142 393 9\n142 402 29\n142 414 47\n142 459 20\n142 478 35\n142 484 43\n142 535 27\n142 568 13\n142 575 39\n142 608 5\n142 628 5\n142 629 4\n142 637 3\n142 659 14\n142 698 41\n142 719 15\n142 735 0\n142 743 49\n142 774 45\n142 784 22\n142 806 33\n142 810 22\n142 842 34\n142 871 46\n142 876 9\n142 882 27\n142 883 23\n142 919 26\n142 969 30\n142 973 5\n142 990 19\n143 9 25\n143 10 50\n143 12 18\n143 56 38\n143 57 7\n143 62 27\n143 74 43\n143 107 1\n143 121 48\n143 141 30\n143 145 38\n143 171 49\n143 202 7\n143 215 11\n143 227 33\n143 278 31\n143 319 46\n143 333 21\n143 415 42\n143 425 42\n143 440 23\n143 479 26\n143 484 32\n143 520 29\n143 525 4\n143 539 47\n143 587 28\n143 602 14\n143 627 22\n143 643 2\n143 705 43\n143 712 12\n143 755 17\n143 766 2\n143 788 39\n143 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41\n145 750 16\n145 777 18\n145 822 11\n145 841 50\n145 855 27\n145 868 46\n145 877 25\n145 888 20\n145 930 19\n146 23 5\n146 31 43\n146 40 26\n146 46 7\n146 87 19\n146 141 32\n146 151 12\n146 154 42\n146 164 16\n146 174 33\n146 184 43\n146 193 15\n146 210 26\n146 214 50\n146 312 46\n146 319 5\n146 322 36\n146 331 1\n146 352 8\n146 360 40\n146 362 24\n146 371 37\n146 376 6\n146 379 26\n146 384 15\n146 402 36\n146 423 39\n146 442 10\n146 446 46\n146 498 42\n146 499 28\n146 541 1\n146 551 22\n146 574 45\n146 576 47\n146 579 16\n146 606 44\n146 664 27\n146 674 25\n146 683 20\n146 704 20\n146 722 7\n146 728 25\n146 749 18\n146 751 27\n146 771 24\n146 778 26\n146 827 10\n146 836 45\n146 838 23\n146 854 0\n146 896 19\n146 912 48\n146 979 8\n147 32 10\n147 37 29\n147 59 -2\n147 113 10\n147 136 -1\n147 151 22\n147 188 11\n147 214 40\n147 226 16\n147 231 46\n147 299 47\n147 306 15\n147 345 37\n147 350 49\n147 413 16\n147 452 22\n147 474 33\n147 486 12\n147 495 17\n147 498 10\n147 516 42\n147 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32\n150 701 47\n150 706 44\n150 740 -2\n150 760 15\n150 773 13\n150 789 44\n150 802 32\n150 848 4\n150 896 44\n150 911 2\n150 922 36\n150 932 5\n150 964 0\n151 7 24\n151 46 8\n151 48 43\n151 112 50\n151 114 37\n151 128 44\n151 155 25\n151 160 4\n151 167 13\n151 208 29\n151 262 47\n151 286 0\n151 301 19\n151 303 0\n151 319 19\n151 328 21\n151 345 27\n151 347 33\n151 359 35\n151 380 43\n151 381 24\n151 395 49\n151 404 23\n151 441 40\n151 476 29\n151 484 39\n151 509 48\n151 525 14\n151 532 50\n151 573 36\n151 574 26\n151 580 38\n151 594 13\n151 598 7\n151 608 29\n151 621 22\n151 647 49\n151 657 30\n151 669 42\n151 670 49\n151 693 33\n151 713 10\n151 745 14\n151 750 45\n151 757 39\n151 774 33\n151 789 38\n151 821 27\n151 826 33\n151 838 2\n151 857 10\n151 869 12\n151 884 1\n151 885 46\n151 906 24\n151 910 5\n151 991 37\n152 3 38\n152 26 6\n152 46 4\n152 139 29\n152 190 47\n152 202 35\n152 204 20\n152 205 25\n152 264 2\n152 286 8\n152 290 25\n152 297 29\n152 300 49\n152 303 8\n152 324 30\n152 329 23\n152 332 47\n152 363 38\n152 467 37\n152 478 6\n152 480 25\n152 512 36\n152 527 -1\n152 531 19\n152 597 31\n152 606 25\n152 623 22\n152 631 36\n152 635 44\n152 648 47\n152 692 31\n152 700 43\n152 710 32\n152 730 13\n152 758 49\n152 778 50\n152 782 29\n152 790 0\n152 800 39\n152 853 45\n152 859 32\n152 881 7\n152 897 45\n152 924 36\n152 935 8\n152 972 20\n153 15 48\n153 23 7\n153 43 42\n153 138 50\n153 233 29\n153 241 45\n153 260 49\n153 280 12\n153 300 20\n153 303 0\n153 307 29\n153 310 20\n153 321 13\n153 324 28\n153 327 44\n153 328 24\n153 332 31\n153 339 16\n153 361 25\n153 408 4\n153 516 31\n153 520 43\n153 630 12\n153 662 8\n153 704 7\n153 717 43\n153 734 4\n153 748 42\n153 758 21\n153 775 8\n153 790 45\n153 791 4\n153 809 1\n153 838 15\n153 843 44\n153 872 1\n153 878 39\n153 890 19\n153 924 30\n153 926 -2\n153 941 24\n153 962 26\n153 968 18\n154 24 5\n154 26 45\n154 66 -1\n154 77 34\n154 88 39\n154 145 12\n154 155 31\n154 160 22\n154 166 16\n154 192 36\n154 206 40\n154 216 38\n154 307 19\n154 340 -2\n154 367 29\n154 402 15\n154 408 11\n154 410 40\n154 462 49\n154 485 -2\n154 511 45\n154 590 45\n154 599 33\n154 602 25\n154 624 27\n154 636 48\n154 638 6\n154 650 13\n154 652 43\n154 668 20\n154 675 40\n154 684 11\n154 696 39\n154 714 10\n154 726 49\n154 735 35\n154 739 46\n154 777 7\n154 815 -2\n154 858 1\n154 876 13\n154 884 4\n154 898 49\n154 921 38\n154 936 23\n154 978 30\n154 997 26\n155 17 14\n155 29 36\n155 41 4\n155 61 46\n155 91 -1\n155 111 13\n155 123 0\n155 163 38\n155 174 4\n155 194 27\n155 228 14\n155 271 10\n155 299 4\n155 301 31\n155 316 1\n155 321 5\n155 323 40\n155 326 4\n155 377 34\n155 417 28\n155 452 -1\n155 463 34\n155 514 9\n155 529 5\n155 555 37\n155 556 41\n155 582 14\n155 607 49\n155 659 40\n155 665 12\n155 677 7\n155 680 16\n155 684 -2\n155 700 50\n155 716 18\n155 743 48\n155 748 4\n155 782 5\n155 785 41\n155 800 20\n155 835 21\n155 856 -1\n155 890 3\n155 916 32\n155 917 49\n155 972 44\n155 981 24\n156 9 19\n156 14 25\n156 56 16\n156 59 17\n156 90 45\n156 96 14\n156 109 2\n156 110 15\n156 130 26\n156 167 5\n156 182 22\n156 191 4\n156 222 41\n156 239 25\n156 273 24\n156 331 50\n156 339 11\n156 365 24\n156 373 48\n156 377 6\n156 422 48\n156 448 42\n156 461 41\n156 478 37\n156 480 19\n156 518 3\n156 536 17\n156 596 4\n156 639 38\n156 642 -2\n156 703 10\n156 705 45\n156 720 36\n156 750 15\n156 754 21\n156 818 41\n156 845 50\n156 848 31\n156 865 1\n156 885 12\n156 890 24\n156 908 -2\n156 914 48\n156 927 34\n156 947 19\n156 984 34\n156 985 46\n156 988 17\n156 993 41\n156 1000 29\n157 4 40\n157 33 17\n157 35 29\n157 60 20\n157 66 43\n157 70 27\n157 122 31\n157 162 6\n157 173 42\n157 176 30\n157 184 20\n157 237 29\n157 283 10\n157 284 39\n157 305 26\n157 311 19\n157 315 48\n157 329 18\n157 397 6\n157 518 10\n157 521 40\n157 561 29\n157 605 42\n157 610 16\n157 637 25\n157 646 36\n157 694 30\n157 696 18\n157 729 34\n157 772 27\n157 773 24\n157 811 44\n157 839 11\n157 844 2\n157 865 48\n157 888 13\n157 902 10\n157 943 41\n157 988 20\n158 31 25\n158 39 4\n158 51 25\n158 66 7\n158 77 49\n158 81 43\n158 93 18\n158 94 45\n158 103 0\n158 129 47\n158 161 11\n158 164 31\n158 206 21\n158 211 49\n158 212 20\n158 215 1\n158 236 46\n158 250 8\n158 263 18\n158 324 7\n158 339 50\n158 343 18\n158 373 38\n158 391 40\n158 413 39\n158 425 43\n158 445 25\n158 474 38\n158 492 -2\n158 499 43\n158 523 41\n158 540 35\n158 552 47\n158 565 16\n158 568 19\n158 572 48\n158 592 13\n158 612 13\n158 627 43\n158 633 3\n158 650 25\n158 677 12\n158 710 43\n158 720 39\n158 739 31\n158 750 24\n158 752 32\n158 757 10\n158 769 38\n158 780 43\n158 783 2\n158 814 3\n158 816 16\n158 828 41\n158 838 50\n158 847 39\n158 873 22\n158 876 23\n158 879 36\n158 893 9\n158 900 39\n158 908 45\n158 920 41\n158 939 28\n159 9 33\n159 15 9\n159 37 44\n159 44 11\n159 52 10\n159 59 17\n159 62 25\n159 64 5\n159 67 15\n159 74 43\n159 77 21\n159 101 16\n159 109 24\n159 140 35\n159 151 11\n159 186 43\n159 256 31\n159 329 35\n159 330 9\n159 349 42\n159 375 20\n159 409 21\n159 452 36\n159 455 45\n159 489 23\n159 504 13\n159 518 41\n159 524 47\n159 527 15\n159 536 40\n159 539 20\n159 557 49\n159 593 47\n159 609 42\n159 624 34\n159 625 34\n159 682 8\n159 697 15\n159 737 10\n159 738 24\n159 758 -2\n159 794 1\n159 802 13\n159 805 15\n159 879 3\n159 881 38\n159 899 24\n159 910 40\n159 913 8\n159 924 39\n159 976 3\n160 69 11\n160 89 33\n160 93 4\n160 98 3\n160 114 13\n160 143 39\n160 154 16\n160 199 13\n160 213 3\n160 215 1\n160 301 2\n160 330 37\n160 335 46\n160 342 26\n160 349 19\n160 353 46\n160 363 46\n160 364 5\n160 386 21\n160 388 14\n160 437 39\n160 456 43\n160 477 40\n160 484 33\n160 491 6\n160 511 13\n160 513 19\n160 526 39\n160 532 2\n160 539 16\n160 547 45\n160 580 22\n160 590 41\n160 600 14\n160 601 48\n160 640 45\n160 685 44\n160 699 17\n160 701 38\n160 706 30\n160 753 17\n160 772 37\n160 781 5\n160 806 33\n160 811 9\n160 844 20\n160 857 13\n160 904 22\n160 929 8\n160 971 15\n160 976 26\n160 981 11\n160 989 25\n161 46 39\n161 79 13\n161 118 32\n161 124 24\n161 189 28\n161 199 36\n161 238 31\n161 262 7\n161 268 36\n161 301 22\n161 303 8\n161 327 10\n161 351 39\n161 358 35\n161 393 -1\n161 406 36\n161 445 26\n161 448 22\n161 471 30\n161 478 40\n161 487 25\n161 490 -2\n161 547 3\n161 558 36\n161 593 28\n161 610 38\n161 622 5\n161 628 11\n161 632 45\n161 634 22\n161 665 15\n161 673 31\n161 694 2\n161 695 47\n161 711 50\n161 714 40\n161 742 46\n161 746 9\n161 840 17\n161 843 46\n161 846 5\n161 862 34\n161 885 44\n161 898 5\n161 910 2\n161 913 18\n161 922 16\n161 923 36\n161 925 5\n161 933 43\n161 934 20\n161 942 36\n161 944 36\n161 969 42\n161 982 48\n161 992 30\n162 4 3\n162 31 43\n162 36 35\n162 65 48\n162 67 45\n162 68 -1\n162 79 38\n162 86 39\n162 113 44\n162 117 34\n162 142 18\n162 155 15\n162 177 49\n162 192 18\n162 232 11\n162 240 12\n162 247 50\n162 251 0\n162 269 35\n162 287 20\n162 291 47\n162 345 45\n162 400 31\n162 405 4\n162 423 50\n162 445 28\n162 450 17\n162 535 48\n162 538 29\n162 553 31\n162 562 34\n162 574 24\n162 635 42\n162 656 18\n162 686 5\n162 702 49\n162 706 7\n162 722 44\n162 734 22\n162 743 -1\n162 755 28\n162 758 49\n162 793 31\n162 812 31\n162 854 28\n163 12 4\n163 43 7\n163 59 0\n163 72 17\n163 175 0\n163 179 27\n163 212 48\n163 239 28\n163 245 5\n163 287 33\n163 305 32\n163 320 3\n163 329 16\n163 452 12\n163 461 23\n163 464 6\n163 484 14\n163 523 27\n163 549 21\n163 553 20\n163 560 25\n163 634 3\n163 721 39\n163 731 4\n163 744 0\n163 785 5\n163 786 7\n163 795 10\n163 796 49\n163 825 18\n163 848 10\n163 854 46\n163 885 13\n163 904 36\n163 916 50\n163 933 37\n163 955 35\n164 18 38\n164 33 25\n164 42 22\n164 44 41\n164 52 34\n164 56 3\n164 66 34\n164 79 45\n164 98 36\n164 118 8\n164 143 9\n164 144 45\n164 153 45\n164 222 6\n164 230 13\n164 242 25\n164 256 48\n164 264 13\n164 275 4\n164 288 42\n164 295 34\n164 298 46\n164 320 5\n164 374 37\n164 472 4\n164 484 48\n164 521 10\n164 531 40\n164 544 35\n164 572 49\n164 573 16\n164 585 4\n164 590 37\n164 593 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398 45\n166 457 47\n166 494 15\n166 515 49\n166 519 13\n166 546 19\n166 562 22\n166 600 18\n166 622 10\n166 640 18\n166 654 8\n166 664 8\n166 672 2\n166 677 21\n166 707 41\n166 717 9\n166 732 17\n166 795 2\n166 805 49\n166 821 37\n166 863 15\n166 870 13\n166 881 26\n166 895 16\n166 902 14\n166 906 13\n166 920 33\n166 921 33\n166 935 9\n166 950 33\n166 975 11\n166 978 12\n166 991 0\n167 26 19\n167 31 10\n167 84 37\n167 89 34\n167 99 38\n167 111 37\n167 127 -1\n167 141 -2\n167 147 14\n167 154 32\n167 160 9\n167 166 11\n167 202 21\n167 241 25\n167 251 46\n167 284 28\n167 285 26\n167 290 35\n167 298 15\n167 304 34\n167 324 38\n167 330 35\n167 333 26\n167 359 35\n167 466 21\n167 476 26\n167 523 40\n167 528 15\n167 559 44\n167 565 17\n167 571 41\n167 572 44\n167 589 46\n167 592 25\n167 688 15\n167 706 32\n167 747 46\n167 754 24\n167 758 42\n167 759 10\n167 777 6\n167 835 29\n167 924 28\n167 927 49\n167 942 13\n167 954 42\n167 959 15\n167 990 3\n167 995 33\n168 32 36\n168 53 17\n168 86 13\n168 103 8\n168 109 21\n168 128 15\n168 143 10\n168 241 31\n168 308 6\n168 321 7\n168 326 38\n168 344 26\n168 403 20\n168 408 41\n168 442 39\n168 453 9\n168 460 10\n168 463 8\n168 494 39\n168 512 27\n168 524 43\n168 525 20\n168 533 9\n168 541 10\n168 568 35\n168 581 36\n168 596 45\n168 609 39\n168 610 46\n168 620 27\n168 647 27\n168 661 20\n168 675 42\n168 678 35\n168 679 30\n168 690 36\n168 731 23\n168 743 8\n168 766 30\n168 785 49\n168 821 6\n168 835 50\n168 843 17\n168 846 47\n168 875 30\n168 929 25\n168 938 17\n168 974 12\n169 24 33\n169 34 42\n169 101 46\n169 117 -2\n169 144 27\n169 148 -1\n169 173 19\n169 175 24\n169 199 28\n169 201 21\n169 231 0\n169 246 38\n169 285 44\n169 293 10\n169 336 40\n169 368 39\n169 393 45\n169 414 20\n169 429 47\n169 430 5\n169 437 17\n169 449 37\n169 458 13\n169 462 30\n169 465 10\n169 468 27\n169 475 0\n169 481 2\n169 483 30\n169 484 31\n169 507 7\n169 515 11\n169 519 36\n169 527 40\n169 529 9\n169 552 21\n169 572 39\n169 588 38\n169 620 28\n169 624 46\n169 632 45\n169 671 19\n169 687 23\n169 695 32\n169 708 0\n169 728 1\n169 814 3\n169 815 46\n169 827 40\n169 833 47\n169 850 48\n169 851 9\n169 854 27\n169 935 25\n169 937 48\n169 938 49\n169 947 40\n169 964 37\n169 986 45\n169 995 34\n169 997 31\n170 4 -2\n170 30 32\n170 54 22\n170 73 41\n170 88 1\n170 89 17\n170 100 39\n170 126 14\n170 149 21\n170 159 30\n170 186 9\n170 192 41\n170 223 47\n170 263 -2\n170 282 43\n170 328 8\n170 333 42\n170 385 12\n170 389 7\n170 395 -2\n170 416 28\n170 459 24\n170 472 48\n170 483 29\n170 539 34\n170 544 5\n170 557 29\n170 644 3\n170 645 34\n170 653 24\n170 666 12\n170 685 17\n170 687 44\n170 757 27\n170 827 11\n170 832 44\n170 861 10\n170 885 27\n170 917 8\n170 921 0\n170 955 30\n170 960 22\n170 964 28\n170 969 43\n170 996 18\n171 6 17\n171 41 41\n171 54 48\n171 86 15\n171 93 46\n171 118 23\n171 131 16\n171 149 47\n171 186 8\n171 208 44\n171 217 17\n171 254 50\n171 259 11\n171 305 50\n171 315 10\n171 320 30\n171 331 9\n171 359 3\n171 366 18\n171 367 21\n171 382 41\n171 383 41\n171 409 40\n171 410 18\n171 428 25\n171 441 6\n171 448 41\n171 491 -1\n171 515 4\n171 527 3\n171 532 48\n171 543 35\n171 558 12\n171 570 29\n171 601 15\n171 621 8\n171 636 28\n171 681 6\n171 685 15\n171 704 17\n171 720 26\n171 733 18\n171 734 25\n171 765 50\n171 845 31\n171 853 20\n171 872 21\n171 896 49\n171 902 41\n171 953 35\n171 974 6\n171 978 42\n171 982 31\n171 989 20\n172 4 26\n172 50 29\n172 53 42\n172 114 27\n172 150 33\n172 177 21\n172 210 3\n172 214 24\n172 255 15\n172 265 8\n172 278 50\n172 337 46\n172 351 31\n172 359 15\n172 379 40\n172 391 11\n172 398 19\n172 461 29\n172 477 11\n172 520 20\n172 618 38\n172 622 7\n172 637 36\n172 638 15\n172 642 24\n172 679 23\n172 680 23\n172 681 9\n172 734 20\n172 769 25\n172 771 44\n172 778 48\n172 792 27\n172 816 28\n172 848 0\n172 870 35\n172 878 49\n172 906 31\n172 911 4\n172 926 5\n172 971 49\n172 990 35\n173 6 41\n173 8 32\n173 21 4\n173 37 47\n173 62 7\n173 85 0\n173 108 17\n173 112 33\n173 119 0\n173 126 49\n173 134 50\n173 139 42\n173 145 31\n173 168 15\n173 172 -1\n173 178 20\n173 201 26\n173 208 36\n173 265 27\n173 273 23\n173 275 38\n173 337 31\n173 345 16\n173 352 5\n173 354 41\n173 355 20\n173 365 43\n173 391 6\n173 395 1\n173 412 20\n173 418 10\n173 427 15\n173 431 42\n173 504 21\n173 505 44\n173 544 18\n173 559 48\n173 580 6\n173 596 38\n173 639 32\n173 647 41\n173 662 -2\n173 804 -1\n173 813 41\n173 858 18\n173 859 15\n173 924 49\n173 957 19\n173 959 45\n173 974 20\n173 992 19\n174 10 2\n174 62 38\n174 74 8\n174 89 47\n174 102 24\n174 120 31\n174 211 15\n174 221 28\n174 224 10\n174 289 42\n174 299 20\n174 330 8\n174 332 42\n174 333 11\n174 351 50\n174 356 2\n174 360 14\n174 366 42\n174 381 43\n174 388 0\n174 447 50\n174 473 42\n174 487 37\n174 495 41\n174 501 4\n174 510 37\n174 525 47\n174 528 19\n174 554 3\n174 559 35\n174 580 50\n174 599 24\n174 601 32\n174 608 -1\n174 633 26\n174 707 40\n174 711 6\n174 762 21\n174 823 27\n174 831 2\n174 840 16\n174 849 28\n174 856 8\n174 864 0\n174 866 22\n174 915 2\n174 920 0\n174 952 37\n174 998 43\n175 60 47\n175 109 47\n175 159 23\n175 163 31\n175 201 28\n175 256 26\n175 275 17\n175 373 26\n175 379 13\n175 394 27\n175 400 3\n175 466 17\n175 509 16\n175 523 7\n175 528 42\n175 567 31\n175 612 28\n175 614 3\n175 623 18\n175 631 -2\n175 646 33\n175 676 40\n175 678 36\n175 687 26\n175 701 28\n175 717 40\n175 731 0\n175 735 25\n175 747 15\n175 756 45\n175 814 42\n175 815 30\n175 819 48\n175 865 22\n175 880 -2\n175 882 28\n175 885 49\n175 910 25\n175 934 50\n175 983 10\n175 996 8\n175 998 49\n176 51 42\n176 66 35\n176 83 16\n176 102 31\n176 108 13\n176 132 9\n176 146 49\n176 149 15\n176 152 6\n176 161 2\n176 174 27\n176 179 7\n176 185 24\n176 198 34\n176 224 22\n176 258 28\n176 309 38\n176 315 39\n176 357 14\n176 382 42\n176 396 -1\n176 401 7\n176 422 0\n176 426 -2\n176 440 22\n176 459 38\n176 487 21\n176 507 38\n176 546 41\n176 570 2\n176 579 2\n176 604 47\n176 607 16\n176 624 12\n176 701 33\n176 702 22\n176 711 39\n176 746 44\n176 771 33\n176 775 42\n176 781 4\n176 790 32\n176 811 33\n176 812 39\n176 813 23\n176 842 35\n176 851 36\n176 880 21\n176 896 47\n176 959 20\n176 973 23\n176 974 8\n177 1 15\n177 14 48\n177 41 -1\n177 45 8\n177 70 45\n177 77 9\n177 127 10\n177 149 36\n177 183 43\n177 212 49\n177 300 49\n177 313 45\n177 338 32\n177 366 27\n177 401 29\n177 421 4\n177 426 49\n177 427 44\n177 428 33\n177 447 27\n177 472 43\n177 504 46\n177 505 24\n177 577 28\n177 585 20\n177 605 46\n177 615 28\n177 635 49\n177 637 50\n177 643 0\n177 644 27\n177 648 27\n177 650 36\n177 791 42\n177 792 29\n177 809 6\n177 821 15\n177 840 34\n177 859 46\n177 896 4\n177 905 36\n177 986 19\n177 1000 30\n178 4 49\n178 10 45\n178 35 13\n178 40 13\n178 51 48\n178 73 18\n178 85 28\n178 131 32\n178 143 36\n178 151 27\n178 172 28\n178 176 10\n178 251 7\n178 259 31\n178 270 46\n178 289 36\n178 302 46\n178 330 13\n178 332 29\n178 342 47\n178 377 44\n178 461 20\n178 494 11\n178 553 9\n178 573 48\n178 603 44\n178 609 13\n178 625 29\n178 646 50\n178 654 35\n178 686 25\n178 703 36\n178 729 27\n178 749 49\n178 755 46\n178 802 24\n178 833 37\n178 869 35\n178 872 12\n178 888 35\n178 891 16\n178 902 47\n178 912 47\n178 943 44\n178 951 22\n179 26 7\n179 48 8\n179 74 38\n179 86 33\n179 105 10\n179 115 5\n179 116 43\n179 232 20\n179 302 15\n179 308 4\n179 316 47\n179 335 32\n179 357 24\n179 370 -2\n179 374 49\n179 376 1\n179 394 23\n179 397 7\n179 408 24\n179 425 13\n179 466 1\n179 490 32\n179 492 -1\n179 675 40\n179 717 43\n179 799 24\n179 801 25\n179 823 24\n179 832 6\n179 833 0\n179 846 12\n179 867 37\n179 909 1\n179 923 20\n179 990 38\n180 25 14\n180 30 11\n180 56 22\n180 65 12\n180 83 7\n180 94 50\n180 106 44\n180 173 1\n180 182 7\n180 194 22\n180 211 46\n180 215 7\n180 244 37\n180 245 29\n180 263 4\n180 312 11\n180 316 4\n180 319 31\n180 328 40\n180 337 2\n180 376 44\n180 400 47\n180 420 25\n180 450 28\n180 453 27\n180 457 25\n180 461 20\n180 525 6\n180 549 0\n180 552 49\n180 586 15\n180 672 17\n180 684 40\n180 689 3\n180 699 36\n180 703 23\n180 723 26\n180 746 39\n180 772 9\n180 799 29\n180 828 13\n180 863 8\n180 876 33\n180 880 7\n180 908 31\n180 922 48\n180 960 1\n180 962 44\n181 16 15\n181 20 10\n181 23 14\n181 38 23\n181 45 9\n181 81 8\n181 124 22\n181 158 3\n181 174 20\n181 215 38\n181 218 42\n181 246 14\n181 264 2\n181 265 7\n181 279 41\n181 283 24\n181 287 37\n181 289 50\n181 345 20\n181 362 41\n181 376 24\n181 400 5\n181 412 45\n181 418 47\n181 456 42\n181 464 11\n181 470 37\n181 474 19\n181 488 9\n181 510 26\n181 516 25\n181 602 17\n181 605 28\n181 611 10\n181 641 11\n181 643 17\n181 645 16\n181 721 1\n181 758 22\n181 762 36\n181 801 -2\n181 857 15\n181 870 21\n181 876 47\n181 887 32\n181 933 19\n181 936 7\n181 951 44\n181 977 16\n182 14 43\n182 37 6\n182 63 4\n182 64 0\n182 72 39\n182 98 4\n182 101 1\n182 126 2\n182 151 40\n182 152 36\n182 163 7\n182 187 18\n182 197 4\n182 204 -1\n182 216 46\n182 220 17\n182 241 15\n182 246 0\n182 252 18\n182 307 48\n182 319 27\n182 320 6\n182 345 44\n182 353 28\n182 376 4\n182 416 36\n182 430 6\n182 450 23\n182 488 27\n182 593 20\n182 595 16\n182 604 25\n182 613 34\n182 671 45\n182 690 36\n182 695 17\n182 714 4\n182 719 36\n182 723 33\n182 734 16\n182 751 12\n182 811 26\n182 868 0\n182 871 4\n182 905 5\n182 946 46\n182 951 10\n182 966 47\n182 976 4\n182 994 16\n183 2 36\n183 6 45\n183 18 3\n183 23 25\n183 25 24\n183 64 20\n183 73 10\n183 81 12\n183 86 0\n183 157 19\n183 165 12\n183 169 16\n183 170 7\n183 199 -1\n183 222 18\n183 236 3\n183 256 36\n183 272 27\n183 342 49\n183 389 14\n183 396 1\n183 423 18\n183 426 33\n183 436 24\n183 454 30\n183 490 38\n183 496 17\n183 501 42\n183 502 7\n183 567 32\n183 584 42\n183 591 4\n183 603 19\n183 618 17\n183 626 45\n183 644 15\n183 661 34\n183 690 29\n183 716 17\n183 765 30\n183 776 31\n183 805 14\n183 821 45\n183 836 41\n183 892 44\n183 907 49\n183 933 28\n183 967 27\n183 969 18\n184 5 12\n184 26 14\n184 32 34\n184 33 36\n184 59 29\n184 86 17\n184 96 22\n184 139 18\n184 146 27\n184 213 26\n184 230 24\n184 253 12\n184 276 45\n184 280 25\n184 286 45\n184 289 33\n184 316 7\n184 343 8\n184 344 46\n184 345 2\n184 369 26\n184 444 24\n184 506 28\n184 517 15\n184 535 45\n184 563 40\n184 595 18\n184 610 33\n184 618 29\n184 667 0\n184 699 45\n184 705 31\n184 747 17\n184 789 35\n184 791 -1\n184 793 4\n184 837 6\n184 856 8\n184 859 34\n184 871 31\n184 915 1\n184 922 6\n184 924 46\n184 992 21\n185 11 -2\n185 36 23\n185 46 32\n185 52 3\n185 54 50\n185 57 27\n185 82 47\n185 104 8\n185 107 39\n185 147 21\n185 176 49\n185 180 36\n185 206 30\n185 218 14\n185 223 8\n185 230 40\n185 261 29\n185 275 36\n185 300 25\n185 308 7\n185 385 17\n185 387 43\n185 394 48\n185 465 41\n185 485 12\n185 506 45\n185 517 -2\n185 533 42\n185 544 38\n185 582 8\n185 595 24\n185 596 50\n185 643 36\n185 720 2\n185 761 16\n185 781 9\n185 796 28\n185 797 34\n185 802 47\n185 808 40\n185 815 45\n185 852 49\n185 854 2\n185 864 25\n185 872 1\n185 891 50\n185 913 29\n185 944 43\n185 948 12\n185 984 5\n185 986 4\n186 29 37\n186 34 40\n186 56 45\n186 85 4\n186 91 41\n186 154 29\n186 161 35\n186 171 42\n186 205 26\n186 211 31\n186 224 18\n186 228 32\n186 229 8\n186 260 12\n186 279 29\n186 284 13\n186 287 22\n186 335 15\n186 352 44\n186 359 27\n186 366 1\n186 406 15\n186 454 31\n186 467 25\n186 472 7\n186 504 13\n186 552 40\n186 574 29\n186 578 44\n186 605 7\n186 616 27\n186 645 49\n186 655 41\n186 661 32\n186 674 7\n186 675 21\n186 694 29\n186 712 18\n186 734 33\n186 745 41\n186 773 11\n186 777 18\n186 778 20\n186 783 10\n186 865 -2\n186 917 44\n186 929 35\n186 966 40\n186 995 39\n187 10 14\n187 32 26\n187 40 1\n187 90 18\n187 94 41\n187 108 42\n187 110 34\n187 114 20\n187 115 44\n187 117 39\n187 143 43\n187 253 16\n187 256 0\n187 266 22\n187 275 32\n187 288 39\n187 295 14\n187 359 9\n187 401 22\n187 402 43\n187 408 41\n187 417 35\n187 458 26\n187 470 45\n187 471 10\n187 488 32\n187 504 46\n187 507 29\n187 534 25\n187 597 47\n187 603 40\n187 613 33\n187 636 34\n187 679 25\n187 729 39\n187 736 31\n187 739 46\n187 765 43\n187 768 28\n187 797 45\n187 798 37\n187 808 16\n187 842 50\n187 893 3\n187 903 48\n187 915 33\n188 4 20\n188 16 1\n188 28 14\n188 43 49\n188 88 15\n188 92 28\n188 143 32\n188 149 34\n188 186 12\n188 205 23\n188 225 29\n188 246 12\n188 310 2\n188 323 32\n188 325 15\n188 336 7\n188 384 19\n188 399 0\n188 406 8\n188 411 27\n188 423 6\n188 424 5\n188 457 4\n188 471 15\n188 490 37\n188 491 12\n188 546 31\n188 570 42\n188 579 45\n188 593 16\n188 594 24\n188 667 41\n188 668 19\n188 691 48\n188 717 18\n188 726 26\n188 730 44\n188 734 5\n188 748 -1\n188 761 0\n188 767 1\n188 863 1\n188 894 15\n188 901 18\n188 905 31\n188 913 0\n188 959 48\n188 963 33\n188 964 40\n188 966 6\n188 985 29\n189 13 27\n189 23 40\n189 30 33\n189 39 20\n189 58 0\n189 62 27\n189 65 19\n189 92 39\n189 132 28\n189 146 38\n189 148 42\n189 159 5\n189 166 48\n189 186 29\n189 196 -1\n189 206 49\n189 249 28\n189 252 36\n189 257 14\n189 278 18\n189 280 43\n189 320 24\n189 330 6\n189 334 5\n189 347 21\n189 353 13\n189 354 17\n189 385 47\n189 434 30\n189 456 27\n189 487 6\n189 497 10\n189 498 43\n189 523 21\n189 528 33\n189 582 22\n189 585 37\n189 592 2\n189 594 7\n189 634 17\n189 677 34\n189 683 46\n189 704 20\n189 731 6\n189 746 6\n189 751 29\n189 783 9\n189 812 9\n189 815 20\n189 875 50\n189 883 9\n189 942 6\n189 971 14\n189 999 8\n190 4 42\n190 21 47\n190 24 33\n190 25 31\n190 87 29\n190 98 12\n190 99 10\n190 106 35\n190 147 29\n190 159 5\n190 264 28\n190 290 13\n190 312 18\n190 365 30\n190 366 39\n190 379 49\n190 380 7\n190 384 49\n190 434 5\n190 438 27\n190 456 1\n190 467 16\n190 490 39\n190 554 34\n190 569 10\n190 583 44\n190 665 42\n190 673 36\n190 680 49\n190 716 36\n190 733 21\n190 752 -2\n190 787 22\n190 794 35\n190 841 33\n190 846 9\n190 855 50\n190 868 3\n190 875 36\n190 918 22\n190 923 38\n190 927 48\n190 935 11\n190 936 21\n190 937 34\n190 956 0\n191 5 35\n191 56 16\n191 58 6\n191 102 28\n191 136 35\n191 162 -2\n191 180 30\n191 202 32\n191 203 6\n191 204 1\n191 205 43\n191 212 44\n191 220 17\n191 232 31\n191 245 24\n191 263 38\n191 268 42\n191 278 24\n191 282 27\n191 298 38\n191 309 34\n191 315 28\n191 317 4\n191 350 9\n191 360 47\n191 404 39\n191 429 33\n191 492 13\n191 501 -1\n191 552 34\n191 554 47\n191 555 25\n191 583 20\n191 724 8\n191 730 39\n191 749 11\n191 759 8\n191 778 28\n191 783 36\n191 819 49\n191 832 50\n191 843 44\n191 878 47\n191 881 4\n191 910 23\n191 928 34\n191 940 41\n191 977 44\n191 990 27\n192 7 12\n192 8 46\n192 27 16\n192 39 43\n192 44 -1\n192 51 24\n192 113 6\n192 117 36\n192 132 35\n192 163 9\n192 166 27\n192 176 12\n192 184 16\n192 185 6\n192 186 42\n192 187 39\n192 205 7\n192 225 6\n192 250 24\n192 266 45\n192 323 20\n192 342 38\n192 374 14\n192 379 6\n192 396 43\n192 416 48\n192 422 48\n192 439 48\n192 442 18\n192 465 14\n192 496 33\n192 505 3\n192 523 43\n192 524 34\n192 556 28\n192 569 32\n192 574 10\n192 575 40\n192 613 19\n192 623 21\n192 630 28\n192 635 42\n192 690 29\n192 710 22\n192 739 40\n192 741 49\n192 807 11\n192 824 18\n192 862 44\n192 869 34\n192 880 14\n192 915 9\n192 932 23\n192 934 49\n192 945 6\n192 951 2\n193 21 46\n193 52 16\n193 112 28\n193 149 14\n193 151 11\n193 179 14\n193 182 29\n193 192 30\n193 197 2\n193 230 49\n193 251 32\n193 329 43\n193 379 45\n193 381 1\n193 433 50\n193 456 26\n193 544 49\n193 585 48\n193 620 13\n193 645 8\n193 647 21\n193 653 32\n193 670 32\n193 686 35\n193 729 34\n193 744 31\n193 753 19\n193 785 22\n193 820 36\n193 869 11\n193 872 37\n194 31 35\n194 53 44\n194 72 19\n194 94 26\n194 102 5\n194 108 25\n194 122 21\n194 163 34\n194 166 44\n194 178 20\n194 218 8\n194 254 48\n194 264 43\n194 268 13\n194 284 19\n194 335 18\n194 345 25\n194 355 33\n194 357 49\n194 369 7\n194 374 4\n194 396 34\n194 417 39\n194 450 40\n194 463 40\n194 481 8\n194 515 21\n194 546 37\n194 597 8\n194 613 0\n194 634 5\n194 667 4\n194 691 45\n194 717 45\n194 731 27\n194 742 42\n194 746 36\n194 752 37\n194 765 10\n194 778 14\n194 791 36\n194 814 24\n194 830 49\n194 834 22\n194 844 8\n194 846 40\n194 869 41\n194 888 50\n194 895 50\n194 903 36\n194 927 26\n194 938 27\n194 987 11\n195 10 32\n195 14 48\n195 21 9\n195 22 19\n195 34 33\n195 79 4\n195 101 30\n195 104 38\n195 144 3\n195 154 47\n195 164 19\n195 167 20\n195 199 24\n195 205 26\n195 216 4\n195 245 -2\n195 282 26\n195 285 20\n195 286 16\n195 318 9\n195 337 33\n195 353 11\n195 389 27\n195 428 2\n195 448 36\n195 468 40\n195 475 12\n195 483 13\n195 487 14\n195 505 9\n195 535 10\n195 563 5\n195 579 20\n195 616 20\n195 645 13\n195 650 31\n195 652 37\n195 657 35\n195 679 16\n195 697 0\n195 720 20\n195 732 32\n195 762 -1\n195 782 1\n195 789 0\n195 816 16\n195 828 33\n195 846 27\n195 857 6\n195 870 3\n195 873 45\n195 912 22\n195 913 42\n195 922 38\n195 935 2\n195 976 43\n195 977 47\n196 17 24\n196 25 0\n196 57 34\n196 117 46\n196 154 10\n196 165 37\n196 182 38\n196 253 18\n196 276 8\n196 329 9\n196 339 43\n196 351 37\n196 357 38\n196 374 29\n196 410 5\n196 437 25\n196 464 39\n196 470 50\n196 483 26\n196 493 12\n196 498 -2\n196 542 25\n196 557 43\n196 573 40\n196 622 18\n196 625 16\n196 634 32\n196 644 35\n196 659 38\n196 681 32\n196 700 4\n196 703 24\n196 718 50\n196 724 19\n196 777 39\n196 836 40\n196 849 28\n196 854 7\n196 891 3\n196 963 40\n196 996 31\n197 1 8\n197 17 15\n197 32 7\n197 34 12\n197 45 5\n197 50 20\n197 51 17\n197 102 26\n197 216 17\n197 220 5\n197 246 17\n197 276 19\n197 280 22\n197 295 41\n197 308 7\n197 333 42\n197 337 33\n197 364 19\n197 370 11\n197 380 1\n197 409 42\n197 436 19\n197 440 18\n197 463 18\n197 496 31\n197 498 1\n197 512 18\n197 523 32\n197 540 30\n197 572 10\n197 601 1\n197 620 3\n197 655 35\n197 662 20\n197 700 46\n197 733 40\n197 759 45\n197 770 27\n197 798 47\n197 815 32\n197 823 17\n197 841 15\n197 847 44\n197 863 48\n197 869 10\n197 878 43\n197 889 19\n197 893 49\n197 908 40\n197 953 32\n197 960 37\n197 968 35\n198 19 18\n198 44 30\n198 68 24\n198 77 -2\n198 87 15\n198 93 32\n198 97 34\n198 114 24\n198 130 11\n198 153 13\n198 159 9\n198 164 33\n198 171 3\n198 177 13\n198 189 22\n198 201 32\n198 210 19\n198 220 20\n198 221 2\n198 226 46\n198 235 49\n198 256 33\n198 271 33\n198 278 14\n198 293 3\n198 306 44\n198 332 34\n198 338 22\n198 355 21\n198 356 2\n198 405 6\n198 413 41\n198 421 15\n198 452 22\n198 464 42\n198 483 10\n198 523 49\n198 531 0\n198 539 16\n198 606 7\n198 666 32\n198 668 17\n198 681 35\n198 691 13\n198 700 41\n198 717 4\n198 741 7\n198 742 14\n198 744 33\n198 755 33\n198 761 18\n198 767 25\n198 805 14\n198 863 25\n198 866 19\n198 873 34\n198 880 13\n198 909 38\n198 920 24\n198 937 44\n198 948 15\n198 972 37\n198 999 3\n199 1 31\n199 5 20\n199 16 30\n199 28 5\n199 53 15\n199 55 49\n199 64 14\n199 122 21\n199 156 21\n199 177 25\n199 207 24\n199 214 0\n199 220 4\n199 243 36\n199 259 10\n199 266 50\n199 288 38\n199 293 20\n199 364 41\n199 388 10\n199 412 1\n199 457 12\n199 459 9\n199 460 3\n199 481 40\n199 505 33\n199 510 0\n199 514 48\n199 570 8\n199 592 35\n199 604 22\n199 617 5\n199 705 38\n199 706 17\n199 734 41\n199 742 33\n199 778 23\n199 805 28\n199 830 7\n199 833 7\n199 851 1\n199 864 25\n199 866 1\n199 871 9\n199 873 7\n199 895 -2\n199 905 28\n199 963 15\n199 969 21\n199 989 -2\n200 4 24\n200 7 25\n200 11 9\n200 64 49\n200 66 -1\n200 74 4\n200 120 49\n200 124 17\n200 154 22\n200 180 48\n200 181 10\n200 185 43\n200 206 31\n200 220 36\n200 236 4\n200 246 43\n200 251 1\n200 254 36\n200 257 13\n200 261 25\n200 280 37\n200 300 24\n200 311 4\n200 315 24\n200 343 2\n200 354 31\n200 406 22\n200 414 19\n200 422 41\n200 438 35\n200 440 24\n200 447 33\n200 483 33\n200 490 10\n200 535 18\n200 542 1\n200 552 9\n200 564 26\n200 573 29\n200 586 9\n200 592 44\n200 598 24\n200 619 4\n200 673 7\n200 674 17\n200 690 23\n200 691 22\n200 697 26\n200 719 4\n200 748 47\n200 763 24\n200 852 21\n200 873 13\n200 958 32\n200 974 36\n200 992 17\n201 54 26\n201 60 24\n201 66 27\n201 68 39\n201 85 31\n201 116 31\n201 125 35\n201 198 44\n201 209 39\n201 222 35\n201 272 46\n201 273 21\n201 311 49\n201 313 15\n201 325 27\n201 327 39\n201 386 33\n201 390 47\n201 445 8\n201 470 14\n201 474 33\n201 498 33\n201 499 19\n201 515 11\n201 544 34\n201 547 42\n201 560 33\n201 562 7\n201 564 7\n201 582 35\n201 587 27\n201 588 42\n201 595 37\n201 624 41\n201 641 36\n201 648 30\n201 650 45\n201 741 6\n201 748 32\n201 788 3\n201 813 5\n201 833 42\n201 844 26\n201 893 5\n201 900 8\n201 904 20\n201 906 18\n201 928 9\n201 930 43\n201 950 47\n201 981 40\n201 984 31\n202 40 12\n202 55 47\n202 56 11\n202 67 26\n202 69 45\n202 105 6\n202 106 -2\n202 124 1\n202 129 5\n202 131 46\n202 138 33\n202 143 10\n202 147 9\n202 148 39\n202 167 46\n202 174 46\n202 178 8\n202 186 39\n202 192 5\n202 197 15\n202 204 19\n202 211 9\n202 234 19\n202 249 -2\n202 254 48\n202 272 14\n202 279 36\n202 298 18\n202 316 2\n202 331 -1\n202 362 41\n202 379 25\n202 456 11\n202 491 11\n202 506 29\n202 521 44\n202 539 31\n202 545 31\n202 565 16\n202 589 43\n202 622 6\n202 665 23\n202 667 26\n202 672 29\n202 695 5\n202 700 19\n202 736 39\n202 777 15\n202 778 31\n202 786 -2\n202 803 35\n202 811 18\n202 821 43\n202 848 2\n202 866 11\n202 870 47\n202 901 7\n202 945 32\n202 954 25\n202 980 27\n202 990 11\n202 992 29\n203 3 -2\n203 16 10\n203 33 11\n203 53 18\n203 95 2\n203 106 49\n203 107 12\n203 150 33\n203 179 41\n203 183 49\n203 252 19\n203 291 16\n203 324 40\n203 333 36\n203 336 22\n203 351 44\n203 370 41\n203 410 44\n203 440 47\n203 457 16\n203 560 15\n203 579 34\n203 590 19\n203 594 11\n203 600 42\n203 610 11\n203 654 41\n203 738 14\n203 749 43\n203 776 42\n203 782 28\n203 784 36\n203 824 21\n203 864 32\n203 865 37\n203 867 13\n203 868 17\n203 898 49\n203 933 44\n203 937 0\n203 952 38\n203 987 46\n204 4 47\n204 26 45\n204 44 5\n204 78 22\n204 132 26\n204 156 26\n204 202 31\n204 216 29\n204 228 47\n204 252 44\n204 276 9\n204 285 15\n204 334 15\n204 335 15\n204 344 47\n204 376 44\n204 383 24\n204 393 43\n204 404 26\n204 405 22\n204 413 25\n204 417 48\n204 464 39\n204 476 38\n204 524 25\n204 537 42\n204 550 2\n204 570 11\n204 592 50\n204 596 24\n204 651 43\n204 665 8\n204 670 48\n204 673 49\n204 676 34\n204 700 32\n204 746 50\n204 776 14\n204 801 26\n204 836 35\n204 861 14\n204 878 45\n204 901 7\n204 937 49\n204 948 20\n204 968 46\n204 999 20\n205 20 41\n205 21 10\n205 25 27\n205 41 48\n205 43 15\n205 46 50\n205 65 16\n205 105 25\n205 118 10\n205 186 14\n205 196 35\n205 210 44\n205 215 34\n205 222 34\n205 232 41\n205 245 30\n205 276 18\n205 281 42\n205 301 16\n205 364 35\n205 368 26\n205 379 23\n205 386 31\n205 409 9\n205 422 12\n205 451 47\n205 482 24\n205 493 50\n205 500 43\n205 504 11\n205 526 8\n205 554 31\n205 596 37\n205 636 50\n205 652 9\n205 653 30\n205 731 30\n205 732 34\n205 748 42\n205 777 42\n205 787 10\n205 802 24\n205 817 8\n205 818 39\n205 845 37\n205 872 36\n205 876 7\n205 880 6\n205 894 3\n205 915 25\n205 920 31\n205 927 24\n205 983 23\n205 991 15\n206 42 13\n206 57 17\n206 87 40\n206 103 13\n206 156 -2\n206 160 3\n206 182 39\n206 187 18\n206 199 47\n206 235 8\n206 275 47\n206 287 31\n206 305 23\n206 339 33\n206 423 45\n206 456 20\n206 513 21\n206 558 20\n206 604 45\n206 622 39\n206 624 8\n206 708 38\n206 712 26\n206 720 9\n206 728 13\n206 758 2\n206 820 34\n206 821 30\n206 840 -2\n206 843 17\n206 861 39\n206 887 15\n206 944 48\n206 995 39\n207 11 -1\n207 83 19\n207 91 31\n207 120 42\n207 125 20\n207 138 31\n207 145 50\n207 160 -2\n207 172 0\n207 183 3\n207 186 1\n207 193 11\n207 221 1\n207 224 5\n207 231 17\n207 247 50\n207 254 38\n207 304 15\n207 307 7\n207 329 26\n207 330 36\n207 342 14\n207 351 16\n207 386 31\n207 391 25\n207 406 30\n207 425 26\n207 457 39\n207 503 44\n207 515 3\n207 555 28\n207 584 50\n207 639 39\n207 671 33\n207 694 31\n207 735 39\n207 766 48\n207 784 36\n207 851 8\n207 863 40\n207 874 16\n207 889 14\n207 898 8\n207 901 5\n207 966 25\n207 968 9\n207 980 26\n207 988 6\n208 12 8\n208 23 37\n208 44 45\n208 62 22\n208 63 48\n208 84 23\n208 100 45\n208 105 -2\n208 110 17\n208 153 45\n208 160 39\n208 178 41\n208 193 6\n208 207 24\n208 343 -1\n208 347 48\n208 348 5\n208 363 14\n208 373 -1\n208 399 9\n208 437 13\n208 500 43\n208 532 28\n208 543 14\n208 572 3\n208 588 4\n208 608 4\n208 653 48\n208 677 39\n208 759 50\n208 765 13\n208 771 24\n208 775 41\n208 791 41\n208 840 4\n208 849 44\n208 852 26\n208 866 29\n208 882 13\n208 917 14\n208 920 16\n208 944 -2\n208 953 3\n208 959 20\n208 963 44\n208 964 6\n208 999 3\n208 1000 46\n209 1 49\n209 5 18\n209 12 41\n209 21 47\n209 33 0\n209 101 31\n209 151 29\n209 192 7\n209 199 39\n209 215 49\n209 241 47\n209 247 34\n209 277 -1\n209 286 1\n209 300 32\n209 349 33\n209 381 3\n209 398 46\n209 401 37\n209 403 0\n209 457 42\n209 555 25\n209 571 15\n209 581 16\n209 614 25\n209 645 -1\n209 646 0\n209 737 33\n209 756 16\n209 790 11\n209 797 44\n209 798 5\n209 807 40\n209 821 18\n209 871 9\n209 919 38\n209 927 42\n209 947 24\n209 948 3\n209 951 23\n209 958 40\n209 977 37\n210 12 32\n210 34 19\n210 35 36\n210 67 9\n210 111 5\n210 112 32\n210 121 22\n210 139 9\n210 204 12\n210 231 16\n210 241 48\n210 273 5\n210 328 37\n210 387 8\n210 400 31\n210 411 12\n210 423 14\n210 454 23\n210 481 14\n210 488 41\n210 500 26\n210 526 23\n210 528 34\n210 578 50\n210 592 49\n210 599 11\n210 613 33\n210 638 29\n210 647 43\n210 683 49\n210 696 24\n210 699 24\n210 710 23\n210 724 13\n210 749 44\n210 915 9\n210 938 31\n210 941 2\n210 963 28\n210 967 7\n211 7 29\n211 10 47\n211 34 29\n211 81 42\n211 105 15\n211 142 18\n211 171 37\n211 203 42\n211 209 37\n211 237 40\n211 239 13\n211 246 24\n211 269 5\n211 273 48\n211 274 22\n211 278 26\n211 289 10\n211 364 41\n211 376 27\n211 378 44\n211 391 29\n211 402 49\n211 422 36\n211 439 29\n211 443 49\n211 480 4\n211 491 38\n211 502 43\n211 546 15\n211 565 24\n211 577 45\n211 594 32\n211 601 12\n211 619 14\n211 695 22\n211 715 24\n211 789 14\n211 801 13\n211 806 36\n211 807 19\n211 809 33\n211 820 35\n211 859 15\n211 882 32\n211 885 18\n211 909 47\n211 929 34\n211 932 35\n211 936 41\n211 949 29\n211 983 24\n211 988 44\n211 992 18\n212 15 42\n212 34 50\n212 35 44\n212 48 -1\n212 72 34\n212 110 16\n212 114 40\n212 132 2\n212 133 14\n212 154 26\n212 186 3\n212 223 -1\n212 227 9\n212 254 36\n212 283 30\n212 294 9\n212 296 19\n212 314 47\n212 322 48\n212 324 46\n212 326 21\n212 337 33\n212 350 3\n212 372 -1\n212 373 39\n212 374 43\n212 427 45\n212 458 32\n212 475 0\n212 492 10\n212 514 21\n212 542 -2\n212 565 34\n212 629 7\n212 630 13\n212 663 1\n212 676 38\n212 677 5\n212 680 21\n212 807 -1\n212 856 41\n212 866 18\n212 890 45\n212 898 17\n212 899 11\n212 905 -2\n212 911 47\n212 930 27\n212 956 14\n212 961 37\n213 30 34\n213 44 45\n213 49 40\n213 60 29\n213 68 41\n213 85 31\n213 112 37\n213 152 38\n213 205 26\n213 206 27\n213 212 38\n213 298 26\n213 343 45\n213 351 34\n213 361 46\n213 367 41\n213 375 6\n213 396 36\n213 411 35\n213 416 47\n213 423 30\n213 445 11\n213 468 16\n213 517 2\n213 525 45\n213 543 30\n213 558 32\n213 560 49\n213 615 27\n213 617 14\n213 644 15\n213 648 50\n213 667 46\n213 680 35\n213 733 14\n213 752 -1\n213 781 19\n213 807 43\n213 831 42\n213 834 22\n213 848 36\n213 883 28\n213 884 46\n213 893 18\n213 897 6\n213 918 40\n213 983 8\n214 4 25\n214 16 50\n214 48 -1\n214 59 28\n214 85 45\n214 87 3\n214 94 48\n214 137 41\n214 163 -2\n214 193 39\n214 246 42\n214 281 26\n214 292 15\n214 293 12\n214 301 19\n214 419 10\n214 430 50\n214 460 -1\n214 461 45\n214 476 32\n214 483 35\n214 504 28\n214 525 9\n214 541 32\n214 547 22\n214 575 6\n214 598 10\n214 656 27\n214 695 29\n214 716 16\n214 727 17\n214 760 46\n214 783 31\n214 807 23\n214 822 31\n214 846 7\n214 903 18\n214 928 19\n214 941 -1\n214 955 33\n214 977 35\n214 988 20\n214 992 15\n215 5 50\n215 89 38\n215 96 5\n215 106 28\n215 108 40\n215 109 10\n215 110 13\n215 122 21\n215 123 35\n215 124 16\n215 139 4\n215 142 8\n215 240 14\n215 250 14\n215 264 48\n215 271 23\n215 311 42\n215 352 16\n215 389 23\n215 400 7\n215 402 46\n215 405 3\n215 441 3\n215 461 49\n215 470 13\n215 473 50\n215 474 42\n215 492 33\n215 498 43\n215 500 36\n215 519 11\n215 523 32\n215 563 48\n215 579 33\n215 610 4\n215 616 23\n215 639 25\n215 654 29\n215 665 34\n215 682 36\n215 690 15\n215 700 -1\n215 706 43\n215 707 40\n215 714 21\n215 717 49\n215 725 10\n215 742 50\n215 770 39\n215 778 14\n215 806 48\n215 807 6\n215 809 40\n215 812 21\n215 826 42\n215 866 8\n215 880 48\n215 891 16\n215 907 47\n215 909 1\n215 929 3\n215 943 20\n215 947 3\n215 957 3\n215 987 31\n216 5 -2\n216 28 30\n216 30 4\n216 53 30\n216 154 2\n216 253 -1\n216 256 24\n216 266 15\n216 301 27\n216 324 40\n216 335 13\n216 372 42\n216 475 42\n216 486 47\n216 488 14\n216 595 24\n216 614 10\n216 654 20\n216 657 -2\n216 664 40\n216 678 11\n216 681 20\n216 700 25\n216 707 0\n216 715 33\n216 792 25\n216 806 47\n216 852 9\n216 857 36\n216 875 36\n216 896 36\n216 902 0\n216 916 32\n216 925 48\n216 940 39\n216 968 27\n216 970 24\n216 997 14\n217 59 18\n217 75 6\n217 79 47\n217 144 45\n217 173 9\n217 207 12\n217 238 36\n217 253 10\n217 267 15\n217 308 1\n217 334 22\n217 362 21\n217 370 24\n217 379 23\n217 411 36\n217 465 13\n217 487 20\n217 529 46\n217 537 41\n217 538 1\n217 545 39\n217 557 29\n217 581 43\n217 594 17\n217 606 25\n217 617 27\n217 642 18\n217 671 50\n217 711 44\n217 733 19\n217 738 8\n217 769 33\n217 771 41\n217 776 29\n217 791 12\n217 798 34\n217 808 50\n217 818 15\n217 842 26\n217 859 16\n217 877 50\n217 879 1\n217 904 39\n217 915 41\n217 916 42\n217 921 12\n217 933 16\n217 937 43\n217 965 45\n217 974 37\n217 981 39\n218 26 28\n218 44 29\n218 47 8\n218 86 26\n218 105 17\n218 128 38\n218 131 10\n218 174 17\n218 199 12\n218 224 24\n218 237 48\n218 251 31\n218 292 33\n218 300 5\n218 315 36\n218 341 19\n218 353 21\n218 378 28\n218 397 42\n218 399 3\n218 444 15\n218 485 34\n218 532 31\n218 541 39\n218 542 28\n218 570 8\n218 631 31\n218 693 34\n218 698 6\n218 710 50\n218 718 33\n218 734 35\n218 736 10\n218 738 28\n218 770 5\n218 781 8\n218 797 12\n218 801 10\n218 803 34\n218 811 22\n218 823 38\n218 890 36\n218 932 49\n218 956 15\n218 991 21\n219 5 39\n219 41 49\n219 74 34\n219 78 32\n219 81 40\n219 83 23\n219 103 41\n219 109 49\n219 120 24\n219 146 -2\n219 230 2\n219 233 2\n219 275 34\n219 312 41\n219 351 48\n219 393 3\n219 425 -2\n219 430 6\n219 438 35\n219 449 28\n219 466 36\n219 472 41\n219 480 29\n219 501 1\n219 568 30\n219 581 42\n219 583 8\n219 600 37\n219 602 19\n219 603 17\n219 604 11\n219 615 40\n219 631 34\n219 636 35\n219 651 25\n219 667 4\n219 670 8\n219 677 44\n219 694 36\n219 708 24\n219 720 20\n219 723 30\n219 745 50\n219 746 19\n219 751 29\n219 831 18\n219 863 8\n219 868 15\n219 870 7\n219 871 46\n219 886 15\n219 931 49\n219 934 28\n219 938 36\n219 950 42\n219 962 48\n220 13 28\n220 20 29\n220 53 17\n220 70 22\n220 76 12\n220 165 15\n220 181 25\n220 201 23\n220 235 11\n220 258 14\n220 275 48\n220 323 30\n220 333 24\n220 338 34\n220 346 43\n220 378 15\n220 380 48\n220 386 1\n220 398 22\n220 419 3\n220 422 49\n220 425 41\n220 453 15\n220 476 20\n220 487 12\n220 493 30\n220 499 17\n220 522 44\n220 526 11\n220 541 30\n220 551 32\n220 558 31\n220 566 24\n220 575 39\n220 582 36\n220 603 33\n220 610 -1\n220 612 26\n220 664 23\n220 666 44\n220 667 -2\n220 684 17\n220 716 50\n220 741 6\n220 747 16\n220 755 39\n220 787 46\n220 810 26\n220 813 37\n220 817 48\n220 870 29\n220 913 35\n220 921 35\n220 931 11\n220 933 18\n221 21 30\n221 55 21\n221 60 50\n221 137 10\n221 187 36\n221 206 23\n221 267 24\n221 292 32\n221 331 7\n221 338 42\n221 388 36\n221 449 29\n221 481 25\n221 505 47\n221 540 15\n221 542 16\n221 551 14\n221 562 27\n221 570 47\n221 580 45\n221 610 12\n221 623 31\n221 707 45\n221 710 43\n221 712 30\n221 726 42\n221 794 50\n221 799 40\n221 902 15\n221 915 49\n221 927 45\n221 957 44\n221 971 34\n222 20 39\n222 41 -2\n222 45 28\n222 113 27\n222 142 31\n222 148 15\n222 215 32\n222 245 11\n222 255 11\n222 256 4\n222 280 44\n222 302 34\n222 330 31\n222 337 42\n222 395 26\n222 419 15\n222 471 42\n222 540 33\n222 590 16\n222 607 11\n222 615 21\n222 641 27\n222 657 45\n222 658 38\n222 675 15\n222 770 4\n222 787 12\n222 801 48\n222 811 46\n222 815 2\n222 850 47\n222 863 47\n222 868 39\n222 883 19\n222 886 50\n222 925 26\n222 963 16\n222 994 25\n222 998 11\n223 14 17\n223 40 47\n223 46 35\n223 117 34\n223 130 21\n223 149 27\n223 150 38\n223 169 44\n223 184 18\n223 202 21\n223 211 31\n223 222 8\n223 229 7\n223 234 22\n223 254 -1\n223 271 36\n223 272 17\n223 278 9\n223 282 11\n223 294 35\n223 318 28\n223 330 17\n223 331 27\n223 350 50\n223 367 50\n223 373 15\n223 414 33\n223 417 42\n223 441 15\n223 508 41\n223 528 28\n223 561 12\n223 593 34\n223 615 43\n223 617 21\n223 647 14\n223 665 9\n223 687 37\n223 705 1\n223 718 19\n223 732 39\n223 739 19\n223 786 50\n223 801 25\n223 807 20\n223 828 40\n223 835 33\n223 867 12\n223 883 14\n223 896 38\n223 906 5\n223 914 25\n223 917 19\n223 948 23\n223 987 36\n224 11 35\n224 42 20\n224 43 6\n224 46 18\n224 50 38\n224 61 48\n224 86 24\n224 130 1\n224 160 25\n224 167 34\n224 175 43\n224 202 21\n224 242 33\n224 260 9\n224 263 10\n224 268 44\n224 280 9\n224 347 17\n224 378 8\n224 383 50\n224 396 7\n224 399 42\n224 409 35\n224 437 50\n224 444 11\n224 522 30\n224 579 24\n224 594 40\n224 602 8\n224 613 40\n224 625 38\n224 627 24\n224 628 33\n224 635 30\n224 637 10\n224 661 36\n224 667 7\n224 702 48\n224 717 18\n224 731 30\n224 739 17\n224 799 45\n224 809 40\n224 825 24\n224 837 34\n224 849 42\n224 876 44\n224 891 3\n224 895 32\n224 924 48\n224 935 47\n224 956 16\n224 973 31\n225 22 22\n225 27 27\n225 48 20\n225 53 42\n225 70 26\n225 84 41\n225 141 10\n225 160 28\n225 183 45\n225 247 1\n225 279 5\n225 305 3\n225 317 21\n225 344 6\n225 359 -2\n225 368 41\n225 411 28\n225 460 43\n225 497 8\n225 562 24\n225 591 36\n225 592 20\n225 674 13\n225 714 0\n225 727 6\n225 762 20\n225 782 47\n225 788 8\n225 793 49\n225 794 3\n225 818 49\n225 829 48\n225 878 20\n225 884 35\n225 924 28\n225 972 39\n225 975 4\n226 2 6\n226 12 34\n226 35 48\n226 36 7\n226 59 46\n226 99 29\n226 110 36\n226 111 1\n226 121 1\n226 141 21\n226 189 37\n226 191 22\n226 214 29\n226 238 39\n226 263 16\n226 286 32\n226 304 13\n226 310 28\n226 324 0\n226 334 44\n226 339 15\n226 378 23\n226 383 50\n226 384 17\n226 411 41\n226 430 11\n226 438 30\n226 488 27\n226 493 2\n226 563 33\n226 587 18\n226 593 23\n226 599 38\n226 612 44\n226 648 37\n226 674 45\n226 675 27\n226 701 49\n226 746 32\n226 755 15\n226 765 28\n226 783 48\n226 791 35\n226 824 8\n226 837 38\n226 893 14\n226 902 23\n226 906 0\n226 934 28\n226 971 35\n227 24 23\n227 41 49\n227 48 0\n227 80 17\n227 96 47\n227 99 11\n227 113 24\n227 120 5\n227 171 44\n227 177 0\n227 180 17\n227 186 16\n227 193 18\n227 195 34\n227 238 0\n227 267 30\n227 301 10\n227 306 45\n227 365 42\n227 369 37\n227 378 19\n227 391 -1\n227 414 24\n227 423 47\n227 433 38\n227 447 40\n227 482 9\n227 494 43\n227 498 13\n227 508 24\n227 524 42\n227 536 46\n227 548 30\n227 564 40\n227 585 25\n227 603 12\n227 621 36\n227 642 28\n227 652 10\n227 664 27\n227 673 37\n227 717 13\n227 720 42\n227 739 41\n227 757 35\n227 766 32\n227 814 26\n227 822 11\n227 857 34\n227 863 14\n227 868 33\n227 879 2\n227 887 27\n227 897 2\n227 971 5\n228 8 47\n228 24 24\n228 29 40\n228 78 2\n228 87 48\n228 91 41\n228 97 33\n228 108 47\n228 124 29\n228 136 18\n228 218 41\n228 245 27\n228 287 34\n228 322 22\n228 327 34\n228 340 45\n228 342 17\n228 345 2\n228 476 30\n228 481 40\n228 566 45\n228 599 43\n228 669 37\n228 696 33\n228 715 -2\n228 720 29\n228 747 7\n228 755 33\n228 800 2\n228 816 13\n228 819 7\n228 852 31\n228 876 16\n228 878 -2\n228 927 9\n228 928 0\n228 945 45\n228 962 3\n228 977 5\n228 982 12\n228 989 9\n229 12 46\n229 23 -1\n229 31 8\n229 33 11\n229 41 34\n229 45 27\n229 55 9\n229 68 33\n229 95 11\n229 104 39\n229 217 10\n229 232 29\n229 236 32\n229 251 17\n229 283 36\n229 294 35\n229 300 15\n229 328 37\n229 333 48\n229 349 13\n229 362 31\n229 382 -2\n229 427 4\n229 431 29\n229 487 18\n229 508 8\n229 540 4\n229 638 14\n229 659 47\n229 696 45\n229 706 26\n229 778 36\n229 781 28\n229 782 18\n229 795 19\n229 873 -2\n229 899 27\n229 927 50\n229 938 38\n229 948 46\n229 950 41\n229 970 41\n229 977 20\n230 13 33\n230 19 46\n230 37 27\n230 41 50\n230 75 12\n230 95 7\n230 96 50\n230 101 35\n230 143 43\n230 154 15\n230 164 25\n230 169 26\n230 174 43\n230 189 37\n230 199 47\n230 201 35\n230 219 19\n230 223 0\n230 236 14\n230 256 2\n230 296 17\n230 306 27\n230 343 -2\n230 345 40\n230 355 32\n230 363 30\n230 380 12\n230 383 17\n230 392 15\n230 401 31\n230 402 -2\n230 407 39\n230 409 8\n230 425 33\n230 427 21\n230 466 23\n230 540 42\n230 546 19\n230 572 23\n230 578 0\n230 658 29\n230 667 9\n230 669 35\n230 675 37\n230 696 49\n230 715 7\n230 720 37\n230 727 4\n230 749 24\n230 790 11\n230 801 36\n230 804 49\n230 805 3\n230 816 10\n230 833 42\n230 878 7\n230 882 2\n230 885 39\n230 914 46\n230 956 38\n230 972 40\n230 992 25\n231 35 47\n231 38 6\n231 54 41\n231 56 13\n231 63 0\n231 70 32\n231 80 5\n231 91 38\n231 106 4\n231 205 39\n231 216 38\n231 290 17\n231 293 10\n231 312 47\n231 343 11\n231 356 -1\n231 391 7\n231 399 14\n231 418 47\n231 453 37\n231 481 37\n231 487 0\n231 495 45\n231 514 18\n231 516 13\n231 580 7\n231 611 35\n231 636 33\n231 656 41\n231 669 40\n231 699 44\n231 716 18\n231 723 26\n231 724 12\n231 767 2\n231 793 42\n231 795 19\n231 804 49\n231 814 -2\n231 816 20\n231 875 50\n231 898 21\n232 10 28\n232 16 22\n232 17 36\n232 26 27\n232 34 40\n232 46 39\n232 60 48\n232 67 48\n232 73 3\n232 78 8\n232 90 20\n232 93 10\n232 108 34\n232 111 9\n232 124 18\n232 136 9\n232 150 24\n232 153 24\n232 165 21\n232 169 32\n232 185 15\n232 201 18\n232 213 26\n232 216 27\n232 247 27\n232 251 34\n232 271 41\n232 292 46\n232 315 29\n232 336 28\n232 341 14\n232 352 32\n232 371 48\n232 379 6\n232 386 36\n232 409 33\n232 448 34\n232 482 22\n232 507 19\n232 518 45\n232 519 46\n232 554 5\n232 598 41\n232 668 17\n232 708 41\n232 731 19\n232 763 50\n232 775 30\n232 788 17\n232 793 20\n232 812 29\n232 819 8\n232 829 15\n232 844 16\n232 875 40\n232 895 20\n232 931 47\n232 996 29\n233 5 29\n233 78 16\n233 182 5\n233 203 22\n233 352 33\n233 375 21\n233 392 32\n233 416 18\n233 446 42\n233 450 14\n233 498 7\n233 512 30\n233 527 37\n233 546 46\n233 567 3\n233 585 50\n233 674 47\n233 702 50\n233 711 33\n233 716 41\n233 761 23\n233 766 17\n233 769 19\n233 772 32\n233 809 49\n233 829 16\n233 884 43\n233 896 32\n233 903 35\n233 919 47\n233 936 45\n233 944 41\n233 949 34\n233 957 44\n233 973 6\n233 976 40\n233 979 31\n233 981 29\n233 986 40\n233 993 32\n234 3 23\n234 32 50\n234 72 19\n234 96 24\n234 140 22\n234 143 47\n234 171 29\n234 197 40\n234 204 46\n234 211 34\n234 216 34\n234 235 24\n234 258 44\n234 287 17\n234 328 33\n234 339 30\n234 361 5\n234 392 25\n234 406 14\n234 408 42\n234 413 42\n234 435 29\n234 443 36\n234 470 28\n234 547 18\n234 576 24\n234 584 43\n234 598 32\n234 610 50\n234 617 4\n234 657 12\n234 671 48\n234 685 7\n234 695 44\n234 705 4\n234 730 33\n234 736 43\n234 748 31\n234 782 2\n234 803 23\n234 827 8\n234 832 22\n234 863 -2\n234 872 36\n234 896 14\n234 901 37\n234 954 12\n234 957 7\n234 997 50\n235 4 2\n235 10 5\n235 12 4\n235 15 12\n235 39 47\n235 44 37\n235 48 22\n235 65 26\n235 79 35\n235 106 6\n235 115 47\n235 124 28\n235 140 22\n235 144 12\n235 154 21\n235 158 40\n235 236 41\n235 243 25\n235 251 17\n235 261 36\n235 277 29\n235 287 14\n235 319 10\n235 339 3\n235 353 16\n235 367 24\n235 372 14\n235 373 22\n235 381 32\n235 384 -1\n235 400 29\n235 426 16\n235 444 1\n235 463 0\n235 514 2\n235 522 22\n235 531 48\n235 558 3\n235 621 44\n235 622 39\n235 626 1\n235 632 10\n235 637 23\n235 639 31\n235 641 18\n235 660 47\n235 732 50\n235 739 0\n235 743 16\n235 751 1\n235 784 24\n235 786 36\n235 790 43\n235 799 43\n235 874 46\n235 905 13\n235 916 47\n235 928 18\n235 933 2\n235 983 40\n236 18 33\n236 37 19\n236 56 15\n236 88 -2\n236 89 19\n236 117 26\n236 138 35\n236 163 35\n236 185 6\n236 215 1\n236 220 50\n236 226 -1\n236 231 2\n236 248 37\n236 251 30\n236 256 19\n236 285 38\n236 290 28\n236 298 8\n236 323 41\n236 358 0\n236 361 12\n236 379 34\n236 393 32\n236 405 24\n236 409 23\n236 412 20\n236 430 -2\n236 438 34\n236 449 43\n236 485 36\n236 489 39\n236 510 4\n236 521 32\n236 522 24\n236 556 8\n236 599 38\n236 621 26\n236 663 43\n236 682 36\n236 688 35\n236 703 -2\n236 712 49\n236 714 18\n236 760 41\n236 845 11\n236 848 6\n236 865 9\n236 895 17\n236 896 5\n236 918 36\n236 945 50\n236 946 35\n237 20 17\n237 23 1\n237 26 5\n237 47 37\n237 136 24\n237 194 27\n237 199 24\n237 215 18\n237 217 0\n237 257 20\n237 291 33\n237 327 22\n237 336 18\n237 361 8\n237 362 40\n237 422 42\n237 424 -1\n237 433 -1\n237 470 39\n237 525 22\n237 536 0\n237 568 34\n237 580 2\n237 649 43\n237 667 31\n237 724 32\n237 725 -1\n237 729 11\n237 732 6\n237 778 30\n237 788 30\n237 804 1\n237 822 42\n237 859 10\n237 866 50\n237 918 10\n237 983 -2\n237 984 -1\n238 4 34\n238 47 34\n238 48 32\n238 136 45\n238 161 29\n238 165 46\n238 191 38\n238 199 47\n238 221 15\n238 280 29\n238 281 10\n238 284 41\n238 321 19\n238 347 44\n238 349 27\n238 372 24\n238 380 14\n238 388 9\n238 423 47\n238 424 21\n238 489 10\n238 494 29\n238 498 37\n238 532 48\n238 537 33\n238 608 10\n238 630 15\n238 637 47\n238 642 17\n238 647 9\n238 658 8\n238 659 11\n238 662 24\n238 664 24\n238 692 12\n238 696 19\n238 737 19\n238 747 5\n238 782 44\n238 849 47\n238 855 16\n238 872 27\n238 877 26\n238 882 35\n238 905 50\n238 909 7\n238 921 48\n238 956 45\n238 983 35\n239 35 23\n239 38 18\n239 55 29\n239 72 11\n239 86 11\n239 113 2\n239 119 44\n239 138 12\n239 158 18\n239 161 46\n239 166 50\n239 187 44\n239 194 38\n239 209 23\n239 215 20\n239 230 25\n239 242 23\n239 297 45\n239 327 11\n239 350 42\n239 364 16\n239 366 7\n239 400 24\n239 415 37\n239 421 46\n239 433 18\n239 449 37\n239 455 34\n239 476 26\n239 518 40\n239 598 47\n239 644 32\n239 657 14\n239 660 -2\n239 665 41\n239 669 24\n239 678 40\n239 717 1\n239 723 17\n239 731 17\n239 735 17\n239 824 18\n239 873 34\n239 874 28\n239 875 33\n239 890 18\n239 898 20\n239 906 13\n239 910 4\n239 920 43\n239 972 12\n239 987 49\n240 15 36\n240 68 28\n240 90 32\n240 94 48\n240 96 40\n240 119 22\n240 134 8\n240 144 14\n240 147 33\n240 168 40\n240 177 33\n240 188 37\n240 231 49\n240 280 45\n240 294 35\n240 318 31\n240 379 33\n240 413 10\n240 419 3\n240 429 8\n240 472 37\n240 474 46\n240 622 4\n240 632 -2\n240 645 45\n240 653 31\n240 668 44\n240 683 15\n240 688 39\n240 699 47\n240 705 25\n240 716 17\n240 732 10\n240 736 34\n240 741 18\n240 769 2\n240 774 27\n240 790 37\n240 800 21\n240 805 16\n240 822 9\n240 827 8\n240 855 -1\n240 877 37\n240 899 7\n240 930 15\n240 952 10\n240 970 40\n241 46 28\n241 47 19\n241 56 35\n241 83 -1\n241 129 32\n241 131 27\n241 136 7\n241 169 11\n241 179 36\n241 206 37\n241 218 47\n241 226 34\n241 248 20\n241 300 8\n241 309 32\n241 317 18\n241 327 46\n241 367 16\n241 389 21\n241 421 12\n241 429 30\n241 442 40\n241 449 47\n241 484 39\n241 524 19\n241 562 25\n241 607 37\n241 613 49\n241 624 16\n241 639 29\n241 648 13\n241 659 45\n241 684 22\n241 691 37\n241 693 45\n241 695 50\n241 712 40\n241 724 15\n241 754 0\n241 778 38\n241 782 17\n241 784 6\n241 794 22\n241 795 14\n241 816 12\n241 853 31\n241 860 36\n241 867 11\n241 900 19\n241 913 23\n241 924 48\n242 18 29\n242 22 15\n242 31 1\n242 38 47\n242 41 8\n242 56 49\n242 68 17\n242 71 7\n242 122 16\n242 136 2\n242 139 12\n242 162 38\n242 203 9\n242 238 18\n242 243 42\n242 247 4\n242 249 35\n242 276 0\n242 285 2\n242 323 3\n242 342 13\n242 354 9\n242 377 46\n242 385 4\n242 396 33\n242 423 32\n242 447 19\n242 455 17\n242 484 21\n242 511 18\n242 517 28\n242 573 11\n242 663 9\n242 694 7\n242 699 6\n242 712 25\n242 735 47\n242 743 13\n242 761 43\n242 791 13\n242 817 49\n242 833 29\n242 873 33\n242 913 40\n242 925 30\n242 926 38\n242 929 25\n242 935 27\n243 6 26\n243 19 12\n243 73 27\n243 75 23\n243 101 45\n243 116 22\n243 212 36\n243 230 20\n243 244 9\n243 251 33\n243 366 44\n243 410 46\n243 419 15\n243 475 46\n243 511 10\n243 513 27\n243 571 41\n243 622 9\n243 640 25\n243 667 17\n243 670 34\n243 672 43\n243 685 22\n243 729 33\n243 778 34\n243 790 27\n243 794 31\n243 842 20\n243 857 13\n243 864 28\n243 886 46\n243 934 16\n243 944 28\n243 994 48\n244 2 37\n244 23 32\n244 96 37\n244 101 50\n244 103 38\n244 116 20\n244 123 27\n244 133 48\n244 138 48\n244 154 8\n244 173 27\n244 177 1\n244 207 47\n244 219 38\n244 224 36\n244 266 50\n244 318 29\n244 393 38\n244 421 34\n244 422 3\n244 471 46\n244 486 10\n244 494 37\n244 500 24\n244 505 0\n244 517 32\n244 526 23\n244 554 22\n244 566 47\n244 576 32\n244 591 30\n244 600 26\n244 602 48\n244 603 12\n244 624 28\n244 640 7\n244 646 8\n244 647 3\n244 722 18\n244 725 43\n244 735 4\n244 748 14\n244 752 34\n244 794 28\n244 799 30\n244 814 17\n244 815 3\n244 897 9\n244 984 50\n244 987 35\n244 992 31\n244 998 19\n245 16 44\n245 27 50\n245 29 39\n245 36 -1\n245 51 30\n245 69 47\n245 72 43\n245 73 1\n245 100 8\n245 104 48\n245 126 42\n245 142 24\n245 184 12\n245 200 48\n245 211 40\n245 216 35\n245 225 22\n245 251 18\n245 252 50\n245 256 37\n245 273 17\n245 315 37\n245 330 20\n245 367 21\n245 381 4\n245 402 5\n245 438 8\n245 446 13\n245 476 9\n245 519 2\n245 535 47\n245 565 -2\n245 577 18\n245 581 1\n245 585 33\n245 632 5\n245 639 38\n245 640 45\n245 690 48\n245 691 7\n245 710 24\n245 713 29\n245 726 48\n245 728 39\n245 740 10\n245 811 40\n245 846 35\n245 852 23\n245 870 39\n245 873 44\n245 877 19\n245 880 46\n245 930 36\n245 937 14\n245 948 48\n245 961 40\n246 4 49\n246 56 46\n246 89 -2\n246 145 8\n246 173 34\n246 191 0\n246 212 27\n246 259 11\n246 274 28\n246 290 4\n246 291 43\n246 292 5\n246 299 15\n246 321 29\n246 330 -2\n246 338 21\n246 348 28\n246 351 48\n246 362 27\n246 410 11\n246 414 44\n246 425 38\n246 463 50\n246 471 33\n246 485 29\n246 512 21\n246 549 36\n246 551 33\n246 575 45\n246 579 10\n246 601 39\n246 633 10\n246 647 6\n246 648 16\n246 657 24\n246 665 47\n246 678 27\n246 679 34\n246 682 42\n246 699 35\n246 729 4\n246 740 37\n246 753 27\n246 773 34\n246 802 45\n246 877 6\n246 908 47\n246 914 44\n246 967 31\n246 976 3\n246 985 20\n246 998 33\n247 34 29\n247 36 -2\n247 98 37\n247 104 -2\n247 105 12\n247 107 18\n247 110 28\n247 115 50\n247 187 43\n247 188 45\n247 202 27\n247 238 5\n247 250 4\n247 261 32\n247 311 26\n247 343 14\n247 368 9\n247 374 35\n247 419 40\n247 422 50\n247 446 10\n247 509 9\n247 516 41\n247 517 18\n247 530 33\n247 541 10\n247 548 27\n247 551 7\n247 563 39\n247 576 17\n247 607 50\n247 612 11\n247 671 13\n247 673 30\n247 700 4\n247 704 44\n247 730 49\n247 737 14\n247 778 27\n247 793 46\n247 802 39\n247 810 36\n247 822 8\n247 852 34\n247 867 39\n247 891 3\n247 899 40\n247 906 -1\n247 929 37\n247 939 14\n247 940 37\n247 953 3\n247 964 29\n247 970 10\n247 988 43\n248 4 1\n248 74 41\n248 99 39\n248 103 15\n248 165 15\n248 175 36\n248 191 24\n248 241 6\n248 258 42\n248 263 39\n248 266 35\n248 281 4\n248 298 31\n248 319 39\n248 329 2\n248 346 14\n248 350 2\n248 454 47\n248 456 19\n248 481 37\n248 485 7\n248 526 19\n248 567 44\n248 579 -1\n248 587 2\n248 590 25\n248 594 2\n248 599 31\n248 604 38\n248 636 18\n248 655 46\n248 656 29\n248 662 16\n248 663 29\n248 681 48\n248 688 11\n248 716 40\n248 735 27\n248 750 48\n248 814 28\n248 849 9\n248 864 4\n248 868 21\n248 884 10\n248 911 5\n248 914 40\n248 933 -2\n248 951 33\n248 955 -1\n248 982 39\n249 25 13\n249 86 37\n249 88 8\n249 118 36\n249 149 29\n249 186 34\n249 266 49\n249 280 19\n249 290 41\n249 309 38\n249 318 50\n249 421 13\n249 427 17\n249 477 21\n249 484 31\n249 549 18\n249 582 11\n249 606 39\n249 621 45\n249 651 35\n249 682 17\n249 686 11\n249 701 49\n249 724 35\n249 750 48\n249 769 24\n249 776 5\n249 778 4\n249 786 42\n249 820 7\n249 880 14\n249 885 42\n249 886 35\n249 914 28\n249 917 22\n249 928 49\n249 939 12\n249 955 1\n249 973 12\n249 987 10\n250 55 28\n250 58 -2\n250 91 40\n250 93 16\n250 98 37\n250 147 36\n250 206 42\n250 306 46\n250 310 8\n250 330 26\n250 356 18\n250 429 50\n250 454 50\n250 461 17\n250 466 1\n250 468 1\n250 486 27\n250 498 4\n250 505 24\n250 543 13\n250 562 49\n250 576 3\n250 593 19\n250 594 15\n250 604 37\n250 620 6\n250 634 41\n250 637 40\n250 672 43\n250 675 7\n250 682 24\n250 723 -2\n250 757 41\n250 782 -1\n250 808 30\n250 811 5\n250 819 21\n250 824 18\n250 863 21\n250 882 25\n250 901 6\n250 926 -1\n250 938 -1\n250 942 21\n250 967 49\n250 969 6\n251 6 34\n251 51 29\n251 66 46\n251 75 24\n251 141 36\n251 153 36\n251 201 43\n251 223 33\n251 234 37\n251 304 48\n251 317 23\n251 340 30\n251 341 30\n251 342 33\n251 345 13\n251 390 23\n251 409 5\n251 490 39\n251 506 45\n251 516 14\n251 518 7\n251 534 49\n251 568 24\n251 601 32\n251 635 23\n251 655 18\n251 693 23\n251 705 49\n251 724 26\n251 740 24\n251 747 25\n251 763 35\n251 773 14\n251 837 48\n251 846 40\n251 854 11\n251 865 -2\n251 894 44\n251 917 26\n251 933 22\n251 937 4\n251 941 50\n252 13 19\n252 28 41\n252 33 27\n252 70 32\n252 91 28\n252 94 39\n252 133 32\n252 172 13\n252 184 10\n252 191 9\n252 210 6\n252 234 21\n252 261 47\n252 263 3\n252 264 11\n252 265 25\n252 278 44\n252 310 20\n252 320 9\n252 333 12\n252 338 13\n252 364 10\n252 371 41\n252 406 41\n252 414 32\n252 480 50\n252 487 35\n252 508 49\n252 509 24\n252 516 34\n252 547 45\n252 564 4\n252 578 30\n252 579 36\n252 630 13\n252 642 14\n252 654 45\n252 660 -2\n252 674 37\n252 690 14\n252 691 39\n252 694 12\n252 699 45\n252 705 37\n252 711 26\n252 717 23\n252 737 31\n252 755 16\n252 778 7\n252 788 1\n252 798 49\n252 805 12\n252 809 9\n252 816 50\n252 837 16\n252 849 49\n252 862 35\n252 875 30\n252 905 19\n252 907 10\n252 920 49\n252 921 50\n252 949 10\n252 998 48\n253 13 6\n253 18 9\n253 19 48\n253 24 37\n253 32 47\n253 35 48\n253 50 17\n253 58 44\n253 133 8\n253 135 47\n253 151 40\n253 159 18\n253 169 35\n253 179 17\n253 203 3\n253 217 46\n253 237 37\n253 238 41\n253 254 18\n253 263 8\n253 269 18\n253 271 34\n253 274 25\n253 282 5\n253 296 20\n253 326 30\n253 330 16\n253 366 18\n253 453 33\n253 468 9\n253 500 7\n253 501 36\n253 511 43\n253 543 0\n253 561 46\n253 562 25\n253 603 35\n253 609 25\n253 613 24\n253 616 15\n253 619 8\n253 671 35\n253 698 13\n253 751 17\n253 793 42\n253 797 47\n253 800 18\n253 805 50\n253 818 44\n253 834 20\n253 911 12\n253 957 23\n253 964 13\n253 966 18\n253 969 6\n254 24 49\n254 42 40\n254 71 15\n254 80 34\n254 86 24\n254 130 15\n254 156 41\n254 162 33\n254 191 11\n254 194 14\n254 196 20\n254 229 7\n254 263 26\n254 267 41\n254 281 34\n254 298 28\n254 348 3\n254 380 44\n254 386 26\n254 404 34\n254 446 15\n254 447 20\n254 492 22\n254 515 39\n254 541 12\n254 548 41\n254 556 23\n254 570 26\n254 594 37\n254 649 39\n254 672 5\n254 675 29\n254 700 25\n254 724 35\n254 743 4\n254 781 46\n254 800 27\n254 808 24\n254 813 7\n254 821 33\n254 835 28\n254 917 33\n254 923 27\n254 959 33\n254 969 12\n254 976 30\n254 990 26\n255 9 7\n255 37 22\n255 42 17\n255 105 15\n255 109 30\n255 190 8\n255 195 17\n255 232 14\n255 233 34\n255 258 11\n255 284 25\n255 364 42\n255 371 21\n255 373 23\n255 392 14\n255 400 42\n255 401 4\n255 410 16\n255 434 50\n255 452 31\n255 476 46\n255 481 35\n255 531 36\n255 542 17\n255 545 37\n255 554 3\n255 574 50\n255 589 7\n255 628 4\n255 665 40\n255 691 22\n255 695 43\n255 700 19\n255 711 37\n255 733 23\n255 771 24\n255 784 21\n255 856 11\n255 890 26\n255 916 36\n255 930 27\n255 945 25\n255 983 45\n256 55 26\n256 83 50\n256 125 32\n256 136 36\n256 146 47\n256 150 45\n256 185 33\n256 187 11\n256 188 16\n256 198 21\n256 203 44\n256 217 11\n256 320 25\n256 343 19\n256 345 21\n256 360 42\n256 375 26\n256 419 45\n256 427 -1\n256 441 19\n256 455 32\n256 499 24\n256 518 33\n256 532 45\n256 558 48\n256 600 36\n256 602 29\n256 608 26\n256 639 44\n256 645 11\n256 711 22\n256 712 -2\n256 718 46\n256 735 25\n256 736 45\n256 756 20\n256 792 35\n256 848 14\n256 885 18\n256 911 34\n256 919 29\n256 964 10\n256 967 39\n257 53 4\n257 58 38\n257 63 47\n257 77 -1\n257 103 16\n257 105 3\n257 134 18\n257 135 1\n257 142 1\n257 161 27\n257 166 3\n257 169 25\n257 188 11\n257 211 3\n257 250 7\n257 253 31\n257 256 15\n257 314 25\n257 317 11\n257 359 18\n257 370 31\n257 371 22\n257 376 34\n257 408 26\n257 483 43\n257 506 32\n257 509 15\n257 518 12\n257 555 42\n257 579 29\n257 582 49\n257 621 24\n257 628 23\n257 650 17\n257 653 44\n257 707 18\n257 713 50\n257 716 40\n257 814 28\n257 855 50\n257 883 49\n257 891 47\n257 896 36\n257 911 39\n257 930 40\n257 942 14\n257 943 34\n257 948 40\n257 994 20\n258 9 9\n258 20 28\n258 27 20\n258 59 29\n258 72 15\n258 78 16\n258 99 28\n258 103 31\n258 177 12\n258 182 18\n258 197 -1\n258 230 34\n258 250 15\n258 463 14\n258 467 16\n258 472 28\n258 490 6\n258 505 42\n258 517 1\n258 540 42\n258 569 7\n258 620 27\n258 625 44\n258 636 32\n258 685 43\n258 715 9\n258 757 5\n258 761 19\n258 763 41\n258 787 10\n258 813 24\n258 846 0\n258 862 8\n258 863 46\n258 889 -1\n258 891 3\n258 902 14\n258 916 7\n258 930 46\n258 931 33\n258 962 5\n258 978 21\n259 49 36\n259 97 44\n259 119 47\n259 123 32\n259 160 26\n259 165 -2\n259 196 33\n259 236 5\n259 258 35\n259 272 14\n259 278 33\n259 303 47\n259 311 11\n259 378 26\n259 408 3\n259 472 10\n259 488 23\n259 511 26\n259 539 37\n259 541 15\n259 562 4\n259 564 14\n259 592 10\n259 598 31\n259 607 26\n259 615 5\n259 617 3\n259 620 7\n259 628 23\n259 678 45\n259 682 1\n259 738 26\n259 756 49\n259 771 6\n259 772 46\n259 800 24\n259 833 28\n259 840 36\n259 843 13\n259 846 42\n259 860 33\n259 880 50\n259 892 6\n259 909 -2\n259 919 33\n259 924 41\n259 925 31\n259 932 23\n259 953 13\n259 963 -2\n259 995 37\n259 996 19\n260 17 19\n260 64 29\n260 66 48\n260 115 7\n260 116 22\n260 136 45\n260 145 22\n260 162 33\n260 184 49\n260 210 26\n260 249 31\n260 272 40\n260 282 42\n260 307 11\n260 328 -2\n260 333 47\n260 357 21\n260 368 24\n260 402 26\n260 408 7\n260 457 31\n260 473 18\n260 474 19\n260 493 47\n260 497 48\n260 502 27\n260 504 49\n260 538 37\n260 568 50\n260 582 45\n260 604 23\n260 612 24\n260 629 42\n260 635 10\n260 653 32\n260 679 39\n260 706 13\n260 740 9\n260 744 0\n260 751 1\n260 775 17\n260 787 6\n260 892 25\n260 964 38\n260 986 38\n261 4 -2\n261 8 45\n261 24 31\n261 26 23\n261 59 44\n261 64 31\n261 76 48\n261 78 4\n261 85 33\n261 115 33\n261 135 34\n261 140 1\n261 143 47\n261 151 38\n261 166 39\n261 192 32\n261 203 45\n261 204 48\n261 244 11\n261 251 19\n261 265 44\n261 267 9\n261 298 3\n261 314 2\n261 319 42\n261 353 35\n261 357 19\n261 404 5\n261 412 33\n261 423 42\n261 443 26\n261 455 11\n261 466 42\n261 472 -1\n261 475 8\n261 510 1\n261 538 50\n261 590 2\n261 691 44\n261 715 20\n261 729 12\n261 732 12\n261 770 30\n261 789 14\n261 833 40\n261 835 25\n261 841 31\n261 843 25\n261 861 12\n261 864 21\n261 877 45\n261 922 -1\n261 955 6\n261 971 2\n261 973 32\n262 58 32\n262 61 29\n262 92 0\n262 116 6\n262 123 45\n262 142 39\n262 171 11\n262 177 39\n262 189 41\n262 190 27\n262 209 43\n262 251 34\n262 282 44\n262 348 44\n262 355 18\n262 385 49\n262 401 40\n262 463 46\n262 476 23\n262 500 13\n262 511 33\n262 524 3\n262 526 33\n262 558 -2\n262 571 38\n262 597 39\n262 615 42\n262 616 9\n262 619 30\n262 654 5\n262 660 8\n262 683 11\n262 684 19\n262 706 50\n262 750 43\n262 791 27\n262 808 3\n262 813 16\n262 825 46\n262 832 37\n262 840 37\n262 854 25\n262 857 15\n262 887 8\n262 891 40\n262 904 41\n262 940 46\n262 947 11\n262 978 22\n263 23 36\n263 94 35\n263 95 24\n263 102 33\n263 116 16\n263 153 42\n263 167 42\n263 175 25\n263 198 30\n263 212 12\n263 216 20\n263 257 29\n263 283 13\n263 326 28\n263 328 40\n263 333 15\n263 364 47\n263 413 19\n263 416 12\n263 448 26\n263 463 49\n263 497 40\n263 522 10\n263 535 48\n263 549 15\n263 607 12\n263 610 25\n263 623 13\n263 657 21\n263 674 34\n263 676 33\n263 678 19\n263 686 23\n263 714 46\n263 718 37\n263 743 14\n263 751 50\n263 793 33\n263 825 13\n263 867 18\n263 877 48\n263 892 1\n263 895 46\n263 916 41\n263 958 17\n263 961 49\n264 23 38\n264 67 -2\n264 102 46\n264 112 14\n264 126 28\n264 130 43\n264 140 14\n264 158 0\n264 189 14\n264 228 35\n264 245 41\n264 283 6\n264 287 -1\n264 326 29\n264 340 4\n264 358 48\n264 385 48\n264 395 3\n264 407 48\n264 408 30\n264 447 31\n264 492 50\n264 501 1\n264 527 41\n264 548 14\n264 560 41\n264 572 30\n264 603 45\n264 609 50\n264 615 3\n264 617 25\n264 623 36\n264 629 31\n264 634 31\n264 636 3\n264 637 12\n264 656 29\n264 658 43\n264 664 34\n264 675 11\n264 714 49\n264 744 41\n264 751 0\n264 798 40\n264 809 17\n264 811 14\n264 826 37\n264 877 11\n264 916 29\n264 982 42\n264 992 13\n265 35 38\n265 43 19\n265 97 18\n265 118 50\n265 128 33\n265 196 40\n265 226 39\n265 235 15\n265 278 39\n265 279 49\n265 339 11\n265 367 33\n265 374 17\n265 423 16\n265 480 0\n265 548 0\n265 563 6\n265 608 41\n265 662 18\n265 796 8\n265 847 33\n265 848 37\n265 856 13\n265 879 42\n265 890 16\n265 931 48\n265 945 8\n265 979 42\n265 993 11\n266 2 48\n266 14 25\n266 22 29\n266 26 19\n266 28 23\n266 30 19\n266 47 12\n266 82 22\n266 92 13\n266 110 1\n266 125 43\n266 155 18\n266 168 50\n266 207 11\n266 252 20\n266 259 49\n266 293 26\n266 381 33\n266 488 37\n266 521 46\n266 525 43\n266 527 16\n266 636 20\n266 696 44\n266 704 35\n266 710 23\n266 712 32\n266 729 15\n266 826 31\n266 858 31\n266 864 12\n266 873 40\n266 884 -1\n266 890 14\n266 901 13\n266 910 22\n266 954 22\n266 975 28\n266 993 13\n267 9 24\n267 12 24\n267 33 42\n267 64 15\n267 78 19\n267 90 14\n267 91 49\n267 106 35\n267 120 48\n267 134 50\n267 135 24\n267 137 32\n267 159 9\n267 167 4\n267 177 48\n267 201 41\n267 242 17\n267 299 38\n267 347 5\n267 386 16\n267 406 20\n267 409 35\n267 433 -2\n267 460 20\n267 483 24\n267 487 38\n267 489 16\n267 530 1\n267 555 15\n267 565 47\n267 574 49\n267 586 49\n267 605 48\n267 618 9\n267 639 41\n267 649 41\n267 659 50\n267 667 27\n267 672 4\n267 673 0\n267 678 45\n267 692 5\n267 721 15\n267 816 5\n267 817 12\n267 840 28\n267 897 45\n267 931 1\n267 936 9\n267 948 34\n268 13 20\n268 37 -2\n268 46 37\n268 57 38\n268 60 28\n268 64 5\n268 129 2\n268 145 17\n268 152 38\n268 157 38\n268 191 45\n268 210 29\n268 212 30\n268 248 36\n268 249 19\n268 261 16\n268 264 21\n268 291 11\n268 331 11\n268 333 19\n268 382 -2\n268 383 38\n268 398 48\n268 467 27\n268 495 32\n268 504 15\n268 517 33\n268 559 28\n268 575 15\n268 605 3\n268 642 44\n268 722 31\n268 762 0\n268 763 38\n268 771 27\n268 782 20\n268 790 24\n268 814 16\n268 827 36\n268 855 0\n268 864 28\n268 867 16\n268 908 2\n268 925 34\n268 929 38\n268 989 25\n269 26 -2\n269 32 3\n269 40 12\n269 60 29\n269 92 1\n269 176 6\n269 196 28\n269 248 50\n269 277 36\n269 280 27\n269 309 46\n269 314 32\n269 338 17\n269 343 42\n269 345 17\n269 356 5\n269 357 17\n269 371 17\n269 381 28\n269 391 27\n269 394 14\n269 405 23\n269 450 23\n269 462 40\n269 463 3\n269 479 18\n269 492 33\n269 508 15\n269 514 31\n269 547 37\n269 590 41\n269 645 37\n269 653 18\n269 657 19\n269 673 14\n269 680 46\n269 683 37\n269 686 1\n269 714 45\n269 723 37\n269 725 23\n269 726 0\n269 873 44\n269 876 13\n269 898 11\n269 978 15\n270 24 0\n270 26 24\n270 67 28\n270 99 14\n270 109 6\n270 127 38\n270 146 6\n270 229 9\n270 241 40\n270 255 6\n270 259 23\n270 265 42\n270 297 8\n270 318 40\n270 328 -1\n270 330 0\n270 347 17\n270 353 37\n270 399 -1\n270 407 21\n270 427 23\n270 441 -1\n270 459 3\n270 486 27\n270 497 7\n270 507 16\n270 522 11\n270 568 7\n270 578 44\n270 597 8\n270 629 36\n270 644 31\n270 659 32\n270 700 42\n270 747 43\n270 748 -1\n270 770 44\n270 809 2\n270 810 23\n270 818 39\n270 839 17\n270 871 48\n270 931 16\n270 952 15\n270 955 4\n270 966 12\n270 979 49\n271 5 29\n271 18 14\n271 20 2\n271 26 38\n271 70 14\n271 72 -2\n271 78 40\n271 132 -2\n271 163 5\n271 165 19\n271 174 42\n271 201 28\n271 229 49\n271 247 5\n271 274 34\n271 278 0\n271 281 49\n271 305 26\n271 336 7\n271 419 24\n271 432 11\n271 439 19\n271 445 40\n271 451 41\n271 462 32\n271 479 21\n271 481 -2\n271 539 38\n271 558 9\n271 565 13\n271 601 43\n271 639 50\n271 647 38\n271 659 45\n271 681 36\n271 691 8\n271 742 23\n271 772 3\n271 795 43\n271 826 14\n271 846 29\n271 865 12\n271 927 50\n271 934 24\n271 943 41\n271 963 15\n271 966 23\n271 977 47\n271 981 31\n271 989 32\n271 999 44\n272 17 3\n272 31 0\n272 40 22\n272 63 20\n272 65 -1\n272 76 41\n272 91 15\n272 94 42\n272 102 15\n272 104 19\n272 110 32\n272 121 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34\n273 596 31\n273 608 20\n273 686 36\n273 701 47\n273 723 19\n273 797 15\n273 830 9\n273 866 42\n273 869 33\n273 891 8\n273 904 48\n273 913 18\n273 922 19\n273 923 31\n273 941 25\n273 993 6\n273 996 1\n274 18 17\n274 19 2\n274 134 12\n274 141 34\n274 147 9\n274 153 46\n274 155 6\n274 173 31\n274 179 16\n274 239 9\n274 268 4\n274 275 43\n274 337 32\n274 339 50\n274 352 3\n274 369 46\n274 391 11\n274 399 41\n274 424 16\n274 473 35\n274 515 43\n274 516 42\n274 530 36\n274 540 28\n274 543 9\n274 558 16\n274 575 34\n274 596 8\n274 597 8\n274 616 33\n274 627 44\n274 631 0\n274 644 4\n274 654 47\n274 661 50\n274 662 37\n274 663 -1\n274 684 30\n274 690 21\n274 698 46\n274 711 9\n274 745 30\n274 845 25\n274 863 13\n274 879 8\n274 899 5\n274 900 10\n274 928 19\n274 942 38\n275 22 18\n275 33 17\n275 38 32\n275 65 31\n275 67 12\n275 91 38\n275 120 13\n275 128 43\n275 156 48\n275 192 44\n275 246 11\n275 302 11\n275 307 46\n275 359 26\n275 379 3\n275 384 42\n275 408 49\n275 423 40\n275 445 13\n275 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68 2\n277 79 4\n277 116 35\n277 173 40\n277 183 10\n277 185 10\n277 235 36\n277 236 32\n277 238 14\n277 259 49\n277 282 21\n277 288 46\n277 289 4\n277 294 27\n277 307 9\n277 308 45\n277 320 10\n277 382 17\n277 432 23\n277 451 47\n277 456 25\n277 474 14\n277 482 15\n277 485 17\n277 493 35\n277 496 31\n277 516 46\n277 535 8\n277 539 46\n277 555 31\n277 558 5\n277 559 36\n277 561 14\n277 594 44\n277 601 0\n277 638 34\n277 645 7\n277 649 30\n277 676 19\n277 680 16\n277 687 24\n277 699 30\n277 703 46\n277 705 -2\n277 708 50\n277 718 18\n277 729 23\n277 736 24\n277 745 17\n277 764 47\n277 781 14\n277 782 46\n277 814 25\n277 839 22\n277 843 13\n277 883 18\n277 938 12\n277 958 34\n277 981 49\n277 989 7\n278 33 31\n278 56 41\n278 78 17\n278 137 32\n278 142 -2\n278 183 31\n278 213 -1\n278 227 41\n278 247 27\n278 251 4\n278 293 23\n278 306 34\n278 334 20\n278 359 25\n278 383 16\n278 390 44\n278 436 17\n278 450 8\n278 454 46\n278 494 21\n278 496 39\n278 517 34\n278 526 8\n278 532 29\n278 541 43\n278 566 46\n278 569 22\n278 615 50\n278 617 49\n278 627 26\n278 631 12\n278 635 20\n278 654 24\n278 695 45\n278 737 10\n278 758 -2\n278 796 6\n278 800 7\n278 877 49\n278 925 27\n278 942 40\n278 946 15\n278 953 -2\n279 2 23\n279 29 21\n279 32 48\n279 70 -1\n279 78 28\n279 125 20\n279 126 45\n279 133 0\n279 148 37\n279 193 17\n279 196 22\n279 256 7\n279 266 29\n279 280 32\n279 284 33\n279 289 45\n279 334 9\n279 344 11\n279 359 22\n279 422 32\n279 428 9\n279 503 25\n279 517 40\n279 534 40\n279 535 21\n279 544 24\n279 560 7\n279 587 23\n279 601 19\n279 644 16\n279 684 37\n279 694 32\n279 715 14\n279 724 11\n279 744 7\n279 746 11\n279 814 31\n279 818 46\n279 820 23\n279 877 43\n279 892 1\n279 898 30\n279 937 14\n279 991 6\n280 32 34\n280 48 40\n280 142 40\n280 201 -1\n280 240 36\n280 288 37\n280 298 33\n280 303 21\n280 311 13\n280 316 30\n280 327 50\n280 345 1\n280 373 40\n280 426 8\n280 451 42\n280 455 48\n280 492 8\n280 520 14\n280 543 25\n280 579 5\n280 584 10\n280 585 33\n280 664 18\n280 675 25\n280 696 9\n280 726 1\n280 751 16\n280 760 11\n280 794 -2\n280 798 9\n280 799 -2\n280 822 31\n280 836 19\n280 840 27\n280 888 14\n280 896 32\n280 913 10\n280 964 49\n280 996 2\n281 15 9\n281 16 27\n281 33 8\n281 87 11\n281 102 46\n281 136 38\n281 151 43\n281 161 21\n281 209 50\n281 223 -1\n281 241 39\n281 262 44\n281 285 43\n281 307 35\n281 313 40\n281 349 7\n281 401 2\n281 426 42\n281 436 48\n281 461 24\n281 488 37\n281 498 34\n281 504 22\n281 535 36\n281 543 12\n281 548 12\n281 566 17\n281 587 33\n281 591 12\n281 594 39\n281 609 42\n281 648 39\n281 697 44\n281 712 45\n281 745 31\n281 756 9\n281 773 18\n281 782 20\n281 785 27\n281 802 20\n281 817 40\n281 835 38\n281 839 23\n281 880 36\n281 884 -2\n281 910 -1\n281 924 44\n281 948 41\n281 963 46\n282 2 38\n282 19 34\n282 41 47\n282 107 43\n282 146 29\n282 151 33\n282 182 46\n282 201 5\n282 208 24\n282 237 46\n282 274 39\n282 347 34\n282 353 46\n282 401 35\n282 432 8\n282 437 50\n282 458 41\n282 474 32\n282 505 43\n282 515 14\n282 524 23\n282 552 44\n282 572 23\n282 604 15\n282 615 9\n282 625 12\n282 626 35\n282 649 31\n282 659 9\n282 663 48\n282 678 35\n282 690 26\n282 703 39\n282 720 25\n282 724 24\n282 805 32\n282 843 14\n282 864 13\n282 872 37\n282 906 8\n282 916 38\n282 974 25\n283 16 24\n283 25 49\n283 40 32\n283 91 40\n283 99 11\n283 115 46\n283 133 49\n283 134 34\n283 155 32\n283 164 50\n283 179 36\n283 221 -1\n283 256 42\n283 265 44\n283 272 20\n283 287 48\n283 289 2\n283 297 23\n283 316 19\n283 317 8\n283 318 9\n283 348 35\n283 356 2\n283 376 17\n283 379 45\n283 435 33\n283 444 43\n283 481 17\n283 496 46\n283 511 3\n283 535 24\n283 584 10\n283 601 7\n283 634 28\n283 649 10\n283 668 35\n283 692 36\n283 704 49\n283 705 13\n283 711 22\n283 722 38\n283 728 20\n283 742 50\n283 765 27\n283 767 15\n283 832 22\n283 848 39\n283 849 50\n283 850 49\n283 856 6\n283 866 9\n283 871 30\n283 927 32\n283 957 9\n284 16 -1\n284 23 17\n284 53 -2\n284 84 24\n284 87 32\n284 97 35\n284 110 32\n284 133 11\n284 150 41\n284 157 32\n284 192 37\n284 220 40\n284 261 21\n284 277 13\n284 294 30\n284 307 40\n284 314 11\n284 363 43\n284 368 27\n284 377 31\n284 403 5\n284 452 26\n284 470 12\n284 522 38\n284 525 5\n284 531 46\n284 549 34\n284 584 11\n284 620 49\n284 621 26\n284 659 12\n284 664 23\n284 665 27\n284 688 30\n284 709 50\n284 713 20\n284 734 37\n284 741 17\n284 760 39\n284 769 12\n284 777 31\n284 792 7\n284 826 26\n284 832 46\n284 877 30\n284 914 40\n284 921 26\n284 938 35\n284 959 35\n284 981 34\n284 998 38\n285 31 19\n285 38 19\n285 39 18\n285 55 14\n285 65 25\n285 76 22\n285 86 33\n285 87 26\n285 90 25\n285 100 26\n285 101 15\n285 110 49\n285 114 45\n285 131 43\n285 181 26\n285 209 37\n285 211 23\n285 221 41\n285 299 -1\n285 301 39\n285 302 17\n285 333 28\n285 350 23\n285 362 27\n285 379 17\n285 401 13\n285 416 50\n285 423 38\n285 440 13\n285 445 8\n285 452 40\n285 461 30\n285 507 22\n285 519 37\n285 550 40\n285 552 15\n285 581 14\n285 583 25\n285 610 7\n285 625 1\n285 671 44\n285 691 34\n285 700 19\n285 723 16\n285 733 19\n285 745 0\n285 749 50\n285 761 33\n285 778 23\n285 797 47\n285 902 37\n285 911 44\n285 919 11\n285 943 32\n285 968 21\n286 6 49\n286 57 2\n286 65 4\n286 100 8\n286 122 11\n286 127 7\n286 128 33\n286 167 20\n286 168 48\n286 201 1\n286 204 22\n286 212 27\n286 216 6\n286 225 7\n286 267 24\n286 283 12\n286 289 39\n286 354 3\n286 365 41\n286 482 8\n286 484 14\n286 511 48\n286 513 50\n286 519 40\n286 548 49\n286 586 27\n286 594 20\n286 615 41\n286 650 8\n286 660 22\n286 677 48\n286 718 39\n286 754 45\n286 781 11\n286 793 50\n286 838 13\n286 898 29\n286 907 34\n286 928 -1\n286 931 26\n286 941 17\n286 973 1\n286 976 10\n286 987 34\n286 996 1\n287 1 11\n287 23 28\n287 47 26\n287 82 9\n287 111 -1\n287 142 9\n287 154 27\n287 187 43\n287 189 33\n287 190 16\n287 213 5\n287 228 37\n287 229 37\n287 230 35\n287 264 16\n287 268 42\n287 306 13\n287 309 16\n287 322 34\n287 338 30\n287 342 0\n287 351 5\n287 370 26\n287 373 25\n287 375 8\n287 391 47\n287 393 7\n287 399 30\n287 403 7\n287 424 6\n287 444 19\n287 478 2\n287 489 13\n287 523 36\n287 552 50\n287 561 14\n287 595 38\n287 732 32\n287 736 20\n287 746 25\n287 755 43\n287 785 33\n287 812 15\n287 823 15\n287 832 12\n287 843 32\n287 847 41\n287 848 46\n287 850 2\n287 851 15\n287 865 20\n287 892 16\n287 893 40\n287 899 42\n287 926 0\n287 990 43\n288 13 9\n288 19 3\n288 82 0\n288 91 11\n288 102 3\n288 140 12\n288 143 50\n288 154 37\n288 169 11\n288 186 6\n288 193 4\n288 200 35\n288 226 11\n288 282 12\n288 304 22\n288 330 18\n288 334 26\n288 337 50\n288 362 25\n288 379 36\n288 383 2\n288 452 46\n288 474 47\n288 494 13\n288 535 25\n288 550 50\n288 570 33\n288 574 16\n288 588 38\n288 603 42\n288 606 30\n288 629 39\n288 640 21\n288 645 12\n288 646 45\n288 648 -2\n288 653 34\n288 663 39\n288 720 10\n288 721 30\n288 725 50\n288 728 18\n288 738 46\n288 847 50\n288 867 3\n288 951 10\n288 962 31\n288 982 17\n288 988 6\n289 168 38\n289 169 15\n289 214 31\n289 217 38\n289 235 44\n289 237 24\n289 309 25\n289 334 44\n289 339 41\n289 374 26\n289 382 -2\n289 414 16\n289 428 48\n289 531 -2\n289 563 13\n289 570 13\n289 597 5\n289 625 37\n289 647 46\n289 704 36\n289 713 4\n289 724 50\n289 725 12\n289 730 46\n289 744 25\n289 761 50\n289 771 1\n289 774 36\n289 787 48\n289 793 2\n289 863 25\n289 900 23\n289 912 5\n289 938 36\n289 942 27\n289 959 8\n289 960 25\n289 973 35\n290 13 43\n290 23 35\n290 26 38\n290 28 7\n290 72 16\n290 115 43\n290 128 35\n290 139 46\n290 153 35\n290 160 7\n290 176 28\n290 211 32\n290 213 2\n290 215 7\n290 336 8\n290 356 11\n290 361 41\n290 384 46\n290 390 5\n290 411 37\n290 419 6\n290 492 31\n290 501 31\n290 512 41\n290 555 6\n290 581 35\n290 606 46\n290 658 4\n290 674 27\n290 681 6\n290 698 23\n290 719 35\n290 724 -2\n290 753 17\n290 765 16\n290 776 6\n290 799 32\n290 844 21\n290 851 36\n290 853 45\n290 859 4\n290 862 1\n290 871 36\n290 889 22\n290 897 7\n290 912 22\n290 922 39\n290 959 37\n290 976 18\n290 980 35\n291 8 38\n291 11 32\n291 13 12\n291 18 21\n291 28 32\n291 37 3\n291 38 39\n291 54 16\n291 126 32\n291 130 31\n291 147 1\n291 163 -1\n291 210 23\n291 234 17\n291 250 4\n291 254 16\n291 276 2\n291 298 17\n291 311 2\n291 313 13\n291 316 6\n291 361 14\n291 404 35\n291 426 22\n291 456 10\n291 461 49\n291 493 33\n291 499 22\n291 524 35\n291 528 48\n291 541 37\n291 553 15\n291 574 44\n291 581 37\n291 584 44\n291 597 6\n291 601 5\n291 615 24\n291 629 14\n291 638 50\n291 652 29\n291 697 -2\n291 713 3\n291 715 46\n291 725 6\n291 741 41\n291 745 7\n291 783 28\n291 786 24\n291 792 38\n291 825 8\n291 831 27\n291 838 38\n291 847 24\n291 877 43\n291 984 34\n292 24 45\n292 67 11\n292 86 10\n292 123 10\n292 126 0\n292 165 40\n292 176 38\n292 201 35\n292 207 12\n292 226 11\n292 231 -2\n292 236 13\n292 244 0\n292 258 29\n292 305 49\n292 323 41\n292 330 24\n292 378 39\n292 404 17\n292 408 2\n292 415 33\n292 442 14\n292 449 -2\n292 468 34\n292 476 7\n292 488 35\n292 517 2\n292 522 6\n292 530 20\n292 532 49\n292 561 14\n292 571 24\n292 575 21\n292 577 18\n292 586 31\n292 631 41\n292 637 9\n292 641 17\n292 717 -1\n292 730 36\n292 744 34\n292 793 10\n292 812 34\n292 814 35\n292 827 28\n292 830 8\n292 854 33\n292 862 28\n292 912 42\n292 927 38\n292 928 43\n292 986 34\n292 997 36\n292 1000 47\n293 11 11\n293 12 25\n293 27 29\n293 43 50\n293 52 40\n293 79 17\n293 103 3\n293 111 32\n293 126 5\n293 127 23\n293 142 4\n293 156 10\n293 180 9\n293 206 47\n293 223 2\n293 244 13\n293 257 19\n293 260 29\n293 261 29\n293 268 12\n293 288 33\n293 423 3\n293 469 33\n293 526 23\n293 549 38\n293 568 9\n293 607 6\n293 620 9\n293 623 24\n293 629 -1\n293 691 29\n293 707 1\n293 711 12\n293 720 21\n293 761 23\n293 768 14\n293 806 23\n293 814 30\n293 816 21\n293 821 34\n293 877 42\n293 880 9\n293 911 25\n293 945 5\n293 971 28\n293 976 34\n293 980 28\n293 992 44\n294 36 11\n294 91 25\n294 93 23\n294 105 10\n294 121 15\n294 126 19\n294 146 12\n294 159 44\n294 163 2\n294 212 27\n294 213 7\n294 246 11\n294 291 31\n294 320 26\n294 370 22\n294 373 46\n294 381 12\n294 382 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106 48\n296 159 31\n296 202 38\n296 228 40\n296 243 5\n296 261 20\n296 264 5\n296 290 44\n296 293 20\n296 310 46\n296 313 40\n296 324 29\n296 335 34\n296 342 6\n296 347 43\n296 359 48\n296 389 10\n296 391 38\n296 396 32\n296 452 9\n296 472 24\n296 490 6\n296 497 30\n296 502 49\n296 505 11\n296 525 -2\n296 554 23\n296 555 49\n296 559 24\n296 570 30\n296 600 45\n296 620 24\n296 634 42\n296 654 10\n296 661 45\n296 664 32\n296 672 42\n296 680 40\n296 696 49\n296 700 23\n296 714 2\n296 729 6\n296 730 50\n296 767 15\n296 775 30\n296 793 9\n296 799 46\n296 836 40\n296 846 4\n296 856 50\n296 942 45\n296 946 35\n296 971 41\n296 983 26\n296 1000 3\n297 13 28\n297 18 42\n297 35 41\n297 39 31\n297 41 29\n297 47 41\n297 58 38\n297 62 4\n297 64 21\n297 66 24\n297 73 45\n297 96 9\n297 127 43\n297 134 40\n297 151 24\n297 207 19\n297 223 8\n297 229 32\n297 230 19\n297 266 24\n297 268 27\n297 286 1\n297 290 46\n297 310 41\n297 336 13\n297 383 49\n297 411 21\n297 419 49\n297 426 34\n297 427 0\n297 446 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243 16\n304 267 13\n304 268 5\n304 308 24\n304 313 33\n304 320 34\n304 374 37\n304 438 31\n304 448 18\n304 466 -1\n304 487 16\n304 524 2\n304 535 -2\n304 542 32\n304 592 2\n304 666 29\n304 668 -1\n304 671 47\n304 729 42\n304 734 5\n304 738 27\n304 743 29\n304 756 16\n304 830 20\n304 847 14\n304 849 12\n304 851 28\n304 860 39\n304 864 28\n304 884 39\n304 915 47\n304 918 33\n304 963 23\n304 994 16\n305 4 5\n305 30 26\n305 53 10\n305 62 20\n305 100 -1\n305 108 38\n305 110 48\n305 136 36\n305 146 4\n305 148 9\n305 159 45\n305 166 24\n305 175 29\n305 179 32\n305 194 40\n305 222 23\n305 228 30\n305 231 28\n305 234 27\n305 253 9\n305 257 39\n305 281 36\n305 322 26\n305 327 21\n305 420 25\n305 426 2\n305 466 9\n305 472 19\n305 509 40\n305 530 46\n305 627 45\n305 631 -2\n305 675 28\n305 677 23\n305 679 46\n305 700 38\n305 719 14\n305 738 17\n305 739 9\n305 761 14\n305 778 44\n305 800 40\n305 899 38\n305 919 40\n305 922 18\n305 928 19\n305 941 12\n305 961 9\n305 962 50\n305 1000 18\n306 88 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26\n307 868 15\n307 872 23\n307 874 36\n307 913 36\n307 925 38\n307 940 38\n307 981 26\n308 20 22\n308 41 20\n308 86 31\n308 126 12\n308 167 25\n308 171 34\n308 189 33\n308 208 31\n308 216 6\n308 257 13\n308 287 15\n308 297 49\n308 312 15\n308 320 47\n308 325 48\n308 373 14\n308 418 50\n308 419 6\n308 491 10\n308 508 43\n308 516 35\n308 519 3\n308 581 22\n308 609 12\n308 639 36\n308 659 5\n308 661 36\n308 694 43\n308 743 4\n308 876 10\n308 900 13\n308 918 15\n308 927 32\n308 936 44\n308 950 27\n308 951 41\n308 957 25\n308 965 23\n308 998 34\n309 3 11\n309 29 36\n309 47 48\n309 59 17\n309 66 34\n309 68 33\n309 87 27\n309 92 5\n309 102 0\n309 121 9\n309 133 25\n309 144 41\n309 155 21\n309 161 23\n309 183 13\n309 216 32\n309 221 4\n309 222 24\n309 241 18\n309 266 20\n309 287 20\n309 306 37\n309 313 1\n309 346 42\n309 360 14\n309 369 28\n309 376 21\n309 395 21\n309 408 24\n309 414 17\n309 429 8\n309 437 44\n309 440 29\n309 467 26\n309 485 41\n309 489 10\n309 490 18\n309 503 22\n309 508 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36\n311 526 26\n311 545 38\n311 555 36\n311 586 40\n311 633 20\n311 680 41\n311 692 6\n311 707 1\n311 723 13\n311 754 45\n311 758 11\n311 777 22\n311 811 46\n311 812 21\n311 816 36\n311 817 33\n311 868 40\n311 903 13\n311 922 19\n311 932 8\n311 956 23\n311 959 50\n312 26 31\n312 28 37\n312 93 13\n312 111 6\n312 128 43\n312 153 42\n312 168 28\n312 180 31\n312 189 4\n312 191 0\n312 201 44\n312 205 9\n312 220 30\n312 222 39\n312 243 2\n312 258 10\n312 264 31\n312 271 24\n312 335 17\n312 357 30\n312 364 13\n312 396 23\n312 398 20\n312 405 39\n312 423 41\n312 481 42\n312 512 46\n312 519 40\n312 537 23\n312 539 30\n312 547 45\n312 564 39\n312 566 13\n312 575 45\n312 609 26\n312 631 35\n312 636 49\n312 697 -1\n312 724 42\n312 746 38\n312 759 29\n312 836 34\n312 856 47\n312 859 27\n312 907 27\n312 929 2\n312 966 -2\n312 969 23\n312 974 17\n313 98 14\n313 107 2\n313 147 0\n313 178 21\n313 198 3\n313 206 7\n313 216 1\n313 224 16\n313 237 1\n313 256 8\n313 271 26\n313 297 40\n313 300 40\n313 361 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47\n407 361 22\n407 371 13\n407 408 0\n407 411 49\n407 448 13\n407 460 50\n407 527 49\n407 559 28\n407 606 37\n407 621 33\n407 638 8\n407 654 35\n407 698 2\n407 716 40\n407 734 30\n407 743 38\n407 746 28\n407 757 33\n407 769 40\n407 793 7\n407 806 7\n407 809 28\n407 820 44\n407 861 37\n407 883 48\n407 902 9\n407 905 1\n407 920 0\n407 942 1\n407 950 4\n407 987 19\n408 12 4\n408 27 30\n408 34 23\n408 41 32\n408 82 34\n408 136 29\n408 144 12\n408 148 20\n408 159 5\n408 160 47\n408 164 7\n408 174 7\n408 190 13\n408 198 31\n408 217 46\n408 220 7\n408 227 47\n408 232 3\n408 255 0\n408 285 18\n408 330 -1\n408 331 17\n408 338 -1\n408 355 17\n408 362 33\n408 371 20\n408 380 5\n408 410 3\n408 414 39\n408 420 49\n408 423 23\n408 435 39\n408 439 8\n408 473 29\n408 497 3\n408 518 12\n408 536 6\n408 552 44\n408 591 36\n408 614 6\n408 636 5\n408 644 21\n408 662 8\n408 666 26\n408 679 17\n408 715 42\n408 724 -1\n408 742 32\n408 789 13\n408 796 7\n408 805 12\n408 880 39\n408 883 42\n408 905 36\n408 944 11\n408 949 36\n408 965 8\n408 967 28\n408 969 33\n408 994 20\n409 21 6\n409 22 20\n409 65 16\n409 96 37\n409 97 17\n409 99 40\n409 102 5\n409 119 20\n409 124 46\n409 139 39\n409 170 24\n409 180 24\n409 224 19\n409 228 43\n409 240 22\n409 249 34\n409 272 45\n409 275 11\n409 277 29\n409 296 3\n409 358 44\n409 367 24\n409 371 20\n409 410 7\n409 421 11\n409 422 0\n409 448 42\n409 459 50\n409 507 16\n409 508 46\n409 511 15\n409 520 38\n409 541 11\n409 556 29\n409 559 19\n409 576 15\n409 588 48\n409 640 41\n409 657 21\n409 680 9\n409 682 6\n409 700 21\n409 705 34\n409 714 5\n409 763 34\n409 794 17\n409 816 2\n409 843 40\n409 865 2\n409 922 24\n409 939 43\n409 946 9\n409 949 19\n410 1 23\n410 13 5\n410 72 44\n410 86 21\n410 111 7\n410 121 35\n410 149 38\n410 155 42\n410 165 16\n410 186 22\n410 194 20\n410 268 28\n410 303 22\n410 316 6\n410 336 28\n410 337 37\n410 374 25\n410 379 7\n410 418 49\n410 451 49\n410 580 47\n410 589 3\n410 599 22\n410 606 6\n410 626 30\n410 651 34\n410 660 34\n410 679 17\n410 702 5\n410 723 37\n410 753 9\n410 762 29\n410 770 41\n410 783 20\n410 808 32\n410 815 22\n410 825 50\n410 851 36\n410 865 39\n410 995 8\n411 11 20\n411 40 48\n411 56 20\n411 80 48\n411 87 19\n411 92 0\n411 95 2\n411 109 23\n411 119 -2\n411 123 20\n411 138 37\n411 153 1\n411 157 34\n411 173 27\n411 200 46\n411 235 -2\n411 268 40\n411 281 34\n411 340 20\n411 548 19\n411 555 22\n411 591 31\n411 597 13\n411 624 27\n411 632 39\n411 643 8\n411 655 10\n411 666 7\n411 726 26\n411 767 17\n411 773 25\n411 797 39\n411 800 37\n411 815 13\n411 843 45\n411 858 33\n411 871 35\n411 910 13\n411 913 28\n411 919 15\n411 984 21\n411 991 35\n412 24 28\n412 28 25\n412 45 30\n412 53 30\n412 77 32\n412 91 35\n412 99 48\n412 107 40\n412 110 18\n412 120 29\n412 184 28\n412 239 39\n412 257 2\n412 283 9\n412 297 44\n412 313 47\n412 329 15\n412 358 28\n412 443 -2\n412 452 23\n412 476 29\n412 478 39\n412 482 3\n412 490 22\n412 512 12\n412 521 1\n412 525 27\n412 588 16\n412 599 36\n412 636 12\n412 639 39\n412 652 29\n412 653 4\n412 676 28\n412 688 50\n412 692 34\n412 704 6\n412 728 1\n412 750 40\n412 756 30\n412 759 2\n412 763 5\n412 767 35\n412 781 11\n412 783 32\n412 799 10\n412 822 24\n412 840 6\n412 849 28\n413 74 29\n413 158 28\n413 179 13\n413 204 22\n413 223 23\n413 248 28\n413 252 32\n413 276 25\n413 328 1\n413 351 40\n413 371 5\n413 387 21\n413 389 20\n413 405 35\n413 411 17\n413 447 36\n413 473 5\n413 475 29\n413 483 26\n413 538 30\n413 552 37\n413 567 48\n413 614 29\n413 622 30\n413 676 19\n413 719 19\n413 742 11\n413 750 41\n413 752 17\n413 786 19\n413 797 28\n413 801 10\n413 807 4\n413 811 20\n413 812 16\n413 822 39\n413 823 33\n413 968 13\n413 970 47\n414 15 46\n414 73 38\n414 93 -1\n414 97 31\n414 129 45\n414 159 24\n414 164 42\n414 182 30\n414 191 14\n414 221 24\n414 264 32\n414 285 25\n414 289 23\n414 296 50\n414 307 30\n414 358 14\n414 379 50\n414 417 15\n414 424 32\n414 426 20\n414 462 49\n414 484 37\n414 519 2\n414 526 26\n414 530 21\n414 540 26\n414 546 14\n414 576 12\n414 610 5\n414 628 24\n414 706 46\n414 722 28\n414 735 6\n414 737 28\n414 743 39\n414 747 2\n414 751 6\n414 763 47\n414 830 9\n414 840 -2\n414 880 12\n414 882 20\n414 891 29\n414 968 -1\n414 976 13\n415 40 14\n415 64 40\n415 116 22\n415 128 34\n415 134 -2\n415 166 50\n415 197 37\n415 218 40\n415 243 39\n415 262 25\n415 290 23\n415 321 36\n415 326 38\n415 329 10\n415 391 -2\n415 413 16\n415 422 12\n415 426 22\n415 446 3\n415 487 49\n415 488 12\n415 495 44\n415 519 31\n415 536 18\n415 547 33\n415 557 19\n415 571 47\n415 575 17\n415 606 8\n415 609 5\n415 616 3\n415 683 47\n415 686 22\n415 702 2\n415 704 28\n415 716 36\n415 719 8\n415 770 17\n415 825 0\n415 830 20\n415 867 26\n415 876 20\n415 877 28\n415 879 23\n415 880 36\n415 884 21\n415 919 -2\n415 923 28\n415 950 8\n415 953 25\n415 959 -2\n415 968 0\n415 994 31\n415 998 18\n416 12 8\n416 35 24\n416 49 33\n416 73 43\n416 81 47\n416 92 49\n416 110 48\n416 113 45\n416 128 47\n416 149 38\n416 173 29\n416 190 36\n416 218 48\n416 226 8\n416 267 39\n416 269 19\n416 272 16\n416 273 33\n416 329 28\n416 332 15\n416 341 26\n416 424 43\n416 482 -2\n416 508 1\n416 538 23\n416 550 3\n416 589 20\n416 595 34\n416 596 25\n416 605 35\n416 621 16\n416 699 36\n416 748 27\n416 759 13\n416 766 12\n416 769 43\n416 815 26\n416 817 16\n416 892 33\n416 916 34\n416 923 13\n416 946 27\n416 992 49\n417 22 30\n417 26 26\n417 39 31\n417 47 40\n417 86 35\n417 92 47\n417 102 33\n417 107 2\n417 121 21\n417 172 40\n417 177 32\n417 214 27\n417 220 25\n417 248 47\n417 289 44\n417 360 47\n417 367 23\n417 370 45\n417 379 48\n417 381 8\n417 394 26\n417 398 31\n417 407 38\n417 455 38\n417 464 6\n417 473 35\n417 494 35\n417 520 20\n417 523 34\n417 647 14\n417 699 46\n417 701 19\n417 737 20\n417 747 30\n417 780 46\n417 800 5\n417 830 31\n417 845 28\n417 851 8\n417 865 49\n417 879 16\n417 891 49\n417 906 41\n417 924 29\n417 932 29\n417 936 3\n417 940 8\n417 948 29\n417 959 49\n418 3 14\n418 9 5\n418 53 9\n418 61 8\n418 70 9\n418 106 48\n418 116 44\n418 119 5\n418 280 -1\n418 284 9\n418 298 43\n418 308 7\n418 335 39\n418 337 7\n418 373 9\n418 381 40\n418 424 7\n418 485 31\n418 505 10\n418 513 27\n418 516 22\n418 557 -1\n418 612 28\n418 617 36\n418 662 -1\n418 668 33\n418 671 14\n418 681 4\n418 699 17\n418 719 38\n418 720 33\n418 729 22\n418 774 32\n418 790 34\n418 796 34\n418 813 25\n418 823 -2\n418 859 8\n418 866 41\n418 876 3\n418 882 43\n418 883 43\n418 889 38\n418 894 22\n418 920 9\n418 922 -1\n418 927 35\n418 929 30\n418 936 27\n418 946 26\n419 36 21\n419 45 6\n419 65 45\n419 72 30\n419 75 46\n419 93 14\n419 117 -1\n419 136 7\n419 153 4\n419 176 18\n419 206 8\n419 217 22\n419 229 7\n419 234 5\n419 236 6\n419 249 32\n419 263 6\n419 298 26\n419 315 19\n419 319 37\n419 348 22\n419 351 16\n419 361 25\n419 395 16\n419 406 3\n419 427 8\n419 429 48\n419 431 12\n419 449 21\n419 453 -1\n419 472 44\n419 474 3\n419 505 8\n419 540 33\n419 571 43\n419 585 38\n419 611 17\n419 628 4\n419 642 4\n419 703 45\n419 767 44\n419 776 34\n419 801 7\n419 816 5\n419 842 31\n419 854 31\n419 856 8\n419 864 18\n419 942 32\n419 949 47\n419 953 9\n419 954 49\n419 955 2\n419 971 27\n419 995 13\n420 3 31\n420 12 32\n420 16 27\n420 37 25\n420 40 12\n420 45 45\n420 83 38\n420 107 47\n420 141 46\n420 158 13\n420 175 5\n420 200 34\n420 231 29\n420 244 11\n420 284 10\n420 295 14\n420 296 28\n420 349 18\n420 373 48\n420 409 15\n420 469 47\n420 492 13\n420 532 23\n420 564 50\n420 580 20\n420 644 35\n420 652 21\n420 653 44\n420 669 48\n420 710 26\n420 771 36\n420 800 34\n420 861 32\n420 869 43\n420 875 26\n420 938 47\n420 950 34\n420 956 30\n421 79 1\n421 99 32\n421 109 7\n421 122 44\n421 140 21\n421 142 16\n421 150 7\n421 157 27\n421 162 31\n421 205 10\n421 238 39\n421 243 40\n421 267 38\n421 324 20\n421 365 43\n421 366 22\n421 386 42\n421 430 10\n421 443 31\n421 451 47\n421 499 27\n421 576 14\n421 604 31\n421 615 2\n421 633 31\n421 643 21\n421 719 16\n421 731 6\n421 734 50\n421 737 18\n421 748 8\n421 774 29\n421 798 50\n421 811 8\n421 870 13\n421 890 36\n421 895 39\n421 924 35\n421 945 29\n421 976 9\n421 984 10\n421 1000 35\n422 23 48\n422 39 45\n422 60 27\n422 68 5\n422 76 19\n422 169 49\n422 178 18\n422 229 31\n422 232 15\n422 244 24\n422 279 39\n422 335 23\n422 362 20\n422 401 33\n422 427 26\n422 498 5\n422 510 31\n422 513 35\n422 552 8\n422 641 50\n422 647 16\n422 662 32\n422 666 29\n422 670 30\n422 706 3\n422 713 6\n422 725 11\n422 751 35\n422 760 40\n422 762 3\n422 771 29\n422 788 32\n422 805 25\n422 823 17\n422 862 8\n422 870 36\n422 900 44\n422 908 34\n422 940 14\n422 963 41\n422 964 41\n423 48 25\n423 50 47\n423 75 -2\n423 87 0\n423 94 47\n423 95 14\n423 96 15\n423 117 23\n423 120 12\n423 146 12\n423 159 44\n423 167 27\n423 169 45\n423 179 50\n423 234 33\n423 316 22\n423 355 -2\n423 362 12\n423 364 20\n423 375 2\n423 381 21\n423 406 13\n423 409 40\n423 413 17\n423 420 27\n423 424 28\n423 425 14\n423 437 6\n423 447 45\n423 460 35\n423 530 6\n423 543 12\n423 553 41\n423 578 24\n423 583 4\n423 642 50\n423 645 15\n423 688 0\n423 731 31\n423 748 50\n423 750 39\n423 751 41\n423 783 36\n423 819 20\n423 864 7\n423 872 48\n423 899 30\n423 908 10\n423 941 10\n423 954 24\n423 957 24\n423 977 5\n424 24 3\n424 33 17\n424 39 12\n424 43 31\n424 76 12\n424 81 30\n424 95 17\n424 96 45\n424 125 2\n424 129 6\n424 136 20\n424 146 11\n424 154 28\n424 182 48\n424 196 31\n424 238 48\n424 289 29\n424 311 13\n424 327 25\n424 333 26\n424 348 37\n424 350 29\n424 369 15\n424 400 14\n424 416 16\n424 437 22\n424 466 19\n424 471 16\n424 472 30\n424 477 17\n424 478 17\n424 484 27\n424 524 5\n424 530 25\n424 534 10\n424 547 40\n424 552 18\n424 564 32\n424 584 42\n424 586 37\n424 605 1\n424 615 11\n424 651 15\n424 663 40\n424 694 9\n424 723 14\n424 735 16\n424 755 28\n424 777 11\n424 802 47\n424 825 5\n424 842 32\n424 856 9\n424 867 35\n424 887 39\n424 905 49\n424 907 21\n424 918 15\n424 996 10\n425 15 18\n425 18 21\n425 33 37\n425 35 0\n425 59 1\n425 66 32\n425 148 41\n425 161 5\n425 164 35\n425 184 12\n425 217 21\n425 225 44\n425 248 26\n425 249 30\n425 265 24\n425 266 43\n425 332 6\n425 341 44\n425 372 8\n425 397 6\n425 401 8\n425 421 46\n425 435 29\n425 452 49\n425 455 -2\n425 474 38\n425 497 9\n425 503 42\n425 559 23\n425 593 35\n425 613 6\n425 622 1\n425 623 28\n425 626 -2\n425 636 34\n425 657 5\n425 695 42\n425 702 22\n425 753 36\n425 763 5\n425 769 9\n425 778 5\n425 798 22\n425 809 -2\n425 848 49\n425 873 25\n425 899 37\n425 944 34\n425 945 8\n425 953 34\n425 981 -2\n426 14 25\n426 74 2\n426 86 12\n426 94 39\n426 106 9\n426 111 50\n426 114 17\n426 125 19\n426 149 40\n426 182 9\n426 200 13\n426 233 15\n426 234 0\n426 246 26\n426 273 38\n426 276 47\n426 332 48\n426 394 6\n426 416 33\n426 423 50\n426 450 37\n426 453 14\n426 492 31\n426 524 42\n426 548 28\n426 550 5\n426 552 33\n426 587 4\n426 593 13\n426 644 46\n426 662 17\n426 670 31\n426 673 28\n426 688 10\n426 691 28\n426 693 14\n426 696 29\n426 717 21\n426 744 39\n426 760 1\n426 773 21\n426 782 28\n426 806 11\n426 851 39\n426 860 42\n426 966 5\n426 977 8\n426 985 2\n427 32 27\n427 56 41\n427 57 41\n427 68 48\n427 88 13\n427 97 18\n427 140 50\n427 191 28\n427 217 29\n427 249 47\n427 282 18\n427 307 50\n427 329 50\n427 345 33\n427 371 15\n427 385 19\n427 394 44\n427 452 21\n427 463 13\n427 497 9\n427 558 14\n427 637 35\n427 660 23\n427 666 25\n427 678 30\n427 682 37\n427 706 36\n427 715 12\n427 723 10\n427 744 30\n427 803 30\n427 831 49\n427 850 37\n427 913 17\n427 923 39\n427 933 16\n427 979 17\n427 991 25\n428 18 21\n428 20 26\n428 42 22\n428 59 3\n428 60 -2\n428 109 11\n428 135 35\n428 136 5\n428 148 31\n428 155 22\n428 171 46\n428 193 34\n428 224 24\n428 231 42\n428 245 7\n428 249 35\n428 250 15\n428 253 46\n428 262 42\n428 263 43\n428 265 49\n428 275 20\n428 298 47\n428 381 17\n428 443 9\n428 479 50\n428 480 6\n428 485 18\n428 487 30\n428 545 14\n428 602 34\n428 609 25\n428 654 39\n428 666 -2\n428 732 31\n428 735 24\n428 754 47\n428 764 34\n428 778 27\n428 788 24\n428 825 13\n428 830 34\n428 836 14\n428 866 9\n428 920 45\n428 961 46\n428 983 8\n429 42 2\n429 51 36\n429 71 42\n429 85 7\n429 100 6\n429 134 -2\n429 138 6\n429 145 4\n429 151 22\n429 202 16\n429 218 22\n429 232 22\n429 270 40\n429 272 31\n429 277 48\n429 280 8\n429 287 48\n429 315 5\n429 350 6\n429 401 43\n429 435 24\n429 445 43\n429 462 42\n429 468 41\n429 474 10\n429 513 15\n429 517 34\n429 586 14\n429 593 33\n429 599 46\n429 619 35\n429 678 35\n429 692 7\n429 696 23\n429 720 -2\n429 739 13\n429 803 16\n429 832 41\n429 847 21\n429 850 32\n429 884 38\n429 902 36\n430 7 20\n430 24 48\n430 41 40\n430 85 13\n430 100 43\n430 111 10\n430 126 14\n430 136 18\n430 144 44\n430 159 17\n430 178 -2\n430 221 -1\n430 228 27\n430 269 24\n430 285 50\n430 344 27\n430 358 12\n430 382 17\n430 406 5\n430 422 15\n430 423 34\n430 491 32\n430 499 18\n430 500 26\n430 518 9\n430 528 20\n430 549 32\n430 592 42\n430 615 31\n430 635 38\n430 672 35\n430 715 27\n430 733 26\n430 747 8\n430 757 20\n430 781 24\n430 791 14\n430 839 28\n430 937 33\n430 985 15\n431 7 45\n431 48 48\n431 50 30\n431 60 22\n431 64 21\n431 78 37\n431 82 18\n431 83 25\n431 135 8\n431 137 19\n431 152 25\n431 165 5\n431 170 45\n431 177 16\n431 246 28\n431 251 33\n431 299 29\n431 368 45\n431 389 37\n431 418 47\n431 419 33\n431 430 35\n431 449 30\n431 469 50\n431 475 14\n431 497 0\n431 529 32\n431 546 48\n431 564 48\n431 579 31\n431 602 11\n431 603 45\n431 604 25\n431 616 7\n431 626 20\n431 640 0\n431 697 2\n431 724 31\n431 740 15\n431 744 12\n431 757 10\n431 758 21\n431 778 41\n431 787 14\n431 790 36\n431 796 10\n431 799 3\n431 810 48\n431 819 7\n431 835 33\n431 898 32\n431 920 19\n431 967 15\n432 17 -1\n432 48 23\n432 105 21\n432 113 38\n432 156 45\n432 210 24\n432 235 11\n432 241 41\n432 256 12\n432 258 46\n432 300 27\n432 367 10\n432 372 44\n432 407 15\n432 461 40\n432 486 43\n432 501 2\n432 524 21\n432 556 29\n432 567 19\n432 575 5\n432 635 26\n432 639 14\n432 726 21\n432 743 12\n432 746 18\n432 783 38\n432 794 8\n432 897 15\n432 923 42\n432 980 25\n432 992 29\n433 14 32\n433 22 7\n433 48 48\n433 59 27\n433 67 21\n433 74 13\n433 123 26\n433 146 13\n433 170 25\n433 178 49\n433 228 14\n433 244 12\n433 249 8\n433 250 40\n433 253 7\n433 325 0\n433 373 22\n433 379 12\n433 425 31\n433 445 28\n433 451 48\n433 452 29\n433 463 9\n433 470 30\n433 478 4\n433 526 50\n433 555 34\n433 585 25\n433 632 22\n433 635 8\n433 647 41\n433 701 1\n433 708 40\n433 722 26\n433 730 29\n433 731 21\n433 761 34\n433 788 0\n433 866 34\n433 905 17\n433 909 39\n433 917 11\n433 931 14\n433 955 2\n433 999 47\n434 19 30\n434 48 25\n434 79 50\n434 83 21\n434 89 43\n434 92 3\n434 96 47\n434 118 32\n434 119 19\n434 125 11\n434 147 40\n434 155 49\n434 171 49\n434 182 35\n434 183 48\n434 187 48\n434 194 44\n434 218 9\n434 257 28\n434 274 33\n434 281 33\n434 285 35\n434 287 13\n434 290 39\n434 305 20\n434 311 3\n434 314 29\n434 320 32\n434 337 20\n434 342 23\n434 359 42\n434 391 2\n434 408 48\n434 430 33\n434 432 45\n434 445 0\n434 457 4\n434 481 48\n434 493 42\n434 512 30\n434 544 14\n434 555 1\n434 588 38\n434 595 22\n434 617 8\n434 619 32\n434 652 30\n434 653 4\n434 660 21\n434 661 44\n434 690 18\n434 710 -1\n434 745 41\n434 747 21\n434 757 3\n434 762 3\n434 778 7\n434 781 17\n434 785 43\n434 801 17\n434 802 12\n434 810 23\n434 818 31\n434 840 32\n434 873 43\n434 906 9\n434 919 20\n434 939 28\n434 946 50\n434 948 7\n434 954 21\n434 960 36\n435 18 14\n435 22 31\n435 55 28\n435 71 33\n435 82 49\n435 87 24\n435 100 1\n435 130 24\n435 141 5\n435 170 29\n435 178 19\n435 179 16\n435 181 38\n435 221 3\n435 252 23\n435 273 20\n435 284 3\n435 309 30\n435 346 17\n435 457 44\n435 490 18\n435 491 29\n435 509 7\n435 511 10\n435 520 8\n435 541 18\n435 553 11\n435 570 28\n435 572 12\n435 604 16\n435 652 28\n435 654 10\n435 667 26\n435 689 0\n435 721 47\n435 759 31\n435 776 15\n435 799 25\n435 826 27\n435 833 20\n435 882 31\n435 883 49\n435 885 20\n435 896 30\n435 901 15\n435 910 23\n435 920 29\n435 923 13\n435 926 35\n435 950 29\n435 960 37\n435 961 6\n435 983 32\n436 59 2\n436 68 15\n436 74 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47\n441 870 4\n441 874 36\n441 876 7\n441 882 8\n441 900 29\n441 914 48\n441 920 16\n441 931 7\n441 947 42\n441 951 49\n441 978 45\n442 22 5\n442 53 36\n442 57 45\n442 63 27\n442 69 5\n442 78 42\n442 90 1\n442 112 22\n442 116 21\n442 128 -1\n442 165 25\n442 188 14\n442 235 10\n442 258 41\n442 262 21\n442 271 43\n442 277 34\n442 287 13\n442 308 31\n442 314 8\n442 343 8\n442 393 -1\n442 402 42\n442 403 25\n442 414 32\n442 423 44\n442 461 48\n442 478 32\n442 520 2\n442 541 6\n442 585 17\n442 601 38\n442 618 38\n442 622 5\n442 637 32\n442 683 0\n442 690 22\n442 772 48\n442 789 24\n442 817 23\n442 861 44\n442 874 9\n442 877 30\n442 879 35\n442 884 49\n442 890 32\n442 905 26\n442 920 26\n442 930 43\n442 931 30\n442 939 45\n442 949 12\n442 969 7\n442 971 47\n442 990 38\n443 13 40\n443 42 44\n443 45 39\n443 48 45\n443 50 0\n443 85 15\n443 98 45\n443 105 32\n443 119 12\n443 126 8\n443 150 48\n443 189 43\n443 218 32\n443 220 32\n443 223 16\n443 246 35\n443 266 46\n443 292 5\n443 371 42\n443 403 47\n443 404 25\n443 432 36\n443 442 49\n443 446 -1\n443 451 7\n443 458 48\n443 464 19\n443 484 25\n443 505 13\n443 507 37\n443 512 -2\n443 522 27\n443 565 45\n443 574 14\n443 580 45\n443 645 46\n443 718 44\n443 838 26\n443 857 45\n443 900 24\n443 936 13\n443 972 38\n443 981 29\n443 985 8\n443 995 -1\n444 8 38\n444 10 19\n444 51 2\n444 89 43\n444 96 24\n444 98 46\n444 110 17\n444 144 18\n444 163 20\n444 165 10\n444 183 35\n444 187 -1\n444 204 3\n444 237 31\n444 253 11\n444 259 30\n444 271 43\n444 275 31\n444 336 11\n444 347 28\n444 356 26\n444 436 31\n444 453 26\n444 482 35\n444 505 25\n444 518 39\n444 528 46\n444 560 49\n444 563 15\n444 565 14\n444 571 49\n444 594 50\n444 614 26\n444 633 4\n444 648 15\n444 684 50\n444 695 43\n444 697 43\n444 707 15\n444 732 46\n444 778 35\n444 794 10\n444 819 22\n444 822 49\n444 847 41\n444 875 39\n444 885 44\n444 889 11\n444 914 26\n444 936 5\n444 947 34\n444 960 46\n444 967 28\n445 9 16\n445 10 31\n445 27 10\n445 53 19\n445 74 32\n445 89 34\n445 108 11\n445 119 13\n445 122 10\n445 162 4\n445 184 29\n445 198 17\n445 248 1\n445 318 11\n445 327 50\n445 333 38\n445 348 14\n445 420 9\n445 442 50\n445 444 37\n445 449 17\n445 454 27\n445 457 3\n445 481 22\n445 503 23\n445 506 8\n445 556 7\n445 644 5\n445 666 20\n445 669 44\n445 696 -1\n445 737 14\n445 745 5\n445 785 42\n445 805 28\n445 842 23\n445 908 6\n445 942 48\n445 949 30\n445 953 49\n445 954 19\n445 981 18\n446 65 21\n446 71 25\n446 80 35\n446 102 19\n446 110 32\n446 128 26\n446 130 34\n446 147 16\n446 205 32\n446 214 46\n446 273 6\n446 292 29\n446 295 2\n446 296 18\n446 299 19\n446 315 40\n446 324 27\n446 326 25\n446 338 40\n446 348 37\n446 369 49\n446 371 2\n446 377 30\n446 388 3\n446 403 45\n446 406 13\n446 410 3\n446 490 34\n446 505 36\n446 519 48\n446 542 20\n446 570 28\n446 578 22\n446 606 -1\n446 608 44\n446 672 4\n446 700 44\n446 716 50\n446 762 50\n446 785 49\n446 787 20\n446 792 14\n446 805 28\n446 819 -2\n446 842 -1\n446 846 11\n446 873 48\n446 928 21\n446 941 15\n446 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726 50\n448 764 14\n448 766 25\n448 768 15\n448 770 13\n448 809 29\n448 851 26\n448 877 2\n448 907 33\n448 912 49\n448 958 39\n448 960 12\n448 978 44\n448 982 50\n449 5 33\n449 13 12\n449 36 47\n449 91 13\n449 139 40\n449 157 26\n449 164 44\n449 217 19\n449 339 35\n449 371 34\n449 374 32\n449 392 48\n449 395 35\n449 396 24\n449 416 27\n449 456 7\n449 467 31\n449 474 44\n449 509 7\n449 511 23\n449 512 4\n449 519 49\n449 549 45\n449 559 11\n449 575 39\n449 610 19\n449 627 47\n449 637 7\n449 654 18\n449 695 49\n449 753 1\n449 785 14\n449 807 20\n449 876 48\n449 881 28\n449 942 37\n449 985 40\n450 3 5\n450 10 21\n450 60 33\n450 65 31\n450 84 24\n450 88 1\n450 97 44\n450 107 7\n450 109 3\n450 116 18\n450 160 4\n450 183 18\n450 193 34\n450 203 36\n450 207 47\n450 225 5\n450 227 40\n450 230 -1\n450 246 10\n450 251 11\n450 271 11\n450 391 48\n450 412 31\n450 430 50\n450 455 45\n450 475 23\n450 477 37\n450 503 27\n450 521 14\n450 539 25\n450 558 25\n450 559 -1\n450 560 38\n450 563 33\n450 584 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633 15\n454 666 19\n454 671 24\n454 676 21\n454 701 24\n454 704 4\n454 724 21\n454 794 1\n454 798 1\n454 835 9\n454 864 21\n454 900 25\n454 904 39\n454 970 40\n454 991 13\n455 26 27\n455 42 43\n455 59 20\n455 68 19\n455 73 14\n455 103 36\n455 110 27\n455 153 8\n455 168 13\n455 175 14\n455 178 20\n455 182 38\n455 198 26\n455 215 38\n455 230 16\n455 282 25\n455 318 45\n455 320 0\n455 338 34\n455 343 44\n455 354 44\n455 358 9\n455 359 37\n455 362 5\n455 411 19\n455 428 6\n455 497 10\n455 519 17\n455 540 49\n455 574 37\n455 581 15\n455 584 36\n455 586 9\n455 623 30\n455 656 40\n455 667 18\n455 675 25\n455 708 16\n455 709 34\n455 755 -2\n455 765 4\n455 801 4\n455 809 45\n455 823 28\n455 825 40\n455 837 5\n455 853 16\n455 871 13\n455 873 46\n455 874 39\n455 891 10\n455 911 5\n455 918 29\n455 924 44\n455 941 24\n455 942 46\n455 994 17\n455 997 19\n456 15 23\n456 65 12\n456 66 17\n456 82 2\n456 102 -2\n456 107 24\n456 205 16\n456 276 32\n456 409 36\n456 422 8\n456 499 36\n456 529 19\n456 534 31\n456 536 35\n456 544 17\n456 570 40\n456 594 32\n456 606 41\n456 641 25\n456 709 38\n456 744 5\n456 753 15\n456 831 40\n456 868 12\n456 869 50\n456 947 49\n456 973 25\n456 988 34\n456 989 3\n456 996 11\n457 8 23\n457 10 6\n457 26 35\n457 59 20\n457 155 12\n457 210 14\n457 215 30\n457 231 32\n457 250 7\n457 278 50\n457 283 -1\n457 322 36\n457 327 1\n457 351 16\n457 358 1\n457 372 1\n457 412 32\n457 446 -1\n457 462 17\n457 532 14\n457 547 7\n457 566 7\n457 573 38\n457 575 20\n457 597 30\n457 603 7\n457 618 12\n457 619 8\n457 638 28\n457 640 37\n457 654 18\n457 695 11\n457 697 3\n457 705 7\n457 732 10\n457 798 47\n457 814 10\n457 908 14\n457 922 33\n457 950 24\n457 957 28\n457 960 8\n458 26 37\n458 92 35\n458 116 27\n458 117 20\n458 129 44\n458 195 34\n458 245 34\n458 250 46\n458 254 38\n458 279 15\n458 294 12\n458 316 36\n458 327 -1\n458 346 40\n458 414 49\n458 455 0\n458 477 0\n458 494 23\n458 525 19\n458 541 50\n458 603 11\n458 624 6\n458 628 10\n458 638 16\n458 645 50\n458 675 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48\n463 131 49\n463 224 30\n463 261 23\n463 389 27\n463 392 35\n463 410 31\n463 423 29\n463 448 0\n463 449 9\n463 487 44\n463 498 0\n463 506 16\n463 514 0\n463 517 25\n463 530 47\n463 544 20\n463 554 15\n463 555 10\n463 584 26\n463 620 8\n463 627 42\n463 671 18\n463 692 34\n463 710 24\n463 737 0\n463 827 27\n463 848 44\n463 852 0\n463 859 47\n463 892 26\n463 972 20\n463 984 4\n464 4 31\n464 9 19\n464 12 45\n464 35 12\n464 46 8\n464 52 31\n464 66 38\n464 100 5\n464 116 19\n464 141 4\n464 168 14\n464 171 35\n464 185 35\n464 186 17\n464 192 37\n464 200 48\n464 204 47\n464 219 6\n464 222 36\n464 251 17\n464 291 24\n464 309 28\n464 311 22\n464 341 6\n464 395 23\n464 397 -2\n464 405 48\n464 433 32\n464 476 14\n464 503 36\n464 510 43\n464 518 0\n464 539 8\n464 594 13\n464 597 17\n464 624 22\n464 632 12\n464 704 21\n464 751 11\n464 777 39\n464 786 42\n464 804 25\n464 841 41\n464 847 8\n464 861 50\n464 872 10\n464 906 22\n464 913 13\n464 945 16\n464 984 32\n465 9 40\n465 34 13\n465 74 -1\n465 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122 45\n486 125 35\n486 132 38\n486 162 18\n486 167 32\n486 176 38\n486 178 6\n486 214 19\n486 217 11\n486 232 50\n486 291 20\n486 307 28\n486 325 41\n486 335 45\n486 337 26\n486 399 25\n486 421 -1\n486 467 33\n486 471 3\n486 485 43\n486 532 2\n486 537 30\n486 539 42\n486 552 1\n486 553 7\n486 566 30\n486 580 11\n486 615 39\n486 654 35\n486 659 14\n486 680 39\n486 688 22\n486 704 23\n486 710 18\n486 747 4\n486 782 21\n486 792 46\n486 814 21\n486 829 27\n486 842 28\n486 852 25\n486 890 26\n486 911 41\n486 951 8\n486 981 8\n487 42 7\n487 50 33\n487 72 30\n487 81 40\n487 150 49\n487 207 1\n487 253 28\n487 262 14\n487 264 49\n487 271 4\n487 292 10\n487 314 23\n487 325 21\n487 343 10\n487 350 2\n487 357 22\n487 368 29\n487 424 37\n487 454 7\n487 478 23\n487 479 49\n487 499 2\n487 500 16\n487 512 28\n487 545 45\n487 577 50\n487 587 37\n487 609 38\n487 622 -2\n487 658 5\n487 669 35\n487 717 2\n487 719 39\n487 754 40\n487 774 18\n487 796 32\n487 874 3\n487 923 35\n487 952 47\n487 965 19\n487 968 45\n487 994 49\n487 999 48\n488 11 24\n488 16 21\n488 24 37\n488 32 37\n488 81 3\n488 156 48\n488 163 9\n488 179 48\n488 194 16\n488 217 43\n488 228 39\n488 236 14\n488 249 29\n488 297 22\n488 304 31\n488 310 17\n488 314 28\n488 322 44\n488 412 49\n488 437 25\n488 441 50\n488 460 45\n488 463 33\n488 467 37\n488 477 49\n488 519 27\n488 528 23\n488 562 34\n488 567 25\n488 579 10\n488 625 21\n488 634 32\n488 643 38\n488 656 47\n488 658 18\n488 708 -1\n488 725 26\n488 759 36\n488 790 24\n488 817 43\n488 883 40\n488 900 14\n488 919 43\n488 935 45\n488 977 35\n489 8 16\n489 25 42\n489 87 32\n489 91 7\n489 92 15\n489 148 37\n489 196 32\n489 217 34\n489 235 28\n489 259 22\n489 271 34\n489 287 17\n489 292 12\n489 294 45\n489 299 31\n489 313 45\n489 318 12\n489 326 30\n489 371 32\n489 390 45\n489 401 31\n489 402 34\n489 411 15\n489 442 8\n489 445 31\n489 452 20\n489 462 9\n489 488 6\n489 508 16\n489 525 4\n489 552 39\n489 563 20\n489 617 44\n489 619 -2\n489 632 28\n489 652 8\n489 666 40\n489 670 25\n489 681 22\n489 698 20\n489 728 28\n489 732 29\n489 750 45\n489 777 23\n489 788 15\n489 808 35\n489 845 15\n489 847 15\n489 852 25\n489 856 43\n489 858 22\n489 916 9\n489 919 23\n489 934 42\n489 945 47\n489 953 45\n490 19 7\n490 20 35\n490 22 6\n490 43 3\n490 58 4\n490 65 12\n490 66 -1\n490 82 24\n490 104 49\n490 118 43\n490 131 7\n490 138 32\n490 149 13\n490 178 0\n490 184 9\n490 188 31\n490 193 37\n490 209 21\n490 228 10\n490 236 14\n490 251 36\n490 271 33\n490 283 44\n490 323 17\n490 329 7\n490 332 41\n490 366 39\n490 367 26\n490 419 4\n490 491 -2\n490 502 26\n490 506 35\n490 549 36\n490 576 18\n490 583 31\n490 602 19\n490 644 25\n490 645 48\n490 651 19\n490 663 7\n490 685 17\n490 689 41\n490 697 8\n490 701 21\n490 707 27\n490 708 43\n490 709 11\n490 710 2\n490 766 12\n490 786 33\n490 818 -1\n490 833 19\n490 906 34\n490 924 19\n491 3 41\n491 62 9\n491 64 43\n491 93 35\n491 125 45\n491 163 9\n491 179 38\n491 184 35\n491 230 43\n491 252 41\n491 285 23\n491 308 33\n491 320 48\n491 328 6\n491 393 10\n491 408 36\n491 417 22\n491 440 13\n491 494 16\n491 496 30\n491 518 1\n491 551 41\n491 594 33\n491 610 10\n491 613 2\n491 640 40\n491 641 20\n491 661 32\n491 706 5\n491 738 12\n491 759 20\n491 774 50\n491 789 13\n491 806 12\n491 846 38\n491 874 45\n491 892 15\n491 898 44\n491 900 15\n491 918 33\n491 921 1\n491 942 43\n491 953 12\n491 972 7\n491 995 30\n492 8 31\n492 49 37\n492 63 30\n492 89 21\n492 151 15\n492 153 29\n492 177 21\n492 194 37\n492 260 8\n492 318 22\n492 326 7\n492 333 48\n492 351 5\n492 358 20\n492 371 40\n492 379 6\n492 400 10\n492 401 19\n492 419 34\n492 423 19\n492 430 -2\n492 437 18\n492 441 46\n492 464 3\n492 483 40\n492 491 43\n492 532 12\n492 543 -1\n492 596 42\n492 608 23\n492 618 4\n492 622 38\n492 641 15\n492 648 48\n492 670 4\n492 699 45\n492 747 2\n492 750 2\n492 779 34\n492 873 16\n492 904 30\n492 983 19\n492 992 37\n493 10 27\n493 38 50\n493 52 15\n493 98 11\n493 139 1\n493 150 30\n493 162 34\n493 220 23\n493 242 16\n493 284 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25\n494 702 24\n494 712 0\n494 718 17\n494 726 0\n494 747 32\n494 781 26\n494 801 8\n494 846 37\n494 871 48\n494 894 7\n494 920 32\n494 944 25\n494 957 19\n494 973 19\n495 14 30\n495 50 41\n495 54 -2\n495 61 32\n495 75 48\n495 76 27\n495 89 43\n495 90 25\n495 102 46\n495 108 39\n495 138 17\n495 142 35\n495 143 9\n495 193 7\n495 210 15\n495 241 2\n495 243 3\n495 262 -1\n495 274 15\n495 300 43\n495 329 49\n495 343 5\n495 348 32\n495 362 23\n495 389 50\n495 406 34\n495 418 10\n495 420 27\n495 441 5\n495 472 13\n495 483 6\n495 496 8\n495 508 47\n495 550 38\n495 554 31\n495 639 39\n495 641 31\n495 644 36\n495 677 4\n495 729 34\n495 763 15\n495 809 36\n495 834 18\n495 843 5\n495 868 29\n495 903 13\n495 925 10\n495 971 18\n495 979 13\n495 992 30\n495 994 43\n496 23 11\n496 34 20\n496 41 40\n496 52 33\n496 53 26\n496 76 13\n496 87 26\n496 91 7\n496 118 35\n496 134 37\n496 146 50\n496 147 15\n496 191 21\n496 198 27\n496 199 48\n496 258 32\n496 296 15\n496 316 9\n496 320 23\n496 323 8\n496 325 6\n496 362 11\n496 366 38\n496 370 17\n496 382 35\n496 389 15\n496 391 16\n496 419 10\n496 508 1\n496 510 29\n496 513 21\n496 520 22\n496 537 18\n496 543 3\n496 572 36\n496 580 37\n496 610 43\n496 654 20\n496 706 38\n496 714 29\n496 723 13\n496 746 22\n496 749 39\n496 766 46\n496 784 43\n496 789 20\n496 833 25\n496 841 45\n496 862 30\n496 866 45\n496 915 5\n497 32 45\n497 33 14\n497 61 49\n497 100 39\n497 114 16\n497 123 29\n497 144 18\n497 171 37\n497 181 48\n497 233 40\n497 243 9\n497 245 27\n497 271 27\n497 285 26\n497 293 47\n497 331 38\n497 345 19\n497 355 28\n497 395 -1\n497 426 41\n497 435 6\n497 451 35\n497 483 38\n497 505 36\n497 543 33\n497 559 36\n497 561 9\n497 596 -2\n497 610 47\n497 612 45\n497 663 23\n497 745 1\n497 768 31\n497 785 15\n497 829 7\n497 837 49\n497 915 15\n497 931 10\n497 968 30\n497 979 32\n498 5 10\n498 24 41\n498 32 8\n498 35 31\n498 64 15\n498 70 47\n498 78 24\n498 100 19\n498 109 50\n498 149 10\n498 162 41\n498 165 9\n498 227 26\n498 239 41\n498 284 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39\n499 821 38\n499 900 9\n499 976 14\n499 981 20\n500 87 19\n500 93 20\n500 125 11\n500 170 8\n500 176 13\n500 269 10\n500 274 28\n500 293 25\n500 311 21\n500 314 24\n500 330 31\n500 335 44\n500 337 10\n500 365 29\n500 396 15\n500 406 19\n500 431 23\n500 435 31\n500 441 0\n500 503 9\n500 532 4\n500 534 23\n500 581 10\n500 595 46\n500 611 39\n500 650 25\n500 666 46\n500 667 32\n500 669 15\n500 671 40\n500 690 32\n500 700 44\n500 771 1\n500 788 34\n500 802 22\n500 818 28\n500 841 -2\n500 845 35\n500 858 34\n500 886 12\n500 888 17\n500 890 19\n500 891 30\n500 900 39\n500 908 47\n500 944 44\n500 966 19\n500 992 6\n500 997 17\n500 999 5\n501 2 16\n501 33 7\n501 63 32\n501 89 27\n501 100 -2\n501 121 47\n501 133 19\n501 152 11\n501 154 9\n501 250 39\n501 325 48\n501 330 9\n501 371 8\n501 403 30\n501 427 17\n501 450 27\n501 494 34\n501 502 1\n501 510 11\n501 517 41\n501 556 50\n501 572 16\n501 589 12\n501 601 9\n501 689 25\n501 696 24\n501 711 26\n501 717 34\n501 753 10\n501 762 33\n501 786 24\n501 795 33\n501 804 35\n501 835 12\n501 857 23\n501 873 17\n501 891 35\n501 919 17\n501 955 26\n502 91 19\n502 179 50\n502 210 41\n502 228 49\n502 245 6\n502 254 21\n502 261 11\n502 322 43\n502 340 44\n502 360 30\n502 369 4\n502 375 15\n502 380 41\n502 387 44\n502 437 36\n502 486 48\n502 488 14\n502 495 28\n502 504 34\n502 507 12\n502 565 50\n502 579 21\n502 631 1\n502 633 14\n502 671 14\n502 676 24\n502 690 22\n502 729 35\n502 735 35\n502 741 42\n502 779 5\n502 801 18\n502 833 38\n502 835 26\n502 859 15\n502 906 40\n502 979 49\n503 20 42\n503 96 6\n503 101 49\n503 190 44\n503 210 30\n503 213 32\n503 217 47\n503 231 10\n503 260 30\n503 273 34\n503 275 40\n503 309 20\n503 363 26\n503 366 49\n503 369 29\n503 382 36\n503 388 48\n503 401 25\n503 457 40\n503 489 24\n503 502 -1\n503 518 41\n503 528 47\n503 536 49\n503 537 -2\n503 539 14\n503 565 10\n503 592 4\n503 594 23\n503 600 7\n503 652 16\n503 655 43\n503 658 15\n503 681 19\n503 716 32\n503 780 15\n503 781 11\n503 784 49\n503 810 15\n503 811 40\n503 823 31\n503 836 34\n503 843 23\n503 924 9\n503 931 35\n503 981 18\n503 993 9\n503 994 48\n504 17 2\n504 35 -2\n504 64 2\n504 75 28\n504 152 29\n504 159 12\n504 186 34\n504 208 21\n504 223 49\n504 231 40\n504 254 46\n504 265 19\n504 282 26\n504 292 16\n504 296 48\n504 300 34\n504 314 5\n504 341 -2\n504 346 35\n504 347 8\n504 382 13\n504 393 -1\n504 483 47\n504 508 50\n504 525 38\n504 538 38\n504 544 2\n504 605 41\n504 621 50\n504 638 -2\n504 644 49\n504 662 20\n504 695 23\n504 696 49\n504 702 18\n504 714 -1\n504 720 19\n504 722 21\n504 735 13\n504 740 31\n504 761 45\n504 781 46\n504 799 23\n504 863 17\n504 876 20\n504 902 33\n504 910 -1\n504 921 45\n504 922 28\n504 923 46\n504 942 19\n504 955 5\n504 965 11\n504 973 7\n504 995 13\n505 11 -1\n505 33 9\n505 40 13\n505 41 10\n505 76 24\n505 85 22\n505 113 39\n505 133 20\n505 137 42\n505 140 42\n505 143 25\n505 161 26\n505 235 45\n505 249 16\n505 263 21\n505 271 17\n505 304 42\n505 322 6\n505 325 10\n505 341 12\n505 364 10\n505 374 0\n505 411 48\n505 412 1\n505 416 48\n505 472 19\n505 481 35\n505 506 18\n505 514 9\n505 554 15\n505 555 37\n505 571 14\n505 575 48\n505 590 35\n505 599 50\n505 604 9\n505 606 41\n505 607 41\n505 621 31\n505 661 9\n505 665 24\n505 687 48\n505 721 29\n505 740 40\n505 784 11\n505 814 48\n505 841 28\n505 868 7\n505 880 41\n505 882 38\n505 904 27\n505 919 33\n505 926 24\n505 940 15\n505 943 22\n505 954 20\n505 968 30\n505 974 47\n506 25 21\n506 31 30\n506 52 14\n506 62 4\n506 71 49\n506 77 43\n506 99 1\n506 136 24\n506 141 20\n506 162 38\n506 205 41\n506 226 18\n506 296 49\n506 312 35\n506 316 12\n506 366 23\n506 390 -1\n506 411 4\n506 434 34\n506 498 38\n506 527 21\n506 531 22\n506 537 12\n506 549 6\n506 550 32\n506 580 7\n506 628 36\n506 659 21\n506 678 26\n506 682 14\n506 696 24\n506 730 -2\n506 780 38\n506 805 30\n506 816 46\n506 820 2\n506 846 -2\n506 938 25\n506 944 42\n506 963 40\n506 991 42\n506 992 19\n507 9 43\n507 30 9\n507 154 35\n507 193 14\n507 220 48\n507 243 4\n507 253 25\n507 271 20\n507 273 -1\n507 301 22\n507 330 30\n507 355 49\n507 402 10\n507 455 19\n507 461 29\n507 474 31\n507 483 4\n507 516 39\n507 522 33\n507 538 15\n507 547 41\n507 581 28\n507 605 37\n507 662 18\n507 676 11\n507 680 5\n507 691 43\n507 709 6\n507 724 26\n507 740 3\n507 814 48\n507 859 25\n507 867 46\n507 895 31\n507 904 13\n507 928 28\n507 937 3\n507 980 0\n507 981 21\n508 4 39\n508 16 6\n508 17 -1\n508 21 4\n508 25 32\n508 92 33\n508 95 1\n508 108 34\n508 113 42\n508 174 16\n508 183 36\n508 184 22\n508 187 24\n508 201 22\n508 202 30\n508 235 10\n508 266 19\n508 284 14\n508 302 44\n508 303 49\n508 349 14\n508 378 8\n508 380 36\n508 429 25\n508 444 45\n508 451 19\n508 452 29\n508 478 23\n508 488 35\n508 502 3\n508 519 48\n508 533 29\n508 546 44\n508 553 8\n508 560 37\n508 586 20\n508 621 46\n508 623 39\n508 652 1\n508 663 31\n508 744 13\n508 784 47\n508 785 37\n508 815 6\n508 856 47\n508 891 30\n508 932 30\n508 996 20\n509 15 11\n509 26 49\n509 98 18\n509 103 42\n509 107 49\n509 115 35\n509 116 4\n509 168 30\n509 171 44\n509 179 4\n509 191 31\n509 203 34\n509 256 44\n509 280 16\n509 284 35\n509 326 48\n509 346 8\n509 362 49\n509 367 9\n509 370 46\n509 385 0\n509 390 10\n509 412 28\n509 433 4\n509 463 48\n509 488 14\n509 495 46\n509 522 28\n509 561 12\n509 611 31\n509 662 20\n509 685 24\n509 704 45\n509 727 5\n509 761 46\n509 764 49\n509 772 14\n509 781 28\n509 807 31\n509 813 50\n509 814 48\n509 836 17\n509 895 28\n509 919 38\n509 922 37\n509 956 10\n510 33 31\n510 47 42\n510 116 46\n510 127 17\n510 156 37\n510 163 26\n510 164 42\n510 191 0\n510 210 24\n510 230 28\n510 242 36\n510 304 49\n510 308 15\n510 360 32\n510 380 34\n510 384 41\n510 399 22\n510 410 31\n510 412 27\n510 416 41\n510 456 43\n510 473 25\n510 482 35\n510 499 10\n510 560 19\n510 565 41\n510 577 13\n510 581 42\n510 583 17\n510 594 50\n510 723 32\n510 756 47\n510 766 32\n510 776 42\n510 799 6\n510 824 33\n510 836 11\n510 867 17\n510 868 40\n510 874 44\n510 876 49\n510 906 18\n510 909 5\n510 914 12\n510 950 18\n510 979 43\n510 980 41\n510 990 32\n511 44 35\n511 66 42\n511 79 40\n511 119 30\n511 122 31\n511 158 13\n511 188 11\n511 203 17\n511 210 42\n511 241 17\n511 255 12\n511 258 8\n511 322 41\n511 342 5\n511 354 22\n511 357 22\n511 379 44\n511 408 9\n511 420 48\n511 436 50\n511 464 -2\n511 478 37\n511 495 22\n511 510 21\n511 539 39\n511 628 4\n511 638 24\n511 721 16\n511 740 3\n511 741 23\n511 747 26\n511 777 24\n511 786 31\n511 826 25\n511 839 47\n511 868 39\n511 892 35\n511 921 18\n511 951 0\n512 1 50\n512 33 11\n512 70 38\n512 109 21\n512 114 40\n512 119 10\n512 129 31\n512 138 4\n512 178 18\n512 198 48\n512 231 49\n512 233 45\n512 243 10\n512 246 2\n512 247 22\n512 249 40\n512 297 19\n512 309 5\n512 346 50\n512 390 37\n512 391 3\n512 397 13\n512 406 23\n512 443 9\n512 460 43\n512 494 22\n512 552 37\n512 569 21\n512 570 11\n512 595 26\n512 607 8\n512 673 6\n512 684 22\n512 702 8\n512 703 13\n512 721 8\n512 725 25\n512 748 14\n512 797 36\n512 810 39\n512 820 34\n512 846 14\n512 847 9\n512 849 44\n512 871 33\n512 875 46\n512 879 12\n512 886 38\n512 931 35\n512 947 45\n512 960 18\n512 966 7\n512 968 34\n512 975 14\n512 993 21\n513 16 8\n513 33 9\n513 51 28\n513 63 21\n513 70 22\n513 75 27\n513 95 47\n513 101 17\n513 113 21\n513 130 4\n513 155 21\n513 157 26\n513 178 4\n513 180 22\n513 194 1\n513 232 10\n513 233 26\n513 241 -1\n513 260 19\n513 268 14\n513 274 27\n513 279 36\n513 299 32\n513 327 43\n513 405 19\n513 453 32\n513 460 9\n513 473 18\n513 494 39\n513 515 31\n513 588 -2\n513 617 44\n513 636 45\n513 646 33\n513 666 23\n513 695 44\n513 706 -1\n513 721 39\n513 740 36\n513 743 41\n513 746 10\n513 772 16\n513 778 43\n513 783 10\n513 819 18\n513 843 31\n513 852 40\n513 964 48\n514 11 41\n514 18 50\n514 44 -1\n514 54 24\n514 63 17\n514 71 9\n514 81 25\n514 95 37\n514 110 27\n514 141 49\n514 157 0\n514 158 34\n514 180 37\n514 192 28\n514 195 14\n514 241 49\n514 248 41\n514 263 37\n514 265 6\n514 295 19\n514 306 26\n514 325 46\n514 326 10\n514 327 44\n514 330 38\n514 349 15\n514 384 19\n514 385 14\n514 393 11\n514 397 14\n514 407 12\n514 452 33\n514 473 19\n514 475 10\n514 493 38\n514 531 17\n514 631 46\n514 650 28\n514 666 26\n514 674 39\n514 706 41\n514 733 21\n514 770 23\n514 783 14\n514 800 32\n514 806 6\n514 862 -2\n514 863 11\n514 884 32\n514 937 3\n514 951 8\n514 996 30\n515 17 29\n515 32 39\n515 34 0\n515 62 16\n515 80 48\n515 81 20\n515 82 -2\n515 90 32\n515 96 34\n515 180 10\n515 191 0\n515 213 41\n515 227 48\n515 252 12\n515 294 4\n515 396 9\n515 462 26\n515 491 28\n515 526 0\n515 527 23\n515 565 16\n515 598 28\n515 600 39\n515 638 47\n515 649 25\n515 674 46\n515 681 45\n515 696 35\n515 711 14\n515 715 10\n515 742 42\n515 768 24\n515 812 35\n515 817 50\n515 853 50\n515 870 15\n515 875 17\n515 903 8\n515 930 4\n515 932 31\n515 937 25\n516 33 12\n516 50 43\n516 52 34\n516 83 41\n516 85 46\n516 115 3\n516 142 35\n516 158 4\n516 182 37\n516 216 6\n516 227 35\n516 238 46\n516 262 19\n516 285 3\n516 305 39\n516 324 44\n516 326 13\n516 337 16\n516 351 42\n516 352 17\n516 353 43\n516 375 47\n516 386 28\n516 399 28\n516 407 39\n516 418 12\n516 443 22\n516 458 6\n516 512 10\n516 547 28\n516 555 21\n516 567 15\n516 588 44\n516 590 10\n516 621 50\n516 636 9\n516 653 32\n516 694 9\n516 702 13\n516 760 40\n516 806 21\n516 845 39\n516 873 29\n516 876 39\n516 903 28\n517 5 -1\n517 9 17\n517 42 4\n517 51 1\n517 76 16\n517 92 3\n517 110 35\n517 134 33\n517 140 7\n517 188 24\n517 197 10\n517 226 38\n517 272 48\n517 317 46\n517 326 13\n517 353 35\n517 355 35\n517 363 13\n517 412 12\n517 419 -1\n517 428 6\n517 458 10\n517 479 33\n517 497 27\n517 520 36\n517 525 32\n517 532 30\n517 583 45\n517 592 29\n517 593 31\n517 602 41\n517 614 20\n517 618 50\n517 622 49\n517 653 6\n517 684 24\n517 689 19\n517 696 16\n517 794 20\n517 798 33\n517 812 26\n517 848 41\n517 855 49\n517 857 12\n517 894 -2\n517 913 49\n517 979 40\n517 980 38\n518 10 7\n518 18 8\n518 47 25\n518 54 13\n518 61 8\n518 71 15\n518 75 35\n518 108 29\n518 117 47\n518 121 41\n518 153 16\n518 172 20\n518 238 33\n518 246 39\n518 252 21\n518 265 8\n518 273 15\n518 285 42\n518 293 46\n518 318 16\n518 404 2\n518 417 35\n518 419 50\n518 422 12\n518 466 26\n518 512 32\n518 515 8\n518 550 34\n518 555 13\n518 584 -2\n518 591 44\n518 614 9\n518 616 22\n518 635 13\n518 640 10\n518 648 42\n518 671 11\n518 681 11\n518 695 45\n518 705 45\n518 721 18\n518 726 17\n518 756 23\n518 757 30\n518 770 23\n518 780 25\n518 810 14\n518 838 12\n518 872 16\n518 915 50\n518 941 16\n518 951 28\n518 974 30\n518 995 15\n519 11 1\n519 30 23\n519 47 10\n519 70 10\n519 82 44\n519 161 28\n519 166 4\n519 169 21\n519 191 16\n519 226 7\n519 254 41\n519 257 9\n519 320 22\n519 341 30\n519 344 42\n519 347 12\n519 348 42\n519 383 23\n519 387 50\n519 455 10\n519 480 42\n519 490 8\n519 582 35\n519 611 31\n519 624 11\n519 639 2\n519 652 47\n519 684 11\n519 704 21\n519 735 28\n519 743 26\n519 776 44\n519 794 31\n519 907 33\n519 935 34\n519 942 10\n519 975 19\n519 982 14\n519 992 7\n520 36 42\n520 37 0\n520 47 47\n520 61 4\n520 75 30\n520 78 24\n520 84 29\n520 86 2\n520 122 13\n520 123 23\n520 201 6\n520 268 0\n520 285 36\n520 298 29\n520 327 49\n520 348 19\n520 424 38\n520 433 41\n520 498 31\n520 500 16\n520 510 32\n520 515 29\n520 560 39\n520 562 44\n520 585 39\n520 591 14\n520 599 9\n520 619 32\n520 624 40\n520 628 37\n520 666 42\n520 669 21\n520 684 43\n520 704 18\n520 724 33\n520 731 42\n520 767 -1\n520 792 45\n520 908 45\n520 926 23\n520 957 40\n521 26 19\n521 40 13\n521 57 18\n521 88 34\n521 121 24\n521 130 22\n521 152 44\n521 155 29\n521 158 22\n521 168 43\n521 210 37\n521 228 43\n521 254 31\n521 280 32\n521 295 9\n521 308 9\n521 333 21\n521 381 46\n521 414 7\n521 415 34\n521 476 6\n521 480 30\n521 490 3\n521 503 31\n521 555 22\n521 570 43\n521 612 40\n521 689 40\n521 697 22\n521 731 37\n521 739 31\n521 740 45\n521 762 23\n521 774 30\n521 798 15\n521 811 17\n521 813 37\n521 836 9\n521 840 10\n521 881 48\n521 918 1\n521 925 44\n521 926 17\n521 927 21\n521 939 50\n521 951 10\n521 985 5\n521 994 20\n522 3 21\n522 21 42\n522 56 18\n522 64 47\n522 65 3\n522 77 45\n522 79 12\n522 112 42\n522 134 14\n522 192 0\n522 212 4\n522 214 12\n522 231 32\n522 240 3\n522 288 21\n522 317 32\n522 334 20\n522 343 39\n522 367 45\n522 410 37\n522 411 41\n522 416 28\n522 417 18\n522 430 2\n522 475 10\n522 540 0\n522 572 32\n522 583 16\n522 584 29\n522 623 15\n522 635 28\n522 655 34\n522 717 3\n522 726 23\n522 727 25\n522 751 44\n522 752 3\n522 780 42\n522 836 -1\n522 837 44\n522 844 4\n522 857 44\n522 861 7\n522 862 42\n522 893 36\n522 894 3\n522 930 2\n522 972 -1\n523 54 11\n523 55 50\n523 63 15\n523 64 19\n523 73 47\n523 95 1\n523 111 20\n523 127 23\n523 137 5\n523 155 32\n523 170 17\n523 226 -1\n523 239 9\n523 296 23\n523 301 45\n523 306 2\n523 319 42\n523 416 21\n523 449 19\n523 471 20\n523 524 35\n523 528 16\n523 551 31\n523 553 26\n523 557 45\n523 587 18\n523 592 15\n523 598 3\n523 622 45\n523 675 26\n523 691 7\n523 700 17\n523 713 6\n523 730 2\n523 739 36\n523 747 36\n523 758 16\n523 788 24\n523 848 -1\n523 853 0\n523 890 34\n523 900 0\n523 978 16\n524 11 3\n524 40 24\n524 45 40\n524 66 33\n524 69 21\n524 154 22\n524 170 8\n524 180 30\n524 205 5\n524 207 32\n524 233 39\n524 260 34\n524 269 39\n524 282 20\n524 288 17\n524 306 7\n524 307 41\n524 319 47\n524 333 45\n524 337 30\n524 341 2\n524 379 49\n524 385 20\n524 478 17\n524 499 47\n524 500 32\n524 538 26\n524 565 -1\n524 566 39\n524 579 28\n524 620 23\n524 624 39\n524 648 40\n524 699 17\n524 726 33\n524 735 14\n524 743 21\n524 798 44\n524 812 28\n524 816 28\n524 826 13\n524 832 38\n524 880 9\n524 889 42\n524 955 2\n524 1000 33\n525 1 24\n525 30 8\n525 44 17\n525 81 48\n525 109 10\n525 141 30\n525 144 15\n525 156 32\n525 237 39\n525 253 31\n525 263 16\n525 289 32\n525 305 48\n525 329 5\n525 334 50\n525 337 39\n525 348 12\n525 354 18\n525 389 30\n525 458 6\n525 464 37\n525 516 20\n525 538 7\n525 566 47\n525 583 38\n525 607 42\n525 624 1\n525 628 38\n525 675 12\n525 681 37\n525 684 46\n525 741 24\n525 742 29\n525 753 4\n525 761 31\n525 793 -1\n525 819 25\n525 865 39\n525 866 19\n525 902 16\n525 958 35\n525 990 31\n526 8 25\n526 44 3\n526 76 10\n526 88 1\n526 106 11\n526 111 38\n526 121 48\n526 176 50\n526 182 13\n526 192 45\n526 194 44\n526 200 28\n526 226 33\n526 263 11\n526 279 15\n526 286 27\n526 297 44\n526 315 30\n526 318 25\n526 344 16\n526 347 14\n526 352 50\n526 354 50\n526 374 19\n526 421 38\n526 422 -2\n526 438 32\n526 477 42\n526 497 5\n526 500 4\n526 580 8\n526 604 9\n526 685 35\n526 702 22\n526 705 26\n526 721 33\n526 727 1\n526 737 48\n526 743 32\n526 776 10\n526 779 2\n526 805 33\n526 806 32\n526 819 2\n526 822 44\n526 833 18\n526 834 34\n526 855 35\n526 857 39\n526 870 44\n526 892 45\n526 924 4\n526 928 47\n526 944 6\n526 987 26\n527 21 8\n527 53 15\n527 56 42\n527 58 49\n527 68 11\n527 117 45\n527 143 4\n527 155 47\n527 162 48\n527 167 36\n527 202 42\n527 209 17\n527 231 15\n527 234 29\n527 239 48\n527 281 17\n527 287 39\n527 335 50\n527 370 16\n527 381 41\n527 387 38\n527 394 4\n527 425 20\n527 432 16\n527 458 37\n527 460 11\n527 465 35\n527 507 45\n527 511 7\n527 564 4\n527 571 42\n527 574 10\n527 587 32\n527 598 38\n527 604 36\n527 627 2\n527 643 2\n527 664 11\n527 674 9\n527 678 46\n527 682 9\n527 708 21\n527 710 5\n527 758 46\n527 778 45\n527 819 0\n527 827 33\n527 847 48\n527 854 -2\n527 858 18\n527 866 39\n527 870 27\n527 902 1\n527 909 30\n527 946 40\n527 978 22\n528 25 6\n528 80 21\n528 84 23\n528 94 12\n528 108 42\n528 114 36\n528 123 23\n528 148 14\n528 153 -2\n528 170 34\n528 178 22\n528 204 20\n528 216 22\n528 224 7\n528 230 18\n528 263 32\n528 265 5\n528 287 7\n528 317 1\n528 335 10\n528 342 31\n528 418 25\n528 431 0\n528 437 49\n528 467 27\n528 487 15\n528 503 8\n528 520 10\n528 544 18\n528 578 30\n528 591 6\n528 634 48\n528 641 41\n528 653 3\n528 662 11\n528 714 44\n528 745 50\n528 751 19\n528 773 45\n528 785 36\n528 796 50\n528 823 48\n528 851 17\n528 884 37\n528 910 50\n528 912 11\n528 933 22\n528 939 40\n528 949 49\n528 955 36\n529 10 41\n529 13 21\n529 14 3\n529 24 26\n529 49 6\n529 52 6\n529 54 34\n529 89 22\n529 162 7\n529 171 25\n529 178 -1\n529 196 4\n529 201 22\n529 206 -2\n529 219 25\n529 239 30\n529 256 24\n529 261 25\n529 284 33\n529 342 27\n529 345 36\n529 352 15\n529 353 18\n529 354 49\n529 355 4\n529 358 36\n529 391 40\n529 398 42\n529 415 42\n529 448 39\n529 457 8\n529 464 17\n529 488 0\n529 493 33\n529 524 27\n529 525 16\n529 532 21\n529 596 30\n529 613 41\n529 647 48\n529 665 29\n529 678 10\n529 693 49\n529 698 9\n529 728 5\n529 729 13\n529 747 31\n529 750 36\n529 755 20\n529 762 24\n529 764 4\n529 794 5\n529 822 49\n529 857 34\n529 868 49\n529 875 5\n529 909 9\n529 917 27\n529 927 48\n529 930 12\n529 931 34\n529 986 2\n530 11 36\n530 24 10\n530 58 13\n530 94 -2\n530 99 11\n530 118 38\n530 120 5\n530 147 5\n530 156 12\n530 199 44\n530 204 29\n530 210 7\n530 256 7\n530 263 1\n530 270 8\n530 271 19\n530 274 6\n530 280 35\n530 282 36\n530 301 1\n530 322 9\n530 345 43\n530 351 26\n530 363 33\n530 395 27\n530 419 40\n530 428 39\n530 451 9\n530 471 13\n530 476 11\n530 482 2\n530 492 19\n530 504 34\n530 515 11\n530 556 5\n530 570 34\n530 582 1\n530 626 14\n530 629 31\n530 647 12\n530 668 24\n530 748 14\n530 758 30\n530 796 14\n530 831 47\n530 856 29\n530 881 12\n530 898 20\n530 905 39\n530 985 19\n531 39 23\n531 75 14\n531 78 32\n531 102 4\n531 109 -1\n531 123 13\n531 130 43\n531 189 10\n531 193 43\n531 228 26\n531 242 6\n531 252 6\n531 254 34\n531 264 43\n531 267 4\n531 294 39\n531 299 17\n531 305 24\n531 307 13\n531 321 24\n531 393 -1\n531 402 11\n531 436 6\n531 472 12\n531 478 24\n531 533 38\n531 535 18\n531 556 43\n531 584 32\n531 593 21\n531 618 46\n531 690 5\n531 815 8\n531 818 6\n531 822 46\n531 832 47\n531 836 22\n531 845 30\n531 874 22\n531 926 49\n531 939 36\n531 949 30\n531 974 3\n532 7 10\n532 21 18\n532 51 6\n532 65 39\n532 93 30\n532 121 40\n532 219 38\n532 220 38\n532 225 12\n532 257 37\n532 275 47\n532 315 34\n532 419 27\n532 424 48\n532 436 28\n532 443 36\n532 470 18\n532 473 39\n532 480 47\n532 487 36\n532 507 33\n532 510 -1\n532 544 42\n532 602 25\n532 611 14\n532 629 31\n532 658 26\n532 660 1\n532 662 30\n532 667 42\n532 674 39\n532 678 1\n532 680 47\n532 690 20\n532 708 3\n532 724 17\n532 763 49\n532 786 18\n532 794 40\n532 814 34\n532 862 2\n532 883 37\n532 884 34\n532 899 35\n532 905 19\n532 990 34\n533 19 9\n533 57 37\n533 76 44\n533 93 11\n533 108 47\n533 112 19\n533 155 26\n533 157 35\n533 165 47\n533 166 18\n533 173 7\n533 205 6\n533 210 13\n533 234 47\n533 257 29\n533 259 18\n533 266 20\n533 277 47\n533 300 41\n533 313 19\n533 321 43\n533 357 45\n533 372 35\n533 376 47\n533 395 15\n533 414 40\n533 441 7\n533 449 50\n533 523 35\n533 536 1\n533 580 17\n533 627 31\n533 663 19\n533 682 -1\n533 690 2\n533 711 24\n533 727 37\n533 732 29\n533 753 40\n533 755 9\n533 772 -2\n533 784 40\n533 802 10\n533 820 -2\n533 870 28\n533 885 16\n533 886 11\n533 904 28\n533 936 5\n533 941 35\n533 944 39\n533 988 28\n533 992 9\n534 28 17\n534 47 14\n534 49 17\n534 70 37\n534 83 31\n534 96 41\n534 104 11\n534 115 21\n534 156 14\n534 198 35\n534 207 10\n534 210 49\n534 235 14\n534 273 36\n534 289 6\n534 306 42\n534 373 25\n534 396 4\n534 412 21\n534 420 5\n534 436 28\n534 440 17\n534 451 10\n534 457 29\n534 458 36\n534 464 15\n534 469 0\n534 470 50\n534 483 15\n534 532 16\n534 541 0\n534 575 50\n534 584 11\n534 598 1\n534 605 17\n534 627 18\n534 635 18\n534 665 39\n534 691 13\n534 720 30\n534 721 3\n534 779 25\n534 819 22\n534 834 5\n534 846 30\n534 878 41\n534 920 15\n534 936 49\n534 982 28\n535 40 41\n535 64 0\n535 115 37\n535 134 5\n535 151 36\n535 164 20\n535 182 42\n535 211 22\n535 216 26\n535 221 41\n535 235 17\n535 245 46\n535 264 46\n535 282 -2\n535 292 25\n535 342 38\n535 381 25\n535 431 10\n535 440 33\n535 444 4\n535 485 29\n535 491 27\n535 558 29\n535 559 37\n535 615 32\n535 616 26\n535 647 14\n535 704 -1\n535 772 31\n535 777 4\n535 788 4\n535 800 21\n535 836 3\n535 875 34\n535 890 46\n535 938 27\n535 967 28\n535 975 47\n536 13 40\n536 14 18\n536 34 11\n536 55 15\n536 66 38\n536 91 8\n536 107 6\n536 117 47\n536 149 9\n536 168 15\n536 180 24\n536 181 27\n536 194 41\n536 243 40\n536 247 31\n536 257 46\n536 279 50\n536 292 43\n536 334 9\n536 337 30\n536 342 8\n536 356 23\n536 359 22\n536 371 43\n536 372 14\n536 380 13\n536 411 1\n536 413 40\n536 471 24\n536 501 10\n536 511 38\n536 561 1\n536 564 2\n536 588 3\n536 589 16\n536 637 35\n536 647 37\n536 650 28\n536 677 33\n536 715 30\n536 716 11\n536 717 27\n536 730 16\n536 742 7\n536 758 2\n536 771 50\n536 778 18\n536 779 12\n536 825 38\n536 853 47\n536 864 9\n536 872 2\n536 889 20\n536 900 30\n536 969 1\n536 987 2\n536 990 48\n537 43 30\n537 74 49\n537 90 -1\n537 110 16\n537 158 50\n537 192 45\n537 222 29\n537 254 46\n537 281 23\n537 284 5\n537 323 48\n537 377 11\n537 382 0\n537 428 15\n537 513 29\n537 526 24\n537 543 42\n537 549 38\n537 559 48\n537 607 32\n537 629 45\n537 633 33\n537 653 29\n537 659 39\n537 661 45\n537 695 23\n537 732 34\n537 830 16\n537 928 41\n537 933 27\n537 964 17\n537 981 38\n537 997 21\n538 9 17\n538 109 13\n538 117 9\n538 193 6\n538 244 31\n538 267 38\n538 289 31\n538 305 48\n538 337 23\n538 342 16\n538 355 16\n538 404 26\n538 405 7\n538 424 48\n538 426 42\n538 442 15\n538 475 33\n538 485 36\n538 509 25\n538 584 16\n538 587 29\n538 622 43\n538 642 44\n538 659 35\n538 660 31\n538 684 27\n538 700 26\n538 703 26\n538 717 18\n538 722 48\n538 731 28\n538 733 35\n538 764 28\n538 796 13\n538 801 42\n538 819 27\n538 863 41\n538 900 10\n538 924 14\n538 951 4\n538 954 40\n538 964 17\n539 28 1\n539 100 35\n539 104 38\n539 109 13\n539 131 29\n539 144 9\n539 197 19\n539 227 9\n539 250 31\n539 296 48\n539 321 23\n539 341 43\n539 346 27\n539 358 6\n539 419 23\n539 432 45\n539 443 39\n539 454 42\n539 493 46\n539 502 36\n539 503 23\n539 524 41\n539 540 29\n539 552 29\n539 582 43\n539 586 2\n539 627 38\n539 667 0\n539 700 19\n539 703 39\n539 715 46\n539 718 42\n539 729 48\n539 750 -1\n539 769 37\n539 812 22\n539 881 11\n539 892 43\n539 907 41\n539 953 22\n539 961 10\n539 996 32\n540 25 28\n540 92 5\n540 111 7\n540 124 6\n540 130 48\n540 138 27\n540 141 44\n540 147 27\n540 202 29\n540 214 7\n540 254 33\n540 299 17\n540 332 19\n540 375 42\n540 381 41\n540 391 18\n540 400 32\n540 404 33\n540 425 1\n540 445 39\n540 449 29\n540 455 13\n540 467 30\n540 482 45\n540 489 29\n540 506 25\n540 535 47\n540 600 47\n540 627 11\n540 636 41\n540 637 48\n540 648 44\n540 677 24\n540 694 27\n540 699 43\n540 705 3\n540 714 9\n540 756 9\n540 765 14\n540 767 40\n540 785 -2\n540 786 41\n540 806 4\n540 808 45\n540 822 6\n540 834 27\n540 847 18\n540 910 20\n540 936 44\n540 970 -1\n540 979 6\n541 10 47\n541 47 11\n541 48 41\n541 71 28\n541 82 16\n541 117 26\n541 144 10\n541 230 16\n541 244 38\n541 295 12\n541 319 28\n541 341 28\n541 349 43\n541 360 36\n541 371 21\n541 382 24\n541 434 24\n541 437 38\n541 445 50\n541 456 32\n541 518 42\n541 519 34\n541 565 28\n541 598 35\n541 622 6\n541 623 19\n541 626 45\n541 645 11\n541 672 22\n541 688 50\n541 709 30\n541 713 44\n541 773 45\n541 802 27\n541 820 17\n541 907 8\n541 921 14\n541 951 8\n541 974 2\n542 1 29\n542 4 46\n542 12 8\n542 39 47\n542 46 31\n542 50 9\n542 51 26\n542 77 15\n542 78 37\n542 85 42\n542 92 31\n542 101 30\n542 117 43\n542 130 4\n542 146 35\n542 147 28\n542 179 38\n542 222 27\n542 239 6\n542 251 -2\n542 264 17\n542 265 -2\n542 277 50\n542 318 -2\n542 337 11\n542 346 8\n542 352 15\n542 364 30\n542 374 -1\n542 376 15\n542 394 45\n542 395 37\n542 407 36\n542 414 28\n542 433 48\n542 451 26\n542 509 29\n542 537 42\n542 538 47\n542 552 21\n542 623 28\n542 624 42\n542 705 22\n542 768 37\n542 838 36\n542 839 7\n542 846 22\n542 854 47\n542 863 41\n542 902 48\n542 919 6\n542 939 -2\n542 949 14\n542 956 24\n542 991 47\n543 2 26\n543 52 0\n543 76 29\n543 90 41\n543 93 1\n543 115 11\n543 136 50\n543 138 48\n543 156 23\n543 173 44\n543 200 36\n543 222 18\n543 265 39\n543 297 18\n543 305 45\n543 310 43\n543 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47\n622 346 48\n622 352 23\n622 369 10\n622 382 22\n622 392 28\n622 408 23\n622 443 40\n622 472 30\n622 473 3\n622 497 49\n622 507 36\n622 511 45\n622 512 9\n622 561 45\n622 608 8\n622 650 21\n622 685 36\n622 702 2\n622 721 41\n622 746 17\n622 748 18\n622 752 36\n622 754 38\n622 770 20\n622 774 25\n622 835 30\n622 930 49\n622 944 22\n622 994 15\n623 25 36\n623 27 15\n623 79 42\n623 110 16\n623 118 6\n623 131 10\n623 133 28\n623 215 18\n623 218 11\n623 237 30\n623 256 39\n623 290 11\n623 300 45\n623 308 21\n623 310 26\n623 318 -2\n623 390 42\n623 431 17\n623 442 2\n623 464 31\n623 474 21\n623 505 1\n623 580 4\n623 586 12\n623 629 38\n623 667 50\n623 683 -1\n623 692 41\n623 699 16\n623 724 47\n623 732 7\n623 792 34\n623 793 31\n623 813 37\n623 833 38\n623 838 13\n623 921 8\n623 943 10\n623 974 16\n623 977 44\n623 997 14\n624 5 34\n624 10 18\n624 27 27\n624 28 40\n624 66 13\n624 104 32\n624 126 5\n624 180 12\n624 191 30\n624 192 39\n624 225 20\n624 233 32\n624 238 25\n624 284 38\n624 289 16\n624 332 46\n624 342 27\n624 348 3\n624 352 11\n624 365 13\n624 379 13\n624 411 15\n624 418 19\n624 430 1\n624 436 49\n624 468 29\n624 476 38\n624 513 21\n624 553 39\n624 574 39\n624 628 26\n624 630 18\n624 640 44\n624 682 23\n624 703 9\n624 716 20\n624 738 36\n624 739 23\n624 748 36\n624 761 49\n624 762 39\n624 787 9\n624 836 6\n624 853 44\n624 900 39\n624 932 29\n624 990 39\n624 993 40\n624 996 31\n625 90 9\n625 116 46\n625 129 3\n625 142 37\n625 147 50\n625 206 18\n625 231 2\n625 239 3\n625 277 39\n625 292 23\n625 313 29\n625 316 49\n625 325 21\n625 335 30\n625 336 5\n625 356 28\n625 359 27\n625 403 23\n625 405 4\n625 460 10\n625 462 44\n625 476 50\n625 497 3\n625 519 10\n625 528 38\n625 531 10\n625 535 8\n625 539 38\n625 562 39\n625 566 41\n625 568 22\n625 571 30\n625 579 1\n625 580 2\n625 590 12\n625 597 47\n625 600 17\n625 638 42\n625 655 19\n625 658 36\n625 668 8\n625 693 23\n625 694 29\n625 698 4\n625 704 32\n625 739 4\n625 752 13\n625 759 7\n625 773 21\n625 788 1\n625 805 50\n625 815 26\n625 859 46\n625 861 25\n625 881 11\n625 902 20\n625 905 46\n625 907 32\n625 943 15\n625 945 49\n625 998 23\n626 22 35\n626 110 28\n626 138 17\n626 168 37\n626 169 50\n626 175 6\n626 196 47\n626 210 16\n626 241 8\n626 284 24\n626 299 29\n626 334 1\n626 344 47\n626 355 30\n626 359 23\n626 361 47\n626 404 0\n626 413 16\n626 425 37\n626 431 37\n626 434 19\n626 517 33\n626 521 50\n626 552 22\n626 559 45\n626 610 7\n626 622 41\n626 629 3\n626 672 35\n626 677 49\n626 685 38\n626 696 35\n626 752 31\n626 759 0\n626 761 28\n626 770 34\n626 772 7\n626 780 42\n626 784 9\n626 804 37\n626 815 12\n626 819 13\n626 854 40\n626 862 25\n626 864 46\n626 926 30\n626 994 26\n627 19 13\n627 27 8\n627 34 17\n627 48 35\n627 67 11\n627 77 14\n627 92 49\n627 138 33\n627 162 17\n627 165 41\n627 168 15\n627 202 35\n627 206 45\n627 243 31\n627 245 6\n627 248 35\n627 296 2\n627 297 1\n627 328 9\n627 337 1\n627 380 5\n627 392 20\n627 410 11\n627 411 21\n627 427 -2\n627 472 2\n627 504 34\n627 507 41\n627 516 1\n627 519 11\n627 548 19\n627 611 40\n627 615 15\n627 624 36\n627 775 29\n627 781 38\n627 816 10\n627 824 -1\n627 873 26\n627 898 2\n627 908 22\n627 913 19\n627 924 40\n627 927 15\n627 972 46\n628 4 20\n628 33 28\n628 52 16\n628 119 44\n628 134 34\n628 158 29\n628 160 9\n628 180 37\n628 202 13\n628 222 -2\n628 230 20\n628 238 39\n628 242 22\n628 246 8\n628 324 42\n628 333 48\n628 343 11\n628 348 3\n628 360 35\n628 385 28\n628 389 28\n628 398 12\n628 408 30\n628 459 22\n628 474 8\n628 478 40\n628 483 36\n628 501 50\n628 534 40\n628 587 36\n628 590 24\n628 596 13\n628 605 23\n628 612 15\n628 619 41\n628 643 48\n628 647 48\n628 667 6\n628 674 45\n628 681 18\n628 690 21\n628 707 6\n628 709 46\n628 736 48\n628 759 -1\n628 797 38\n628 807 24\n628 851 31\n628 874 29\n628 887 -2\n628 921 9\n628 924 22\n628 945 41\n628 957 31\n628 971 26\n628 982 10\n629 22 30\n629 27 19\n629 39 11\n629 43 8\n629 52 40\n629 55 50\n629 85 27\n629 88 17\n629 92 46\n629 130 9\n629 187 -2\n629 262 7\n629 269 35\n629 281 27\n629 299 11\n629 336 48\n629 344 20\n629 365 32\n629 406 4\n629 408 4\n629 414 2\n629 416 22\n629 422 8\n629 431 28\n629 443 36\n629 464 43\n629 506 11\n629 507 36\n629 581 25\n629 611 42\n629 615 49\n629 632 32\n629 634 0\n629 650 49\n629 654 39\n629 655 48\n629 663 14\n629 698 36\n629 743 42\n629 748 35\n629 761 10\n629 764 35\n629 793 30\n629 834 26\n629 853 15\n629 855 44\n629 867 41\n629 886 45\n629 910 50\n629 919 8\n629 922 45\n629 944 16\n629 960 39\n629 992 34\n630 42 27\n630 51 31\n630 93 31\n630 153 13\n630 182 37\n630 185 43\n630 226 11\n630 228 44\n630 229 48\n630 232 0\n630 238 48\n630 274 8\n630 278 48\n630 283 46\n630 290 47\n630 309 29\n630 317 10\n630 366 11\n630 374 13\n630 411 9\n630 525 -1\n630 590 8\n630 592 14\n630 617 8\n630 641 4\n630 651 26\n630 656 44\n630 657 6\n630 674 28\n630 678 38\n630 692 11\n630 751 14\n630 759 -2\n630 781 31\n630 802 2\n630 837 44\n630 861 16\n630 878 34\n630 884 15\n630 889 32\n630 895 22\n630 989 42\n631 10 11\n631 50 29\n631 59 25\n631 68 1\n631 71 37\n631 78 35\n631 105 49\n631 107 5\n631 110 38\n631 133 41\n631 178 -2\n631 184 30\n631 192 32\n631 198 45\n631 220 13\n631 241 5\n631 260 43\n631 267 11\n631 279 29\n631 290 27\n631 343 50\n631 382 0\n631 423 28\n631 434 11\n631 452 13\n631 516 27\n631 548 18\n631 561 15\n631 582 16\n631 588 17\n631 602 42\n631 623 8\n631 625 23\n631 654 39\n631 660 9\n631 661 25\n631 673 6\n631 693 20\n631 739 17\n631 768 41\n631 846 9\n631 919 23\n631 942 46\n631 969 36\n631 977 41\n631 981 27\n632 6 6\n632 57 28\n632 61 29\n632 79 49\n632 119 20\n632 134 20\n632 153 9\n632 164 41\n632 180 21\n632 205 25\n632 238 16\n632 255 48\n632 286 31\n632 293 40\n632 299 14\n632 302 7\n632 304 22\n632 340 46\n632 362 4\n632 417 43\n632 427 11\n632 439 28\n632 453 3\n632 494 48\n632 499 41\n632 506 46\n632 516 22\n632 580 7\n632 602 5\n632 620 49\n632 631 16\n632 667 21\n632 693 16\n632 694 18\n632 706 1\n632 720 17\n632 723 28\n632 769 34\n632 771 5\n632 778 26\n632 781 12\n632 795 47\n632 812 22\n632 824 11\n632 833 31\n632 911 37\n632 944 39\n632 957 20\n632 959 33\n632 986 21\n633 6 37\n633 18 38\n633 54 42\n633 88 16\n633 127 19\n633 131 49\n633 184 14\n633 188 14\n633 200 43\n633 206 23\n633 232 15\n633 247 17\n633 317 6\n633 342 34\n633 372 27\n633 382 -2\n633 400 44\n633 404 47\n633 410 17\n633 425 33\n633 455 31\n633 500 44\n633 502 1\n633 504 31\n633 520 38\n633 613 26\n633 617 13\n633 655 19\n633 664 37\n633 687 41\n633 720 40\n633 731 3\n633 736 38\n633 799 7\n633 802 18\n633 825 16\n633 839 29\n633 848 2\n633 860 10\n633 861 17\n633 872 35\n633 900 47\n633 906 5\n633 908 38\n633 914 27\n633 956 21\n633 974 9\n633 986 49\n634 11 33\n634 79 26\n634 110 9\n634 138 32\n634 148 8\n634 158 40\n634 161 12\n634 176 27\n634 217 33\n634 247 46\n634 252 25\n634 294 49\n634 304 39\n634 308 47\n634 326 44\n634 361 42\n634 373 36\n634 376 25\n634 388 14\n634 389 4\n634 411 38\n634 462 41\n634 489 37\n634 493 20\n634 531 40\n634 546 26\n634 621 40\n634 623 26\n634 640 41\n634 678 23\n634 705 11\n634 726 25\n634 867 5\n634 869 9\n634 885 25\n634 896 45\n634 903 47\n634 944 26\n634 962 21\n635 1 18\n635 8 42\n635 15 31\n635 34 3\n635 73 21\n635 89 19\n635 114 18\n635 116 32\n635 117 48\n635 140 21\n635 155 17\n635 161 8\n635 163 20\n635 171 44\n635 175 19\n635 205 37\n635 240 46\n635 245 32\n635 260 36\n635 270 47\n635 324 21\n635 359 40\n635 367 -1\n635 375 37\n635 395 34\n635 420 23\n635 445 25\n635 447 27\n635 459 3\n635 502 44\n635 527 -2\n635 531 40\n635 558 0\n635 573 26\n635 595 19\n635 608 37\n635 612 7\n635 616 35\n635 618 6\n635 619 33\n635 631 32\n635 644 36\n635 664 43\n635 667 13\n635 668 37\n635 679 -1\n635 699 32\n635 713 35\n635 786 14\n635 815 27\n635 820 33\n635 835 1\n635 837 44\n635 852 12\n635 857 1\n635 890 42\n635 900 24\n635 921 4\n635 922 25\n635 963 47\n635 974 6\n635 978 6\n635 989 9\n635 991 13\n635 995 49\n636 9 13\n636 14 33\n636 27 45\n636 40 14\n636 59 -1\n636 101 1\n636 147 41\n636 185 41\n636 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12\n641 311 -1\n641 326 21\n641 332 27\n641 343 26\n641 462 28\n641 464 41\n641 472 28\n641 479 31\n641 485 42\n641 506 6\n641 537 6\n641 550 14\n641 567 2\n641 577 34\n641 581 20\n641 607 46\n641 622 21\n641 640 33\n641 660 0\n641 663 39\n641 670 35\n641 687 43\n641 691 17\n641 697 31\n641 733 11\n641 737 7\n641 776 4\n641 779 20\n641 799 22\n641 864 48\n641 865 41\n641 872 16\n641 931 6\n641 948 12\n641 990 50\n641 992 19\n641 996 14\n642 48 25\n642 49 2\n642 97 26\n642 124 30\n642 141 -2\n642 180 22\n642 181 48\n642 224 43\n642 233 1\n642 242 33\n642 279 23\n642 281 0\n642 336 23\n642 345 21\n642 348 38\n642 362 16\n642 367 9\n642 372 25\n642 423 25\n642 453 1\n642 457 26\n642 495 13\n642 526 5\n642 552 23\n642 586 20\n642 606 31\n642 621 10\n642 626 43\n642 663 29\n642 665 26\n642 678 19\n642 730 27\n642 742 40\n642 756 14\n642 759 19\n642 785 35\n642 830 9\n642 836 39\n642 870 10\n642 877 0\n642 891 0\n642 929 48\n642 957 11\n643 6 45\n643 11 34\n643 17 16\n643 28 13\n643 33 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13\n647 34 3\n647 35 5\n647 70 32\n647 75 6\n647 111 49\n647 150 28\n647 193 32\n647 209 20\n647 238 36\n647 240 38\n647 242 17\n647 255 17\n647 279 32\n647 296 6\n647 349 22\n647 356 27\n647 367 48\n647 381 2\n647 384 8\n647 397 30\n647 411 21\n647 412 36\n647 418 24\n647 426 5\n647 441 18\n647 456 44\n647 472 34\n647 482 22\n647 537 26\n647 593 32\n647 605 19\n647 607 21\n647 620 29\n647 635 48\n647 641 47\n647 658 1\n647 688 37\n647 698 50\n647 705 24\n647 724 34\n647 728 29\n647 739 0\n647 798 29\n647 831 10\n647 832 1\n647 871 31\n647 913 45\n647 928 -1\n647 932 5\n647 947 26\n647 960 13\n647 976 9\n648 21 10\n648 38 24\n648 48 38\n648 71 8\n648 79 27\n648 80 28\n648 84 14\n648 122 46\n648 135 37\n648 142 37\n648 151 47\n648 162 35\n648 168 50\n648 174 50\n648 184 37\n648 187 18\n648 194 38\n648 270 27\n648 281 26\n648 332 13\n648 334 6\n648 400 20\n648 406 2\n648 434 38\n648 439 33\n648 488 21\n648 520 34\n648 530 36\n648 535 22\n648 553 4\n648 556 41\n648 560 14\n648 579 11\n648 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420 -1\n650 422 34\n650 424 5\n650 444 13\n650 451 47\n650 460 45\n650 464 20\n650 479 13\n650 481 49\n650 519 39\n650 548 6\n650 557 26\n650 649 19\n650 692 44\n650 698 38\n650 721 -1\n650 782 8\n650 786 36\n650 795 48\n650 806 43\n650 826 36\n650 845 24\n650 863 9\n650 947 16\n650 968 35\n650 983 31\n651 39 36\n651 40 37\n651 49 25\n651 71 21\n651 128 28\n651 172 50\n651 207 39\n651 226 6\n651 259 21\n651 264 10\n651 272 33\n651 321 17\n651 337 41\n651 366 10\n651 377 48\n651 390 27\n651 431 34\n651 443 7\n651 517 15\n651 519 28\n651 525 46\n651 546 41\n651 556 41\n651 568 4\n651 590 37\n651 593 32\n651 603 24\n651 618 17\n651 630 28\n651 664 9\n651 713 32\n651 726 43\n651 734 -1\n651 736 -2\n651 747 10\n651 751 48\n651 761 3\n651 797 11\n651 801 24\n651 808 22\n651 836 36\n651 864 50\n651 866 16\n651 885 25\n651 907 49\n651 928 33\n651 929 45\n651 938 33\n651 959 2\n651 992 50\n651 995 26\n652 9 38\n652 139 8\n652 178 46\n652 180 20\n652 207 27\n652 262 37\n652 270 6\n652 307 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585 41\n655 586 41\n655 587 2\n655 611 0\n655 625 21\n655 646 16\n655 657 40\n655 661 46\n655 662 41\n655 663 23\n655 678 8\n655 740 27\n655 763 17\n655 765 7\n655 767 31\n655 781 40\n655 793 18\n655 797 49\n655 815 44\n655 818 13\n655 831 36\n655 848 13\n655 850 45\n655 855 1\n655 908 15\n655 960 22\n655 962 25\n655 965 48\n655 970 34\n655 974 16\n655 991 32\n656 26 19\n656 29 48\n656 53 18\n656 75 45\n656 82 -1\n656 96 13\n656 117 20\n656 147 26\n656 165 27\n656 199 28\n656 207 8\n656 208 36\n656 211 32\n656 230 8\n656 267 21\n656 284 28\n656 285 21\n656 301 46\n656 310 -2\n656 374 49\n656 389 13\n656 431 46\n656 439 40\n656 494 42\n656 495 12\n656 502 39\n656 538 46\n656 565 6\n656 574 16\n656 593 40\n656 595 26\n656 603 46\n656 613 24\n656 625 9\n656 637 34\n656 646 41\n656 648 17\n656 652 4\n656 688 28\n656 704 8\n656 706 34\n656 707 48\n656 732 -2\n656 790 31\n656 828 16\n656 837 1\n656 904 44\n656 910 42\n656 911 16\n656 922 13\n656 926 7\n656 940 17\n656 976 28\n657 62 46\n657 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2\n658 824 1\n658 844 24\n658 852 1\n658 868 46\n658 877 10\n658 910 38\n658 913 4\n658 925 23\n658 973 23\n658 975 15\n658 997 12\n659 23 11\n659 29 24\n659 44 46\n659 105 40\n659 130 18\n659 147 43\n659 149 27\n659 160 25\n659 173 8\n659 177 37\n659 196 13\n659 198 23\n659 215 33\n659 222 15\n659 232 12\n659 269 38\n659 291 3\n659 318 40\n659 338 9\n659 386 2\n659 387 32\n659 415 33\n659 423 36\n659 437 33\n659 467 27\n659 491 12\n659 522 12\n659 526 18\n659 594 21\n659 622 34\n659 713 12\n659 742 -1\n659 750 48\n659 794 46\n659 819 29\n659 865 36\n659 882 26\n659 890 45\n659 891 9\n659 916 8\n659 933 12\n659 934 7\n659 947 18\n659 974 29\n659 996 1\n660 22 30\n660 39 19\n660 43 38\n660 46 43\n660 77 19\n660 107 42\n660 190 17\n660 278 17\n660 306 24\n660 326 48\n660 332 22\n660 342 27\n660 460 29\n660 493 48\n660 523 23\n660 555 14\n660 583 24\n660 598 24\n660 668 20\n660 711 11\n660 716 47\n660 719 21\n660 730 35\n660 778 41\n660 788 38\n660 808 34\n660 809 -1\n660 810 39\n660 823 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40\n700 278 37\n700 279 44\n700 345 15\n700 346 13\n700 353 21\n700 379 19\n700 383 48\n700 396 40\n700 449 42\n700 485 50\n700 524 39\n700 527 22\n700 534 27\n700 551 48\n700 552 30\n700 556 21\n700 589 44\n700 611 29\n700 613 31\n700 644 27\n700 719 14\n700 782 15\n700 818 34\n700 857 25\n700 861 31\n700 868 27\n700 871 31\n700 872 46\n700 915 46\n700 934 27\n700 980 34\n700 986 28\n700 994 13\n701 1 9\n701 13 50\n701 40 42\n701 44 32\n701 72 50\n701 76 37\n701 77 18\n701 121 5\n701 196 14\n701 211 43\n701 223 -1\n701 246 15\n701 256 -2\n701 270 43\n701 274 45\n701 305 26\n701 344 42\n701 365 31\n701 373 35\n701 378 19\n701 396 20\n701 477 41\n701 531 40\n701 574 21\n701 586 46\n701 626 37\n701 636 20\n701 639 4\n701 654 46\n701 655 43\n701 695 12\n701 708 4\n701 720 48\n701 728 48\n701 780 39\n701 803 47\n701 804 29\n701 830 14\n701 865 7\n701 898 39\n701 918 6\n701 929 18\n701 942 -2\n701 982 35\n702 11 16\n702 12 49\n702 15 19\n702 47 11\n702 78 27\n702 100 47\n702 107 8\n702 127 9\n702 140 3\n702 195 15\n702 206 10\n702 220 7\n702 234 33\n702 270 5\n702 295 9\n702 296 5\n702 303 -1\n702 319 14\n702 345 22\n702 352 -2\n702 357 10\n702 383 49\n702 396 10\n702 424 42\n702 479 28\n702 499 16\n702 509 41\n702 635 18\n702 638 23\n702 647 39\n702 682 34\n702 688 0\n702 759 45\n702 768 28\n702 773 20\n702 797 21\n702 800 24\n702 805 4\n702 812 10\n702 841 22\n702 863 11\n702 869 24\n702 872 14\n702 956 46\n702 957 25\n702 961 39\n702 968 15\n702 982 43\n702 987 20\n702 991 16\n703 5 44\n703 15 25\n703 49 26\n703 83 26\n703 100 13\n703 103 19\n703 109 39\n703 133 17\n703 136 42\n703 165 31\n703 175 48\n703 220 24\n703 232 9\n703 234 47\n703 242 20\n703 252 48\n703 253 45\n703 375 4\n703 408 43\n703 411 3\n703 417 29\n703 466 19\n703 514 28\n703 518 44\n703 539 31\n703 573 11\n703 588 9\n703 607 5\n703 608 31\n703 624 33\n703 637 11\n703 654 8\n703 677 6\n703 706 37\n703 756 16\n703 760 30\n703 825 27\n703 826 9\n703 832 47\n703 884 1\n703 986 30\n704 11 3\n704 37 32\n704 92 7\n704 95 46\n704 123 30\n704 135 36\n704 140 2\n704 145 40\n704 146 3\n704 270 27\n704 281 13\n704 290 20\n704 306 10\n704 309 28\n704 321 47\n704 326 42\n704 336 15\n704 339 10\n704 400 47\n704 418 13\n704 433 8\n704 450 10\n704 461 34\n704 480 16\n704 485 30\n704 527 30\n704 595 48\n704 614 18\n704 621 20\n704 647 20\n704 655 11\n704 665 37\n704 725 43\n704 766 31\n704 767 50\n704 782 31\n704 808 28\n704 810 40\n704 860 23\n704 885 24\n704 896 30\n704 959 31\n705 5 38\n705 34 25\n705 47 45\n705 60 19\n705 68 7\n705 71 13\n705 107 18\n705 137 32\n705 165 9\n705 171 35\n705 188 5\n705 217 25\n705 222 28\n705 257 44\n705 265 19\n705 266 29\n705 274 22\n705 281 38\n705 287 17\n705 328 22\n705 343 8\n705 345 24\n705 372 14\n705 437 25\n705 438 39\n705 454 27\n705 515 18\n705 535 39\n705 553 18\n705 572 50\n705 647 38\n705 656 39\n705 662 49\n705 671 20\n705 679 10\n705 692 24\n705 740 16\n705 748 37\n705 820 45\n705 832 44\n705 838 22\n705 849 42\n705 856 37\n705 861 44\n705 933 16\n705 984 22\n705 1000 26\n706 6 26\n706 13 19\n706 30 4\n706 44 39\n706 54 35\n706 60 14\n706 69 6\n706 74 16\n706 76 39\n706 84 39\n706 97 20\n706 105 39\n706 113 26\n706 126 8\n706 140 20\n706 150 27\n706 159 42\n706 191 31\n706 199 34\n706 223 29\n706 296 22\n706 300 33\n706 347 24\n706 382 34\n706 386 41\n706 403 46\n706 407 30\n706 441 18\n706 478 2\n706 486 43\n706 532 4\n706 597 44\n706 650 5\n706 682 43\n706 749 19\n706 793 22\n706 797 31\n706 831 26\n706 875 37\n706 879 46\n706 887 12\n706 888 48\n706 902 42\n706 918 34\n706 930 10\n706 996 39\n707 44 13\n707 53 44\n707 111 34\n707 117 40\n707 197 10\n707 202 35\n707 203 45\n707 230 10\n707 282 30\n707 292 8\n707 301 26\n707 322 29\n707 344 39\n707 401 38\n707 415 31\n707 443 37\n707 499 7\n707 532 45\n707 562 32\n707 568 36\n707 668 20\n707 678 38\n707 753 32\n707 773 18\n707 832 18\n707 867 26\n707 878 34\n707 895 20\n707 925 30\n707 932 6\n707 936 6\n707 979 3\n707 990 28\n707 996 23\n708 14 33\n708 41 11\n708 71 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9\n711 881 6\n711 895 7\n711 961 40\n711 965 9\n711 978 37\n711 985 0\n712 26 14\n712 93 22\n712 98 26\n712 120 16\n712 125 16\n712 142 38\n712 146 18\n712 154 25\n712 169 40\n712 179 27\n712 201 2\n712 228 22\n712 264 26\n712 268 21\n712 294 24\n712 307 38\n712 314 22\n712 331 16\n712 345 43\n712 356 46\n712 359 17\n712 363 41\n712 373 36\n712 431 25\n712 434 33\n712 521 22\n712 546 45\n712 557 17\n712 613 30\n712 618 32\n712 668 19\n712 686 36\n712 728 13\n712 828 8\n712 832 42\n712 837 48\n712 844 46\n712 845 40\n712 873 13\n712 891 19\n712 898 22\n712 934 38\n712 942 23\n712 945 15\n712 1000 24\n713 19 42\n713 60 23\n713 76 47\n713 79 37\n713 97 18\n713 133 2\n713 163 26\n713 225 7\n713 256 49\n713 276 22\n713 291 24\n713 321 47\n713 345 42\n713 349 16\n713 382 13\n713 383 20\n713 402 -2\n713 408 46\n713 418 38\n713 428 14\n713 438 -2\n713 499 43\n713 505 5\n713 542 9\n713 547 49\n713 571 42\n713 576 37\n713 661 3\n713 687 37\n713 753 15\n713 777 13\n713 784 10\n713 833 7\n713 863 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716 8\n725 780 9\n725 825 -2\n725 835 4\n725 851 31\n725 866 6\n725 869 17\n725 910 49\n725 926 28\n725 929 43\n725 932 22\n725 947 2\n725 952 49\n725 953 33\n725 966 41\n725 971 49\n725 985 21\n725 997 50\n726 32 44\n726 37 28\n726 45 11\n726 203 28\n726 214 44\n726 217 21\n726 237 44\n726 245 50\n726 269 43\n726 271 47\n726 301 26\n726 308 19\n726 335 15\n726 348 9\n726 366 25\n726 380 27\n726 381 12\n726 430 9\n726 455 9\n726 478 14\n726 557 2\n726 579 30\n726 581 32\n726 590 1\n726 595 48\n726 600 27\n726 601 10\n726 606 46\n726 648 37\n726 716 25\n726 785 38\n726 789 9\n726 791 5\n726 822 50\n726 839 -2\n726 857 10\n726 879 38\n726 920 13\n726 950 7\n726 955 44\n726 963 -2\n726 981 35\n726 983 35\n727 4 42\n727 11 26\n727 39 37\n727 72 25\n727 77 41\n727 90 38\n727 109 10\n727 164 11\n727 187 6\n727 194 25\n727 236 -2\n727 243 32\n727 244 14\n727 273 20\n727 284 29\n727 317 29\n727 336 28\n727 403 23\n727 411 39\n727 437 7\n727 513 33\n727 542 31\n727 571 2\n727 583 28\n727 586 16\n727 625 21\n727 632 3\n727 652 -1\n727 663 4\n727 668 21\n727 670 6\n727 694 29\n727 729 49\n727 765 37\n727 800 24\n727 818 11\n727 824 15\n727 834 4\n727 849 16\n727 872 26\n727 912 33\n727 913 11\n727 938 5\n727 969 4\n727 976 1\n727 996 15\n728 2 41\n728 17 31\n728 34 17\n728 43 42\n728 63 29\n728 88 49\n728 117 27\n728 141 23\n728 187 45\n728 225 24\n728 274 26\n728 276 22\n728 280 21\n728 296 20\n728 321 8\n728 353 47\n728 396 49\n728 420 2\n728 435 19\n728 444 32\n728 455 39\n728 467 47\n728 502 42\n728 511 42\n728 523 32\n728 542 10\n728 635 -2\n728 645 39\n728 664 44\n728 696 36\n728 700 25\n728 751 12\n728 769 18\n728 791 25\n728 798 36\n728 808 13\n728 851 28\n728 868 30\n728 902 30\n728 937 43\n728 989 24\n729 13 36\n729 28 49\n729 42 27\n729 63 31\n729 73 46\n729 117 27\n729 149 17\n729 160 20\n729 168 47\n729 173 48\n729 187 7\n729 241 36\n729 262 23\n729 295 13\n729 312 8\n729 313 24\n729 330 9\n729 338 37\n729 368 13\n729 372 40\n729 374 19\n729 402 8\n729 407 40\n729 425 20\n729 471 33\n729 489 50\n729 498 34\n729 564 17\n729 566 47\n729 606 45\n729 608 42\n729 613 29\n729 618 42\n729 626 9\n729 637 16\n729 658 42\n729 688 39\n729 692 30\n729 698 7\n729 702 23\n729 717 24\n729 734 16\n729 735 19\n729 737 3\n729 756 10\n729 782 48\n729 800 46\n729 824 27\n729 834 27\n729 862 45\n729 887 14\n729 907 47\n729 931 36\n729 952 23\n729 963 7\n730 4 48\n730 17 34\n730 44 18\n730 74 48\n730 106 39\n730 133 15\n730 135 47\n730 152 14\n730 215 22\n730 264 21\n730 290 34\n730 339 49\n730 344 38\n730 369 34\n730 384 12\n730 390 29\n730 396 1\n730 397 28\n730 414 13\n730 447 49\n730 449 29\n730 465 50\n730 482 50\n730 501 31\n730 555 30\n730 558 1\n730 562 24\n730 568 30\n730 597 47\n730 622 23\n730 654 42\n730 708 38\n730 868 25\n730 907 14\n730 921 45\n730 925 35\n730 953 46\n730 961 19\n730 962 49\n730 981 20\n730 991 9\n731 10 35\n731 37 22\n731 65 15\n731 76 3\n731 78 38\n731 100 20\n731 127 21\n731 131 31\n731 150 8\n731 152 17\n731 160 42\n731 230 15\n731 231 33\n731 242 46\n731 258 47\n731 271 39\n731 322 46\n731 341 10\n731 350 46\n731 363 31\n731 369 3\n731 378 32\n731 421 48\n731 457 23\n731 481 18\n731 526 19\n731 549 36\n731 586 10\n731 590 47\n731 598 20\n731 632 24\n731 634 31\n731 658 38\n731 674 33\n731 675 49\n731 680 22\n731 699 34\n731 704 3\n731 717 -1\n731 725 23\n731 749 39\n731 807 42\n731 842 23\n731 884 22\n731 902 15\n731 922 5\n731 929 4\n731 933 23\n731 962 45\n731 968 33\n731 985 17\n732 5 24\n732 11 15\n732 12 32\n732 47 19\n732 61 4\n732 62 2\n732 95 27\n732 97 34\n732 121 3\n732 122 31\n732 127 20\n732 151 34\n732 160 46\n732 189 1\n732 255 21\n732 256 41\n732 265 16\n732 278 27\n732 309 50\n732 319 13\n732 335 27\n732 347 10\n732 352 11\n732 355 35\n732 356 12\n732 357 18\n732 392 41\n732 410 10\n732 425 27\n732 442 12\n732 490 30\n732 524 37\n732 559 15\n732 578 36\n732 594 30\n732 615 20\n732 627 14\n732 634 23\n732 656 45\n732 660 33\n732 681 28\n732 700 28\n732 717 33\n732 720 39\n732 722 5\n732 724 25\n732 741 26\n732 758 45\n732 800 6\n732 802 50\n732 820 22\n732 826 33\n732 838 44\n732 849 46\n732 864 23\n732 879 14\n732 920 10\n732 930 21\n732 951 30\n732 970 5\n732 974 1\n732 975 35\n732 995 28\n733 36 39\n733 48 25\n733 50 13\n733 62 47\n733 65 42\n733 96 48\n733 167 19\n733 184 42\n733 201 27\n733 205 2\n733 220 43\n733 223 49\n733 349 3\n733 369 7\n733 408 1\n733 458 1\n733 481 20\n733 504 17\n733 549 32\n733 582 15\n733 608 10\n733 700 33\n733 707 6\n733 730 13\n733 771 43\n733 773 18\n733 796 15\n733 813 41\n733 830 43\n733 848 46\n733 878 30\n733 885 45\n733 887 -2\n733 898 32\n733 931 10\n733 942 49\n733 989 37\n734 10 24\n734 36 23\n734 37 37\n734 58 14\n734 84 42\n734 93 12\n734 95 20\n734 134 50\n734 151 16\n734 162 9\n734 201 27\n734 205 7\n734 208 33\n734 222 47\n734 239 5\n734 275 25\n734 290 24\n734 318 4\n734 361 4\n734 412 37\n734 418 26\n734 455 48\n734 534 39\n734 575 42\n734 576 7\n734 604 44\n734 611 28\n734 619 42\n734 641 44\n734 658 19\n734 667 31\n734 675 29\n734 685 41\n734 705 46\n734 717 9\n734 781 49\n734 815 43\n734 858 37\n734 864 13\n734 890 19\n734 908 21\n734 947 50\n734 949 9\n734 986 26\n734 989 40\n735 11 48\n735 17 40\n735 62 39\n735 86 29\n735 104 26\n735 123 19\n735 128 22\n735 199 8\n735 200 13\n735 210 43\n735 232 24\n735 265 40\n735 286 18\n735 300 2\n735 313 20\n735 320 4\n735 321 35\n735 366 50\n735 368 24\n735 375 4\n735 385 47\n735 389 36\n735 409 3\n735 428 48\n735 442 50\n735 444 15\n735 493 9\n735 509 45\n735 536 8\n735 542 43\n735 555 35\n735 600 12\n735 617 33\n735 621 17\n735 628 -1\n735 634 31\n735 648 23\n735 665 37\n735 691 0\n735 701 39\n735 730 15\n735 737 38\n735 787 37\n735 814 32\n735 841 32\n735 856 42\n735 878 24\n735 898 48\n735 927 22\n735 930 25\n735 947 20\n735 950 43\n736 19 29\n736 70 13\n736 71 16\n736 80 7\n736 91 39\n736 109 25\n736 112 34\n736 134 17\n736 174 18\n736 198 43\n736 304 18\n736 334 3\n736 351 9\n736 368 40\n736 441 47\n736 526 0\n736 528 29\n736 597 13\n736 609 -1\n736 630 23\n736 672 -2\n736 686 36\n736 701 15\n736 723 40\n736 740 11\n736 786 28\n736 790 32\n736 864 8\n736 910 35\n736 940 43\n736 948 27\n736 953 22\n736 955 40\n736 976 5\n736 977 28\n737 1 21\n737 6 33\n737 55 27\n737 77 45\n737 103 28\n737 106 39\n737 109 40\n737 131 18\n737 175 23\n737 219 28\n737 232 37\n737 255 33\n737 283 19\n737 299 36\n737 335 23\n737 347 20\n737 384 4\n737 386 15\n737 387 26\n737 400 34\n737 440 21\n737 473 42\n737 482 33\n737 502 12\n737 528 41\n737 536 48\n737 542 48\n737 572 36\n737 578 26\n737 580 26\n737 581 24\n737 597 29\n737 607 7\n737 618 40\n737 629 32\n737 651 33\n737 701 44\n737 702 29\n737 709 32\n737 713 21\n737 715 22\n737 738 20\n737 749 7\n737 750 28\n737 757 48\n737 788 10\n737 789 36\n737 834 42\n737 847 39\n737 869 19\n737 873 40\n737 882 24\n737 886 2\n737 902 14\n737 912 49\n737 935 19\n737 941 24\n737 962 14\n737 971 44\n737 972 21\n737 981 37\n738 1 47\n738 26 47\n738 42 34\n738 44 35\n738 46 16\n738 56 20\n738 71 1\n738 96 22\n738 99 15\n738 112 38\n738 137 18\n738 160 14\n738 169 13\n738 187 28\n738 193 11\n738 215 34\n738 271 41\n738 312 31\n738 320 36\n738 354 18\n738 366 46\n738 492 33\n738 499 34\n738 503 37\n738 512 33\n738 519 16\n738 532 38\n738 554 17\n738 573 6\n738 630 7\n738 678 5\n738 680 42\n738 727 43\n738 759 43\n738 769 45\n738 785 47\n738 790 12\n738 821 5\n738 849 37\n738 914 29\n738 949 36\n738 986 45\n738 997 7\n739 21 24\n739 39 20\n739 110 18\n739 112 48\n739 133 50\n739 172 43\n739 186 35\n739 210 9\n739 223 50\n739 285 9\n739 296 18\n739 309 9\n739 318 39\n739 320 39\n739 351 16\n739 352 25\n739 378 13\n739 394 16\n739 423 49\n739 429 41\n739 462 24\n739 489 3\n739 518 5\n739 567 27\n739 579 22\n739 590 38\n739 635 9\n739 652 17\n739 710 4\n739 718 22\n739 731 7\n739 743 45\n739 779 11\n739 785 24\n739 799 40\n739 807 40\n739 835 43\n739 839 36\n739 850 41\n739 854 22\n739 871 39\n739 872 48\n739 942 26\n739 986 48\n739 998 44\n740 6 3\n740 11 25\n740 12 5\n740 49 16\n740 54 20\n740 87 42\n740 95 -1\n740 128 1\n740 193 47\n740 196 48\n740 215 40\n740 218 21\n740 220 0\n740 242 22\n740 244 7\n740 297 36\n740 321 26\n740 329 9\n740 345 44\n740 372 43\n740 382 14\n740 428 1\n740 479 35\n740 485 27\n740 529 39\n740 537 44\n740 547 19\n740 558 22\n740 566 41\n740 574 30\n740 580 1\n740 604 24\n740 650 37\n740 679 17\n740 701 12\n740 718 5\n740 726 27\n740 733 1\n740 734 20\n740 802 34\n740 804 25\n740 812 10\n740 850 49\n740 853 23\n740 866 7\n740 883 4\n740 893 43\n740 925 47\n740 926 43\n740 929 21\n740 957 11\n740 964 50\n741 17 5\n741 68 -1\n741 79 20\n741 110 19\n741 145 11\n741 159 38\n741 161 23\n741 165 48\n741 176 13\n741 251 45\n741 276 25\n741 300 4\n741 307 8\n741 334 36\n741 357 22\n741 364 44\n741 375 30\n741 378 5\n741 437 9\n741 443 38\n741 463 35\n741 477 3\n741 488 43\n741 491 39\n741 504 16\n741 530 34\n741 540 17\n741 552 46\n741 559 40\n741 560 10\n741 588 40\n741 604 49\n741 623 44\n741 625 47\n741 673 8\n741 681 40\n741 683 29\n741 686 37\n741 693 14\n741 708 20\n741 746 47\n741 759 48\n741 769 38\n741 806 43\n741 840 24\n741 881 20\n741 905 21\n741 920 49\n741 922 40\n742 23 7\n742 102 21\n742 107 49\n742 115 4\n742 142 50\n742 164 45\n742 188 22\n742 205 39\n742 217 33\n742 232 46\n742 267 11\n742 271 30\n742 280 50\n742 281 43\n742 284 40\n742 294 16\n742 296 43\n742 411 13\n742 420 13\n742 450 48\n742 456 49\n742 463 6\n742 466 34\n742 468 50\n742 474 39\n742 480 21\n742 485 39\n742 503 14\n742 525 4\n742 546 36\n742 559 19\n742 570 28\n742 600 42\n742 613 37\n742 663 38\n742 665 19\n742 677 41\n742 682 5\n742 693 32\n742 714 36\n742 716 20\n742 733 39\n742 737 29\n742 784 35\n742 794 8\n742 824 35\n742 830 41\n742 838 18\n742 921 12\n742 944 11\n742 949 28\n742 951 35\n742 960 20\n742 991 14\n742 996 30\n742 997 42\n743 20 30\n743 27 34\n743 30 23\n743 33 29\n743 45 21\n743 72 40\n743 100 25\n743 108 21\n743 113 6\n743 168 6\n743 184 29\n743 214 17\n743 215 41\n743 238 13\n743 244 16\n743 275 37\n743 276 29\n743 331 48\n743 353 48\n743 361 4\n743 366 37\n743 387 38\n743 454 31\n743 455 35\n743 514 39\n743 515 31\n743 523 6\n743 556 38\n743 586 21\n743 597 37\n743 605 16\n743 615 43\n743 663 49\n743 690 45\n743 716 30\n743 717 24\n743 728 30\n743 735 19\n743 753 26\n743 787 34\n743 832 47\n743 906 21\n743 930 38\n743 954 16\n744 13 9\n744 14 6\n744 42 41\n744 113 45\n744 148 37\n744 227 46\n744 229 2\n744 234 37\n744 307 25\n744 338 23\n744 346 31\n744 422 3\n744 486 26\n744 536 50\n744 573 43\n744 607 10\n744 611 18\n744 620 24\n744 649 40\n744 655 34\n744 657 40\n744 683 41\n744 688 32\n744 747 2\n744 848 8\n744 903 23\n744 921 13\n744 926 19\n744 934 -1\n744 937 34\n744 949 43\n744 960 43\n744 980 43\n744 989 1\n745 21 9\n745 23 8\n745 37 -1\n745 71 1\n745 91 42\n745 103 1\n745 152 24\n745 199 25\n745 212 40\n745 213 40\n745 267 25\n745 281 35\n745 298 38\n745 320 35\n745 336 34\n745 363 0\n745 408 38\n745 438 35\n745 440 5\n745 444 34\n745 451 4\n745 461 17\n745 483 37\n745 572 15\n745 577 23\n745 586 41\n745 604 33\n745 609 50\n745 622 25\n745 640 41\n745 642 38\n745 668 16\n745 709 14\n745 744 32\n745 762 34\n745 774 4\n745 784 21\n745 806 23\n745 818 14\n745 879 12\n745 906 -1\n745 921 39\n745 928 34\n745 931 39\n745 949 23\n746 63 45\n746 82 12\n746 86 14\n746 89 39\n746 91 25\n746 134 4\n746 173 18\n746 184 30\n746 231 42\n746 232 47\n746 233 15\n746 268 24\n746 277 18\n746 282 37\n746 285 27\n746 295 35\n746 315 11\n746 336 49\n746 352 30\n746 355 13\n746 454 8\n746 468 33\n746 485 40\n746 500 31\n746 512 21\n746 515 26\n746 524 1\n746 536 14\n746 584 1\n746 588 39\n746 592 17\n746 624 46\n746 628 29\n746 640 21\n746 664 31\n746 668 17\n746 695 50\n746 725 26\n746 738 26\n746 764 35\n746 831 8\n746 884 18\n746 915 20\n746 946 10\n747 27 17\n747 70 39\n747 78 20\n747 89 47\n747 98 24\n747 160 -1\n747 182 25\n747 189 44\n747 221 6\n747 240 43\n747 278 30\n747 356 5\n747 368 40\n747 419 25\n747 475 23\n747 486 42\n747 504 31\n747 515 22\n747 526 48\n747 542 9\n747 545 40\n747 602 38\n747 624 40\n747 673 -1\n747 702 6\n747 712 33\n747 716 23\n747 749 13\n747 750 20\n747 760 25\n747 763 11\n747 796 17\n747 835 43\n747 840 20\n747 882 5\n747 905 43\n747 917 28\n747 918 20\n747 943 10\n747 963 43\n748 70 10\n748 118 15\n748 123 26\n748 156 30\n748 171 6\n748 175 18\n748 188 12\n748 202 23\n748 229 31\n748 240 4\n748 252 3\n748 255 36\n748 280 33\n748 332 42\n748 363 48\n748 368 41\n748 370 38\n748 387 19\n748 406 24\n748 429 1\n748 435 1\n748 443 9\n748 482 24\n748 497 35\n748 517 19\n748 534 10\n748 536 11\n748 585 17\n748 620 39\n748 624 39\n748 626 23\n748 636 18\n748 656 43\n748 679 31\n748 682 9\n748 712 7\n748 760 18\n748 773 3\n748 798 14\n748 808 7\n748 809 20\n748 810 36\n748 816 9\n748 821 40\n748 825 19\n748 827 28\n748 834 20\n748 837 6\n748 840 48\n748 858 31\n748 882 4\n748 900 23\n748 912 42\n748 929 10\n748 947 27\n748 972 6\n748 988 39\n748 993 30\n749 2 35\n749 35 32\n749 123 18\n749 128 32\n749 133 0\n749 148 47\n749 166 33\n749 174 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778 38\n802 801 41\n802 809 22\n802 822 6\n802 835 43\n802 865 13\n802 888 27\n802 901 32\n802 934 8\n802 951 43\n802 977 36\n802 980 4\n802 999 30\n803 19 30\n803 35 12\n803 55 13\n803 56 44\n803 62 47\n803 75 18\n803 78 45\n803 79 7\n803 86 48\n803 115 21\n803 118 1\n803 129 43\n803 156 25\n803 160 32\n803 172 -1\n803 183 49\n803 263 4\n803 266 38\n803 292 -1\n803 338 0\n803 365 50\n803 366 35\n803 428 49\n803 431 29\n803 432 14\n803 481 16\n803 512 -2\n803 526 18\n803 574 20\n803 584 16\n803 593 3\n803 609 7\n803 612 19\n803 643 34\n803 648 17\n803 654 33\n803 658 21\n803 681 18\n803 697 3\n803 708 13\n803 722 5\n803 728 2\n803 736 32\n803 740 43\n803 788 39\n803 794 20\n803 835 1\n803 857 12\n803 866 16\n803 894 36\n803 931 15\n803 935 31\n804 4 28\n804 14 15\n804 42 38\n804 46 44\n804 53 25\n804 81 3\n804 117 21\n804 178 19\n804 186 14\n804 187 26\n804 189 40\n804 199 42\n804 241 34\n804 303 15\n804 308 7\n804 339 39\n804 355 23\n804 358 22\n804 377 22\n804 385 25\n804 420 31\n804 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292 21\n806 333 50\n806 359 15\n806 392 23\n806 413 42\n806 437 30\n806 438 5\n806 441 41\n806 476 18\n806 502 39\n806 506 50\n806 557 23\n806 574 39\n806 603 39\n806 606 28\n806 635 1\n806 717 24\n806 734 13\n806 785 32\n806 790 27\n806 805 26\n806 807 29\n806 825 37\n806 827 11\n806 831 47\n806 841 21\n806 854 32\n806 856 4\n806 860 7\n806 890 19\n806 922 46\n806 931 8\n806 933 42\n806 966 38\n807 65 39\n807 75 17\n807 85 25\n807 160 13\n807 186 4\n807 218 47\n807 246 13\n807 250 20\n807 273 33\n807 301 34\n807 316 50\n807 323 24\n807 327 38\n807 357 5\n807 358 33\n807 367 43\n807 369 21\n807 418 24\n807 431 15\n807 485 32\n807 492 0\n807 504 17\n807 505 31\n807 521 38\n807 543 21\n807 546 7\n807 558 17\n807 562 7\n807 564 41\n807 576 34\n807 624 37\n807 630 48\n807 653 5\n807 688 21\n807 724 -1\n807 754 4\n807 760 -2\n807 782 16\n807 795 24\n807 830 17\n807 847 23\n807 901 26\n807 926 28\n807 931 17\n807 963 20\n807 968 22\n807 983 33\n807 988 41\n808 3 23\n808 16 4\n808 23 37\n808 28 14\n808 32 10\n808 53 18\n808 76 2\n808 85 24\n808 86 -1\n808 97 27\n808 107 32\n808 111 7\n808 131 49\n808 151 11\n808 190 5\n808 204 3\n808 305 49\n808 309 39\n808 315 41\n808 342 16\n808 370 37\n808 400 -1\n808 406 7\n808 409 29\n808 410 39\n808 420 8\n808 450 20\n808 466 40\n808 541 33\n808 542 43\n808 544 35\n808 564 50\n808 569 16\n808 574 2\n808 599 42\n808 608 39\n808 612 27\n808 688 39\n808 696 41\n808 708 29\n808 793 43\n808 821 25\n808 851 33\n808 859 32\n808 861 0\n808 862 24\n808 875 41\n808 891 12\n808 906 2\n808 908 32\n808 939 4\n808 970 32\n808 976 27\n808 978 1\n808 985 50\n808 992 44\n809 25 24\n809 30 38\n809 66 10\n809 76 19\n809 117 10\n809 137 32\n809 181 40\n809 188 34\n809 214 5\n809 217 0\n809 274 44\n809 280 13\n809 282 13\n809 293 22\n809 365 38\n809 374 35\n809 390 44\n809 404 16\n809 411 15\n809 442 3\n809 509 21\n809 525 32\n809 597 47\n809 622 46\n809 633 47\n809 641 45\n809 651 36\n809 716 48\n809 717 46\n809 750 42\n809 751 31\n809 755 21\n809 758 25\n809 775 29\n809 922 26\n809 939 14\n809 953 31\n809 955 13\n809 987 29\n810 33 6\n810 43 36\n810 67 50\n810 75 38\n810 85 0\n810 127 20\n810 140 -2\n810 141 15\n810 158 4\n810 208 33\n810 211 50\n810 219 21\n810 237 19\n810 337 22\n810 345 35\n810 387 25\n810 392 33\n810 423 31\n810 439 33\n810 479 40\n810 481 39\n810 498 31\n810 500 14\n810 504 9\n810 529 16\n810 547 10\n810 556 5\n810 575 28\n810 636 16\n810 642 1\n810 675 19\n810 686 26\n810 692 -1\n810 705 21\n810 725 17\n810 742 40\n810 758 9\n810 780 21\n810 783 13\n810 793 45\n810 804 34\n810 815 21\n810 816 17\n810 820 35\n810 835 5\n810 861 47\n810 874 29\n810 891 5\n810 894 36\n810 912 -2\n810 929 8\n810 957 34\n810 959 50\n810 989 45\n811 61 3\n811 92 -2\n811 124 24\n811 137 9\n811 170 22\n811 202 6\n811 222 31\n811 257 7\n811 288 36\n811 292 36\n811 298 11\n811 307 27\n811 308 19\n811 319 30\n811 343 45\n811 368 50\n811 394 41\n811 427 7\n811 431 32\n811 437 33\n811 453 23\n811 482 4\n811 499 7\n811 516 0\n811 538 44\n811 550 34\n811 578 46\n811 581 46\n811 591 0\n811 597 35\n811 640 24\n811 642 37\n811 660 33\n811 681 39\n811 698 29\n811 726 26\n811 732 48\n811 787 24\n811 789 31\n811 792 29\n811 800 4\n811 809 23\n811 837 38\n811 847 17\n811 852 49\n811 857 49\n811 859 0\n811 912 6\n811 914 22\n811 916 41\n811 951 9\n811 953 14\n811 956 4\n811 959 34\n811 960 41\n811 969 11\n811 991 6\n812 10 10\n812 11 34\n812 26 8\n812 69 19\n812 80 16\n812 96 18\n812 106 25\n812 198 38\n812 226 35\n812 262 8\n812 280 19\n812 306 45\n812 309 22\n812 312 48\n812 320 2\n812 330 6\n812 372 18\n812 398 37\n812 401 5\n812 411 23\n812 456 14\n812 478 32\n812 496 35\n812 500 25\n812 541 6\n812 561 7\n812 577 26\n812 580 28\n812 675 40\n812 689 9\n812 705 14\n812 729 45\n812 772 45\n812 785 50\n812 797 38\n812 800 41\n812 837 7\n812 916 26\n812 927 38\n812 952 27\n812 960 4\n812 982 25\n812 991 33\n812 1000 42\n813 5 0\n813 24 24\n813 81 21\n813 85 42\n813 125 33\n813 143 28\n813 165 14\n813 174 50\n813 182 26\n813 185 46\n813 208 24\n813 224 18\n813 226 29\n813 229 41\n813 233 30\n813 251 48\n813 300 38\n813 341 30\n813 346 50\n813 373 39\n813 380 30\n813 419 2\n813 435 41\n813 482 -2\n813 486 40\n813 490 20\n813 505 20\n813 512 23\n813 531 14\n813 581 48\n813 594 18\n813 616 40\n813 634 31\n813 654 13\n813 679 24\n813 684 31\n813 693 38\n813 706 23\n813 710 14\n813 737 26\n813 762 30\n813 769 20\n813 785 42\n813 809 20\n813 924 32\n813 926 0\n813 949 15\n813 973 7\n813 990 31\n814 2 16\n814 8 31\n814 11 1\n814 29 24\n814 42 30\n814 44 6\n814 54 26\n814 58 46\n814 126 22\n814 143 27\n814 158 27\n814 203 22\n814 223 21\n814 257 46\n814 279 1\n814 280 49\n814 295 21\n814 309 13\n814 312 9\n814 314 43\n814 355 8\n814 362 9\n814 375 50\n814 379 11\n814 387 37\n814 404 41\n814 417 7\n814 441 12\n814 464 37\n814 471 43\n814 476 23\n814 488 36\n814 542 8\n814 545 33\n814 554 5\n814 574 44\n814 580 28\n814 597 31\n814 610 36\n814 615 13\n814 634 10\n814 639 45\n814 687 22\n814 700 -2\n814 763 -1\n814 776 41\n814 782 25\n814 805 28\n814 846 13\n814 859 10\n814 866 50\n814 892 26\n814 912 16\n814 932 16\n814 996 39\n815 2 21\n815 65 31\n815 67 21\n815 103 35\n815 118 12\n815 131 29\n815 144 23\n815 148 35\n815 160 19\n815 184 46\n815 209 44\n815 299 38\n815 303 26\n815 306 24\n815 329 49\n815 364 7\n815 374 11\n815 391 34\n815 402 11\n815 404 44\n815 429 7\n815 439 14\n815 446 9\n815 502 28\n815 524 16\n815 537 17\n815 547 20\n815 561 14\n815 567 3\n815 604 49\n815 607 17\n815 637 18\n815 684 49\n815 800 46\n815 803 42\n815 828 46\n815 835 35\n815 875 16\n815 904 38\n815 949 46\n815 972 31\n815 987 18\n816 12 9\n816 18 -2\n816 72 36\n816 101 5\n816 108 36\n816 120 46\n816 123 49\n816 155 32\n816 157 33\n816 168 4\n816 189 30\n816 202 22\n816 218 9\n816 220 8\n816 246 27\n816 248 38\n816 252 14\n816 274 20\n816 292 4\n816 301 18\n816 354 6\n816 360 12\n816 364 18\n816 365 26\n816 380 40\n816 394 16\n816 451 18\n816 467 10\n816 516 49\n816 526 2\n816 533 3\n816 578 26\n816 580 40\n816 603 0\n816 663 31\n816 665 29\n816 674 32\n816 677 12\n816 689 9\n816 701 46\n816 780 33\n816 785 45\n816 793 25\n816 824 -1\n816 847 43\n816 862 36\n816 865 8\n816 896 9\n816 901 45\n816 905 5\n816 914 48\n816 922 28\n816 963 43\n816 980 25\n817 56 48\n817 63 48\n817 83 29\n817 108 39\n817 115 41\n817 155 41\n817 160 10\n817 196 50\n817 199 10\n817 222 43\n817 235 40\n817 264 4\n817 315 -1\n817 399 8\n817 432 41\n817 454 5\n817 497 21\n817 504 23\n817 674 33\n817 680 5\n817 689 24\n817 694 39\n817 700 13\n817 706 21\n817 714 30\n817 715 28\n817 717 14\n817 744 49\n817 750 22\n817 782 48\n817 809 17\n817 837 42\n817 845 6\n817 866 -1\n817 875 46\n817 891 14\n817 911 12\n817 956 15\n817 977 46\n817 980 38\n817 996 34\n818 26 23\n818 40 16\n818 60 37\n818 92 7\n818 114 25\n818 115 14\n818 155 21\n818 166 38\n818 168 15\n818 175 16\n818 178 49\n818 181 25\n818 185 3\n818 211 17\n818 219 2\n818 234 23\n818 253 28\n818 311 18\n818 321 26\n818 326 48\n818 334 26\n818 374 48\n818 386 -1\n818 416 36\n818 423 27\n818 434 11\n818 466 47\n818 474 49\n818 487 17\n818 504 4\n818 545 22\n818 555 7\n818 570 1\n818 597 33\n818 621 50\n818 622 29\n818 630 8\n818 649 46\n818 666 19\n818 684 23\n818 721 22\n818 755 8\n818 756 0\n818 774 26\n818 789 11\n818 824 46\n818 876 4\n818 881 49\n818 900 34\n818 905 0\n818 918 40\n818 930 50\n818 938 40\n818 971 9\n818 993 4\n818 999 28\n819 6 39\n819 12 19\n819 13 29\n819 33 45\n819 44 43\n819 69 41\n819 92 31\n819 126 17\n819 167 5\n819 195 3\n819 197 25\n819 208 47\n819 218 20\n819 233 38\n819 235 39\n819 268 31\n819 352 37\n819 357 15\n819 362 20\n819 368 5\n819 383 12\n819 402 36\n819 418 20\n819 423 18\n819 429 4\n819 450 46\n819 485 30\n819 507 10\n819 511 17\n819 553 9\n819 673 -2\n819 685 11\n819 687 17\n819 702 39\n819 707 14\n819 723 41\n819 784 32\n819 792 43\n819 794 48\n819 837 1\n819 842 32\n819 850 43\n819 869 21\n819 926 36\n819 931 4\n819 942 42\n819 955 46\n819 957 17\n819 960 34\n819 964 8\n819 995 29\n820 12 6\n820 23 47\n820 68 22\n820 80 31\n820 96 17\n820 132 39\n820 144 7\n820 187 44\n820 190 20\n820 259 38\n820 281 30\n820 338 21\n820 378 37\n820 379 24\n820 420 40\n820 421 40\n820 423 13\n820 516 23\n820 518 38\n820 545 5\n820 556 24\n820 576 32\n820 599 42\n820 602 37\n820 638 38\n820 646 18\n820 697 48\n820 705 10\n820 710 9\n820 721 47\n820 727 26\n820 728 18\n820 767 49\n820 789 3\n820 791 32\n820 839 15\n820 841 50\n820 850 16\n820 872 39\n820 878 9\n820 888 6\n820 895 23\n820 915 19\n820 947 22\n820 988 43\n820 993 48\n821 2 44\n821 5 33\n821 66 -2\n821 69 46\n821 81 3\n821 114 29\n821 126 17\n821 182 25\n821 207 49\n821 211 5\n821 213 50\n821 224 22\n821 270 27\n821 278 -2\n821 344 30\n821 394 24\n821 420 34\n821 448 39\n821 457 14\n821 458 44\n821 515 33\n821 528 30\n821 590 49\n821 628 29\n821 648 27\n821 651 1\n821 654 37\n821 657 35\n821 710 37\n821 720 29\n821 763 17\n821 778 28\n821 780 23\n821 804 34\n821 816 20\n821 852 42\n821 918 18\n821 931 23\n821 933 42\n821 945 16\n821 981 17\n821 990 43\n821 992 29\n822 9 25\n822 14 20\n822 32 22\n822 33 0\n822 39 33\n822 44 9\n822 58 48\n822 76 23\n822 94 44\n822 101 41\n822 188 45\n822 196 48\n822 213 26\n822 218 8\n822 219 42\n822 227 4\n822 232 44\n822 261 29\n822 265 12\n822 271 35\n822 301 23\n822 306 39\n822 332 12\n822 367 5\n822 370 47\n822 384 5\n822 389 19\n822 396 49\n822 411 36\n822 419 43\n822 421 -1\n822 422 2\n822 456 13\n822 491 -1\n822 494 11\n822 507 23\n822 521 32\n822 535 43\n822 606 24\n822 636 9\n822 641 10\n822 646 31\n822 660 11\n822 668 10\n822 679 11\n822 692 22\n822 709 34\n822 717 22\n822 753 24\n822 762 8\n822 783 26\n822 794 42\n822 804 42\n822 810 36\n822 834 11\n822 839 14\n822 910 28\n822 914 -1\n822 956 41\n822 967 36\n822 983 36\n822 987 45\n822 988 45\n823 7 27\n823 19 40\n823 72 31\n823 79 11\n823 88 18\n823 127 39\n823 129 34\n823 130 29\n823 169 28\n823 185 20\n823 211 0\n823 215 49\n823 228 42\n823 233 43\n823 238 14\n823 250 3\n823 289 8\n823 298 33\n823 351 47\n823 380 28\n823 388 39\n823 390 39\n823 394 38\n823 411 39\n823 433 5\n823 447 8\n823 464 25\n823 492 37\n823 522 40\n823 531 28\n823 565 13\n823 577 11\n823 583 33\n823 643 19\n823 663 39\n823 664 32\n823 732 41\n823 737 31\n823 752 6\n823 764 36\n823 771 48\n823 773 26\n823 799 14\n823 824 35\n823 834 47\n823 837 1\n823 867 0\n823 889 26\n823 932 49\n823 935 30\n823 949 50\n823 952 27\n823 959 1\n823 963 -1\n823 998 8\n824 41 48\n824 88 2\n824 120 5\n824 126 28\n824 127 34\n824 128 0\n824 130 42\n824 145 25\n824 150 5\n824 157 -2\n824 158 28\n824 217 22\n824 230 47\n824 238 18\n824 247 20\n824 278 35\n824 304 12\n824 382 39\n824 386 16\n824 415 21\n824 442 30\n824 461 39\n824 466 33\n824 471 39\n824 478 7\n824 491 25\n824 510 23\n824 517 12\n824 537 12\n824 584 14\n824 592 43\n824 623 2\n824 647 6\n824 654 25\n824 667 34\n824 678 0\n824 699 17\n824 700 17\n824 704 46\n824 706 13\n824 855 45\n824 887 45\n824 915 25\n824 960 30\n824 970 10\n825 60 22\n825 83 30\n825 89 30\n825 113 13\n825 134 24\n825 143 19\n825 144 30\n825 234 48\n825 255 32\n825 313 19\n825 380 29\n825 395 49\n825 415 50\n825 421 26\n825 473 43\n825 475 49\n825 493 47\n825 562 30\n825 574 22\n825 594 41\n825 612 32\n825 632 12\n825 647 35\n825 657 20\n825 669 41\n825 736 14\n825 790 28\n825 801 50\n825 816 3\n825 819 11\n825 821 46\n825 860 18\n825 866 15\n825 917 38\n825 922 23\n825 949 12\n825 957 24\n825 959 45\n825 964 29\n825 998 24\n826 26 17\n826 32 43\n826 46 30\n826 86 -1\n826 99 12\n826 162 50\n826 183 11\n826 194 21\n826 221 45\n826 242 34\n826 268 15\n826 270 6\n826 275 49\n826 281 8\n826 291 36\n826 332 50\n826 358 42\n826 405 46\n826 453 18\n826 473 39\n826 482 10\n826 500 19\n826 504 5\n826 508 4\n826 517 37\n826 523 47\n826 528 30\n826 575 27\n826 703 39\n826 756 0\n826 785 38\n826 812 15\n826 820 11\n826 849 16\n826 869 45\n826 890 30\n826 904 7\n826 966 11\n826 997 32\n827 85 23\n827 117 22\n827 122 47\n827 143 4\n827 154 21\n827 162 24\n827 207 38\n827 215 39\n827 262 15\n827 271 42\n827 321 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23\n830 700 44\n830 737 25\n830 742 17\n830 750 24\n830 764 34\n830 765 31\n830 770 39\n830 780 5\n830 838 47\n830 848 30\n830 896 4\n830 897 27\n830 903 24\n830 922 39\n830 928 44\n830 933 9\n830 959 39\n830 973 32\n831 15 41\n831 26 10\n831 30 41\n831 129 29\n831 133 46\n831 163 42\n831 188 37\n831 195 4\n831 209 10\n831 255 8\n831 275 20\n831 359 45\n831 426 12\n831 444 1\n831 513 35\n831 549 20\n831 550 10\n831 582 26\n831 594 5\n831 595 13\n831 598 41\n831 606 8\n831 608 48\n831 635 5\n831 638 19\n831 676 22\n831 710 41\n831 736 28\n831 745 49\n831 779 36\n831 793 15\n831 905 24\n831 914 37\n831 932 25\n831 959 -1\n831 981 48\n831 982 21\n831 989 41\n831 998 37\n832 62 43\n832 77 37\n832 86 3\n832 92 49\n832 100 32\n832 109 9\n832 116 19\n832 135 23\n832 156 0\n832 189 22\n832 199 7\n832 200 33\n832 206 44\n832 222 11\n832 237 19\n832 245 27\n832 335 36\n832 343 49\n832 349 7\n832 362 46\n832 394 27\n832 412 50\n832 439 33\n832 484 -1\n832 514 1\n832 521 -1\n832 528 33\n832 530 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30\n928 133 8\n928 135 3\n928 147 34\n928 210 30\n928 250 13\n928 254 11\n928 264 31\n928 267 39\n928 269 25\n928 324 44\n928 343 49\n928 368 1\n928 374 50\n928 459 30\n928 473 38\n928 484 4\n928 518 35\n928 522 48\n928 525 19\n928 538 9\n928 562 -2\n928 584 16\n928 639 30\n928 647 28\n928 657 5\n928 668 15\n928 680 49\n928 692 44\n928 747 7\n928 774 49\n928 780 32\n928 825 17\n928 841 21\n928 847 15\n928 888 50\n928 910 -1\n928 912 29\n928 917 6\n928 925 39\n928 937 4\n928 939 28\n928 943 22\n928 950 40\n929 9 12\n929 58 38\n929 63 32\n929 117 9\n929 155 8\n929 158 48\n929 182 33\n929 205 38\n929 212 22\n929 223 32\n929 259 1\n929 261 17\n929 278 3\n929 295 3\n929 347 45\n929 390 40\n929 407 23\n929 418 48\n929 442 40\n929 444 45\n929 466 46\n929 468 6\n929 493 5\n929 497 22\n929 504 41\n929 544 44\n929 582 -2\n929 621 2\n929 641 30\n929 706 17\n929 718 32\n929 727 17\n929 777 3\n929 795 36\n929 796 33\n929 830 34\n929 832 -2\n929 847 11\n929 869 22\n929 882 32\n929 883 50\n929 891 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46\n938 880 7\n938 927 12\n938 929 50\n938 941 2\n938 988 20\n939 20 22\n939 40 10\n939 53 14\n939 76 4\n939 91 19\n939 113 19\n939 144 12\n939 161 38\n939 182 13\n939 200 46\n939 214 38\n939 226 37\n939 229 6\n939 249 46\n939 264 34\n939 303 15\n939 338 37\n939 362 15\n939 398 26\n939 419 26\n939 443 17\n939 455 16\n939 472 20\n939 484 10\n939 502 8\n939 550 23\n939 630 34\n939 636 21\n939 666 34\n939 684 37\n939 714 4\n939 743 38\n939 755 50\n939 780 16\n939 808 23\n939 839 13\n939 874 27\n939 890 37\n939 895 12\n939 926 46\n939 927 27\n939 958 31\n939 983 15\n939 987 45\n939 990 19\n940 4 22\n940 30 29\n940 89 26\n940 91 27\n940 131 21\n940 138 22\n940 161 35\n940 166 22\n940 181 39\n940 192 27\n940 196 -1\n940 206 -1\n940 209 50\n940 224 25\n940 229 22\n940 232 28\n940 311 28\n940 347 21\n940 351 22\n940 362 41\n940 372 24\n940 437 16\n940 446 46\n940 467 37\n940 551 46\n940 566 8\n940 582 14\n940 593 46\n940 598 23\n940 633 39\n940 647 45\n940 656 37\n940 657 5\n940 672 34\n940 677 10\n940 683 20\n940 690 32\n940 759 47\n940 807 43\n940 827 0\n940 830 44\n940 842 49\n940 854 17\n940 862 7\n940 864 11\n940 865 17\n940 876 50\n940 905 15\n940 908 13\n940 921 21\n940 930 35\n940 973 38\n940 980 18\n941 7 22\n941 16 26\n941 31 46\n941 66 44\n941 67 14\n941 80 37\n941 97 41\n941 99 0\n941 215 27\n941 257 50\n941 302 6\n941 310 36\n941 346 7\n941 439 18\n941 451 13\n941 465 40\n941 473 7\n941 474 19\n941 477 20\n941 531 30\n941 544 32\n941 553 32\n941 581 36\n941 594 1\n941 624 14\n941 649 11\n941 654 -1\n941 669 20\n941 671 48\n941 696 27\n941 697 31\n941 716 1\n941 718 49\n941 721 21\n941 724 7\n941 744 9\n941 745 33\n941 747 7\n941 753 42\n941 798 0\n941 837 17\n941 861 38\n941 899 33\n941 950 2\n941 989 23\n941 995 25\n942 56 11\n942 69 32\n942 77 5\n942 79 32\n942 93 3\n942 116 48\n942 150 10\n942 207 33\n942 220 49\n942 236 12\n942 266 26\n942 297 45\n942 308 31\n942 327 48\n942 353 22\n942 372 35\n942 405 21\n942 418 39\n942 433 1\n942 471 29\n942 489 19\n942 516 49\n942 541 38\n942 555 9\n942 626 39\n942 633 18\n942 634 16\n942 637 48\n942 649 14\n942 679 6\n942 700 3\n942 701 15\n942 755 39\n942 786 39\n942 852 23\n942 869 33\n942 873 32\n942 885 9\n942 895 26\n942 898 21\n942 956 17\n943 1 48\n943 14 47\n943 31 19\n943 32 38\n943 38 26\n943 72 25\n943 77 -1\n943 86 8\n943 96 2\n943 118 -2\n943 121 14\n943 129 41\n943 150 20\n943 152 30\n943 163 39\n943 168 24\n943 175 0\n943 185 -1\n943 193 32\n943 231 5\n943 240 -2\n943 274 4\n943 288 3\n943 321 43\n943 343 35\n943 365 37\n943 379 5\n943 381 14\n943 433 18\n943 483 42\n943 492 9\n943 508 7\n943 529 24\n943 533 9\n943 585 7\n943 588 10\n943 592 0\n943 595 5\n943 601 6\n943 608 42\n943 627 48\n943 656 2\n943 660 34\n943 670 35\n943 751 22\n943 758 23\n943 760 41\n943 765 34\n943 767 43\n943 802 6\n943 814 40\n943 815 13\n943 854 49\n943 873 9\n943 910 13\n943 919 41\n943 930 20\n944 3 9\n944 23 45\n944 85 37\n944 86 36\n944 88 45\n944 112 20\n944 121 30\n944 169 28\n944 206 40\n944 226 26\n944 238 33\n944 298 0\n944 322 39\n944 337 22\n944 342 17\n944 345 24\n944 355 18\n944 383 5\n944 386 22\n944 391 9\n944 401 36\n944 405 26\n944 407 45\n944 425 -2\n944 428 41\n944 441 45\n944 471 6\n944 475 12\n944 487 8\n944 496 37\n944 502 34\n944 564 15\n944 578 8\n944 591 38\n944 604 12\n944 632 40\n944 660 13\n944 830 10\n944 862 37\n944 875 22\n944 887 19\n944 932 26\n944 933 3\n944 960 32\n945 21 1\n945 51 42\n945 52 14\n945 108 48\n945 144 27\n945 153 46\n945 167 41\n945 189 39\n945 204 -1\n945 223 5\n945 249 28\n945 311 45\n945 327 41\n945 357 32\n945 365 23\n945 374 38\n945 388 23\n945 395 42\n945 422 7\n945 436 3\n945 442 28\n945 473 10\n945 489 48\n945 493 30\n945 495 29\n945 511 37\n945 515 12\n945 580 33\n945 584 36\n945 616 42\n945 622 19\n945 623 50\n945 661 22\n945 683 50\n945 700 15\n945 720 24\n945 726 28\n945 731 1\n945 745 15\n945 750 13\n945 757 7\n945 769 44\n945 791 37\n945 811 36\n945 813 -1\n945 824 42\n945 845 23\n945 870 17\n945 887 5\n945 906 30\n945 911 12\n945 930 31\n945 943 43\n945 961 21\n945 969 13\n945 973 11\n945 979 7\n946 32 25\n946 36 34\n946 38 4\n946 40 2\n946 41 27\n946 48 19\n946 60 43\n946 63 50\n946 122 35\n946 152 15\n946 192 20\n946 266 26\n946 277 46\n946 289 39\n946 294 36\n946 313 21\n946 323 28\n946 331 7\n946 367 6\n946 371 33\n946 376 15\n946 411 37\n946 415 27\n946 420 41\n946 472 30\n946 477 12\n946 503 21\n946 507 10\n946 514 46\n946 517 25\n946 593 49\n946 643 3\n946 648 40\n946 655 4\n946 666 23\n946 674 49\n946 709 41\n946 746 19\n946 815 34\n946 818 50\n946 823 2\n946 827 2\n946 832 20\n946 857 48\n946 859 3\n946 873 48\n946 884 38\n946 907 37\n946 939 34\n946 957 15\n946 964 14\n946 973 13\n946 993 33\n947 46 22\n947 113 10\n947 118 2\n947 135 12\n947 136 39\n947 171 11\n947 205 4\n947 210 20\n947 268 47\n947 270 37\n947 299 20\n947 302 27\n947 336 -1\n947 370 24\n947 371 37\n947 395 46\n947 407 40\n947 409 4\n947 439 27\n947 444 -2\n947 454 6\n947 469 3\n947 473 44\n947 499 46\n947 550 1\n947 559 5\n947 587 21\n947 597 40\n947 600 26\n947 632 -1\n947 643 15\n947 670 24\n947 672 41\n947 683 16\n947 704 50\n947 706 39\n947 713 13\n947 715 46\n947 739 29\n947 748 4\n947 767 8\n947 775 36\n947 808 42\n947 817 37\n947 818 23\n947 821 30\n947 837 48\n947 864 12\n947 870 26\n947 904 48\n947 911 11\n947 970 11\n947 999 12\n948 1 20\n948 8 39\n948 43 14\n948 88 3\n948 139 34\n948 148 25\n948 161 35\n948 242 0\n948 285 44\n948 302 17\n948 341 38\n948 349 47\n948 358 26\n948 382 44\n948 421 34\n948 429 4\n948 431 5\n948 432 0\n948 433 34\n948 456 9\n948 461 41\n948 475 45\n948 533 50\n948 535 27\n948 547 25\n948 551 25\n948 559 3\n948 564 45\n948 581 0\n948 590 16\n948 606 38\n948 620 10\n948 632 43\n948 648 35\n948 663 16\n948 672 3\n948 685 26\n948 698 7\n948 699 16\n948 715 29\n948 716 31\n948 730 13\n948 762 44\n948 769 3\n948 778 24\n948 804 22\n948 861 -1\n948 871 -2\n948 887 43\n948 889 16\n948 892 20\n948 896 50\n948 906 21\n948 907 23\n948 915 25\n948 917 37\n948 927 17\n948 965 36\n948 978 -2\n948 996 48\n949 32 43\n949 35 31\n949 39 45\n949 54 11\n949 105 48\n949 121 16\n949 147 48\n949 179 34\n949 239 44\n949 248 45\n949 275 32\n949 287 40\n949 320 20\n949 356 24\n949 380 24\n949 393 43\n949 407 2\n949 409 19\n949 412 19\n949 415 22\n949 437 5\n949 456 44\n949 486 46\n949 501 5\n949 514 18\n949 523 35\n949 547 0\n949 552 4\n949 559 3\n949 576 30\n949 612 38\n949 616 6\n949 661 7\n949 663 38\n949 682 44\n949 684 35\n949 697 10\n949 702 20\n949 728 32\n949 834 27\n949 851 11\n949 852 18\n949 902 21\n949 906 -2\n949 911 5\n949 935 8\n949 963 0\n949 977 18\n949 983 41\n949 997 6\n949 1000 34\n950 10 44\n950 11 11\n950 18 26\n950 43 27\n950 48 2\n950 52 3\n950 53 8\n950 97 26\n950 113 32\n950 141 10\n950 154 35\n950 177 46\n950 199 26\n950 201 18\n950 208 42\n950 216 18\n950 237 46\n950 243 41\n950 248 39\n950 254 28\n950 274 47\n950 279 38\n950 322 44\n950 343 41\n950 350 30\n950 389 9\n950 403 23\n950 407 13\n950 427 34\n950 437 45\n950 444 20\n950 450 10\n950 478 29\n950 480 41\n950 490 47\n950 497 38\n950 504 23\n950 538 18\n950 542 39\n950 559 15\n950 590 39\n950 691 32\n950 712 6\n950 714 8\n950 744 22\n950 746 20\n950 756 33\n950 777 13\n950 781 44\n950 796 13\n950 798 5\n950 848 22\n950 878 -2\n950 905 33\n950 911 22\n950 918 8\n950 924 43\n950 985 38\n951 18 43\n951 22 10\n951 41 34\n951 68 37\n951 88 14\n951 108 28\n951 109 43\n951 112 9\n951 189 32\n951 198 47\n951 244 17\n951 268 42\n951 281 25\n951 322 39\n951 333 10\n951 334 50\n951 400 12\n951 421 7\n951 425 49\n951 436 16\n951 442 44\n951 494 14\n951 541 22\n951 552 42\n951 556 8\n951 567 28\n951 587 49\n951 606 43\n951 644 47\n951 658 29\n951 702 22\n951 716 5\n951 720 11\n951 751 15\n951 784 26\n951 834 12\n951 837 31\n951 844 11\n951 880 44\n951 903 33\n951 914 50\n951 926 7\n951 962 32\n951 984 30\n952 19 27\n952 26 37\n952 62 39\n952 100 30\n952 159 45\n952 162 -1\n952 181 4\n952 216 37\n952 237 10\n952 275 5\n952 280 2\n952 305 45\n952 307 7\n952 308 2\n952 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34\n989 789 36\n989 794 14\n989 832 43\n989 838 12\n989 840 41\n989 878 11\n989 884 47\n989 912 26\n989 914 44\n989 932 19\n989 949 43\n989 955 38\n989 958 9\n989 969 15\n989 979 30\n989 988 22\n989 991 7\n990 16 49\n990 64 22\n990 82 39\n990 115 21\n990 134 49\n990 141 34\n990 183 7\n990 198 12\n990 207 12\n990 212 27\n990 236 14\n990 240 13\n990 247 8\n990 249 45\n990 253 49\n990 262 9\n990 263 22\n990 279 24\n990 312 27\n990 316 21\n990 353 9\n990 372 5\n990 382 34\n990 418 31\n990 422 0\n990 446 14\n990 450 24\n990 463 3\n990 473 8\n990 477 46\n990 480 12\n990 498 31\n990 523 25\n990 526 6\n990 565 2\n990 571 27\n990 587 34\n990 599 39\n990 605 8\n990 622 9\n990 685 11\n990 736 19\n990 769 31\n990 778 43\n990 781 17\n990 784 9\n990 806 40\n990 808 34\n990 811 36\n990 833 34\n990 851 17\n990 868 32\n990 881 26\n990 909 27\n990 942 10\n990 992 5\n990 994 46\n991 63 30\n991 87 12\n991 104 48\n991 128 5\n991 129 -2\n991 130 16\n991 162 5\n991 177 48\n991 183 30\n991 226 27\n991 228 11\n991 260 17\n991 287 24\n991 313 1\n991 315 36\n991 336 48\n991 430 17\n991 436 13\n991 438 40\n991 446 44\n991 475 35\n991 510 43\n991 526 7\n991 561 21\n991 567 49\n991 585 3\n991 644 25\n991 664 39\n991 723 33\n991 742 23\n991 766 20\n991 811 0\n991 821 22\n991 837 16\n991 848 35\n991 855 45\n991 920 49\n991 999 38\n992 63 4\n992 91 1\n992 123 46\n992 128 42\n992 158 18\n992 162 45\n992 181 33\n992 211 1\n992 228 16\n992 247 23\n992 292 25\n992 379 8\n992 393 27\n992 408 50\n992 411 11\n992 416 50\n992 423 47\n992 467 39\n992 478 11\n992 490 8\n992 494 41\n992 512 31\n992 515 37\n992 549 23\n992 559 27\n992 572 0\n992 640 14\n992 669 22\n992 681 28\n992 723 8\n992 766 8\n992 802 37\n992 823 38\n992 830 49\n992 867 46\n992 868 33\n992 869 40\n992 927 43\n992 951 30\n992 970 22\n992 973 19\n992 975 14\n992 988 34\n993 1 5\n993 11 -2\n993 43 42\n993 69 26\n993 133 11\n993 161 13\n993 186 12\n993 193 4\n993 223 22\n993 248 33\n993 250 45\n993 277 14\n993 300 28\n993 304 20\n993 313 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46\n994 961 37\n994 978 18\n994 984 47\n994 985 49\n995 6 11\n995 10 7\n995 16 26\n995 19 7\n995 23 46\n995 25 15\n995 32 22\n995 51 12\n995 90 13\n995 95 7\n995 114 20\n995 137 41\n995 150 33\n995 207 32\n995 210 25\n995 236 6\n995 244 27\n995 259 7\n995 265 37\n995 269 17\n995 280 5\n995 294 34\n995 338 21\n995 356 19\n995 423 37\n995 428 44\n995 443 15\n995 477 24\n995 503 29\n995 524 22\n995 526 29\n995 543 49\n995 545 41\n995 548 14\n995 568 49\n995 577 36\n995 667 11\n995 680 28\n995 685 6\n995 761 24\n995 809 11\n995 813 9\n995 826 46\n995 879 30\n995 904 38\n995 905 28\n995 930 33\n995 937 36\n995 962 29\n995 985 26\n995 990 33\n996 10 47\n996 17 21\n996 31 4\n996 32 29\n996 38 22\n996 76 24\n996 88 20\n996 131 2\n996 133 5\n996 145 7\n996 173 35\n996 256 2\n996 273 7\n996 350 49\n996 367 20\n996 380 15\n996 385 4\n996 398 41\n996 436 25\n996 457 27\n996 459 34\n996 478 29\n996 493 22\n996 500 38\n996 521 43\n996 566 19\n996 574 50\n996 582 1\n996 598 36\n996 602 34\n996 651 10\n996 665 45\n996 687 37\n996 705 35\n996 729 38\n996 734 46\n996 738 28\n996 765 41\n996 772 30\n996 783 21\n996 799 41\n996 861 24\n996 882 12\n996 910 30\n996 911 43\n996 926 19\n996 935 16\n996 942 33\n997 18 13\n997 24 2\n997 46 -1\n997 83 44\n997 110 1\n997 223 31\n997 264 48\n997 268 17\n997 289 12\n997 306 30\n997 320 38\n997 333 47\n997 335 27\n997 369 46\n997 371 40\n997 436 14\n997 449 16\n997 468 20\n997 524 35\n997 551 21\n997 597 35\n997 604 43\n997 625 42\n997 632 32\n997 658 43\n997 660 12\n997 661 42\n997 666 5\n997 669 6\n997 684 12\n997 689 48\n997 710 0\n997 727 18\n997 740 19\n997 753 16\n997 811 48\n997 828 44\n997 847 30\n997 850 46\n997 854 45\n997 858 24\n997 873 16\n997 895 11\n997 902 47\n997 915 31\n997 943 -1\n997 978 28\n997 980 26\n998 52 -2\n998 53 26\n998 56 10\n998 88 30\n998 93 14\n998 109 -2\n998 130 29\n998 157 -1\n998 173 38\n998 190 -2\n998 199 9\n998 202 49\n998 223 23\n998 268 8\n998 313 21\n998 333 14\n998 391 1\n998 399 13\n998 418 31\n998 436 7\n998 438 -2\n998 444 6\n998 448 13\n998 479 8\n998 483 15\n998 548 1\n998 593 1\n998 598 2\n998 605 -2\n998 607 3\n998 626 43\n998 637 1\n998 647 -1\n998 680 22\n998 734 6\n998 739 21\n998 774 15\n998 829 5\n998 831 49\n998 869 41\n998 923 4\n998 930 2\n998 935 5\n998 956 44\n998 964 31\n998 992 34\n999 20 32\n999 47 38\n999 66 19\n999 74 17\n999 92 12\n999 102 26\n999 130 21\n999 134 47\n999 135 40\n999 143 17\n999 157 10\n999 170 37\n999 175 16\n999 178 32\n999 190 31\n999 250 13\n999 252 29\n999 283 5\n999 305 47\n999 335 46\n999 365 13\n999 414 43\n999 445 45\n999 460 36\n999 491 34\n999 548 20\n999 559 17\n999 574 41\n999 586 42\n999 595 5\n999 609 39\n999 615 26\n999 621 49\n999 628 31\n999 647 16\n999 663 25\n999 676 32\n999 688 21\n999 703 36\n999 775 47\n999 795 49\n999 799 8\n999 829 28\n999 838 26\n999 858 3\n999 871 15\n999 880 12\n999 888 13\n999 902 29\n999 918 31\n999 949 28\n999 997 15\n1000 21 38\n1000 40 19\n1000 111 46\n1000 143 49\n1000 152 1\n1000 181 32\n1000 212 1\n1000 217 27\n1000 230 21\n1000 240 43\n1000 246 13\n1000 257 19\n1000 268 35\n1000 303 49\n1000 321 47\n1000 325 33\n1000 337 33\n1000 406 22\n1000 412 24\n1000 419 28\n1000 446 34\n1000 447 1\n1000 450 36\n1000 456 12\n1000 457 27\n1000 492 38\n1000 526 28\n1000 544 37\n1000 556 19\n1000 574 39\n1000 581 29\n1000 590 25\n1000 630 23\n1000 648 15\n1000 654 22\n1000 681 23\n1000 707 3\n1000 747 42\n1000 755 47\n1000 759 7\n1000 767 22\n1000 780 16\n1000 787 2\n1000 812 8\n1000 814 16\n1000 838 1\n1000 844 28\n1000 853 49\n1000 856 50\n1000 857 4\n1000 871 23\n1000 897 31\n1000 900 21\n1000 907 42\n1000 916 25\n1000 984 12\n1000 988 3\n"
  },
  {
    "path": "floyd_warshall/problem18.8file3.txt",
    "content": "1000 47978\n1 8 36\n1 33 29\n1 38 18\n1 63 25\n1 76 39\n1 100 26\n1 105 41\n1 120 20\n1 131 34\n1 181 32\n1 221 24\n1 255 16\n1 269 33\n1 278 47\n1 287 33\n1 289 48\n1 307 46\n1 310 13\n1 339 45\n1 340 16\n1 385 24\n1 392 1\n1 430 2\n1 438 31\n1 462 26\n1 470 22\n1 474 5\n1 477 46\n1 494 38\n1 530 29\n1 589 7\n1 628 4\n1 657 8\n1 661 20\n1 664 38\n1 671 33\n1 705 30\n1 711 20\n1 743 37\n1 753 28\n1 766 13\n1 771 32\n1 792 42\n1 806 13\n1 816 40\n1 823 42\n1 828 15\n1 852 9\n1 884 21\n1 891 40\n1 929 30\n1 932 2\n1 946 46\n1 957 38\n1 966 37\n1 995 31\n2 7 20\n2 64 35\n2 68 16\n2 74 46\n2 75 48\n2 92 23\n2 127 -2\n2 149 30\n2 154 13\n2 160 35\n2 199 39\n2 252 39\n2 254 12\n2 258 40\n2 277 26\n2 303 7\n2 314 15\n2 329 -2\n2 345 50\n2 346 8\n2 354 -2\n2 360 36\n2 388 17\n2 441 13\n2 443 33\n2 445 8\n2 451 16\n2 476 16\n2 495 45\n2 501 49\n2 507 9\n2 553 10\n2 599 34\n2 603 25\n2 623 19\n2 632 43\n2 635 -2\n2 668 7\n2 697 38\n2 742 43\n2 766 22\n2 778 36\n2 896 13\n2 906 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721 14\n37 723 15\n37 736 46\n37 757 22\n37 764 40\n37 787 41\n37 814 32\n37 911 30\n37 915 10\n37 922 13\n37 986 16\n38 74 38\n38 101 43\n38 121 30\n38 129 17\n38 164 25\n38 196 33\n38 215 48\n38 222 23\n38 234 50\n38 235 34\n38 250 9\n38 258 29\n38 283 12\n38 294 20\n38 301 13\n38 336 24\n38 348 0\n38 393 21\n38 436 18\n38 446 41\n38 474 15\n38 482 39\n38 490 18\n38 515 30\n38 523 45\n38 524 18\n38 536 42\n38 542 13\n38 559 7\n38 563 38\n38 593 30\n38 616 5\n38 630 0\n38 667 4\n38 701 28\n38 702 4\n38 736 49\n38 766 40\n38 767 14\n38 769 18\n38 771 25\n38 777 46\n38 790 42\n38 815 0\n38 861 8\n38 895 33\n38 896 40\n38 959 4\n38 960 27\n39 10 42\n39 12 35\n39 17 36\n39 22 0\n39 31 -2\n39 34 37\n39 53 49\n39 58 35\n39 73 50\n39 98 4\n39 107 34\n39 124 14\n39 128 0\n39 138 7\n39 147 25\n39 157 50\n39 166 27\n39 249 16\n39 268 24\n39 311 23\n39 320 50\n39 324 11\n39 344 10\n39 377 11\n39 384 11\n39 401 41\n39 407 41\n39 411 25\n39 447 49\n39 461 41\n39 469 29\n39 494 -1\n39 503 34\n39 518 50\n39 524 5\n39 533 12\n39 535 19\n39 563 27\n39 597 -1\n39 622 7\n39 652 43\n39 695 24\n39 733 50\n39 740 29\n39 758 19\n39 784 6\n39 805 45\n39 868 48\n39 889 24\n39 898 16\n39 918 40\n39 921 23\n39 957 13\n39 962 40\n40 34 45\n40 52 38\n40 69 22\n40 121 41\n40 221 41\n40 230 11\n40 231 21\n40 287 2\n40 304 13\n40 306 1\n40 323 2\n40 333 35\n40 358 35\n40 375 -1\n40 385 19\n40 397 35\n40 426 14\n40 470 46\n40 535 15\n40 538 1\n40 589 9\n40 604 5\n40 612 40\n40 614 15\n40 634 17\n40 647 19\n40 675 34\n40 677 6\n40 678 20\n40 771 17\n40 783 29\n40 793 36\n40 796 11\n40 801 40\n40 807 10\n40 817 8\n40 843 2\n40 848 15\n40 883 49\n40 902 33\n40 917 1\n40 928 26\n40 941 -2\n40 964 31\n40 976 11\n41 1 47\n41 57 7\n41 62 9\n41 77 0\n41 102 49\n41 126 7\n41 142 50\n41 148 1\n41 169 33\n41 170 35\n41 186 4\n41 200 2\n41 213 28\n41 231 49\n41 328 3\n41 367 8\n41 369 35\n41 381 40\n41 390 48\n41 396 13\n41 471 19\n41 502 26\n41 503 12\n41 511 37\n41 512 13\n41 526 17\n41 565 30\n41 585 37\n41 590 24\n41 595 21\n41 598 29\n41 608 37\n41 621 1\n41 669 23\n41 681 3\n41 687 40\n41 688 30\n41 705 8\n41 709 41\n41 724 0\n41 726 33\n41 730 6\n41 732 7\n41 750 13\n41 795 38\n41 798 8\n41 808 44\n41 890 28\n41 891 28\n41 902 29\n41 904 16\n41 918 22\n41 929 7\n41 986 8\n41 988 32\n42 20 48\n42 22 30\n42 48 5\n42 60 43\n42 67 20\n42 87 49\n42 90 45\n42 105 35\n42 111 20\n42 151 28\n42 160 1\n42 164 40\n42 179 21\n42 192 40\n42 210 12\n42 228 24\n42 247 4\n42 254 17\n42 256 10\n42 282 26\n42 292 15\n42 311 26\n42 316 12\n42 331 5\n42 361 27\n42 374 50\n42 383 49\n42 392 27\n42 408 23\n42 427 13\n42 448 48\n42 476 37\n42 485 31\n42 530 -1\n42 544 34\n42 560 38\n42 572 43\n42 584 47\n42 596 32\n42 625 42\n42 643 22\n42 668 22\n42 696 38\n42 706 10\n42 717 -2\n42 733 27\n42 737 30\n42 743 50\n42 757 20\n42 759 31\n42 768 1\n42 769 7\n42 783 25\n42 823 21\n42 842 36\n42 881 11\n42 919 37\n42 928 20\n42 936 23\n42 960 48\n42 970 47\n43 1 9\n43 52 5\n43 53 28\n43 73 44\n43 100 42\n43 119 30\n43 146 27\n43 154 3\n43 189 3\n43 195 -2\n43 224 9\n43 245 10\n43 261 39\n43 262 47\n43 289 38\n43 325 20\n43 340 39\n43 349 13\n43 403 40\n43 420 17\n43 455 45\n43 476 46\n43 478 0\n43 498 37\n43 507 50\n43 520 14\n43 538 43\n43 589 25\n43 616 33\n43 618 9\n43 627 18\n43 661 39\n43 663 25\n43 672 49\n43 715 50\n43 776 44\n43 787 37\n43 839 11\n43 847 25\n43 864 28\n43 888 3\n43 939 43\n43 942 25\n43 947 15\n43 957 0\n43 977 23\n43 982 2\n43 988 49\n43 993 19\n44 39 20\n44 66 16\n44 71 22\n44 82 27\n44 86 2\n44 97 19\n44 107 35\n44 111 37\n44 116 4\n44 158 19\n44 166 32\n44 180 32\n44 216 43\n44 224 47\n44 245 24\n44 252 0\n44 254 13\n44 283 47\n44 310 14\n44 355 11\n44 359 38\n44 367 20\n44 378 4\n44 430 3\n44 432 20\n44 446 12\n44 504 48\n44 510 2\n44 512 36\n44 520 5\n44 534 27\n44 542 20\n44 601 6\n44 609 38\n44 615 9\n44 628 40\n44 634 33\n44 647 42\n44 662 9\n44 677 -2\n44 711 9\n44 715 10\n44 749 20\n44 766 31\n44 779 -1\n44 791 3\n44 794 0\n44 798 26\n44 799 13\n44 807 16\n44 860 33\n44 872 30\n44 914 16\n44 917 33\n44 923 1\n44 928 45\n44 992 26\n45 18 33\n45 46 3\n45 75 23\n45 79 7\n45 96 22\n45 109 4\n45 114 9\n45 116 28\n45 118 2\n45 133 28\n45 135 44\n45 154 27\n45 214 0\n45 227 10\n45 243 48\n45 284 33\n45 310 2\n45 318 20\n45 320 49\n45 333 3\n45 343 44\n45 344 40\n45 381 38\n45 395 44\n45 404 -1\n45 414 22\n45 417 19\n45 540 36\n45 554 48\n45 560 50\n45 570 4\n45 571 9\n45 609 9\n45 615 49\n45 620 50\n45 624 30\n45 640 23\n45 641 50\n45 686 48\n45 788 45\n45 830 0\n45 895 25\n45 896 45\n45 905 12\n45 909 48\n45 934 2\n45 941 -2\n45 965 40\n45 999 17\n46 24 38\n46 25 4\n46 82 -2\n46 100 21\n46 102 21\n46 110 22\n46 168 6\n46 175 42\n46 231 4\n46 236 36\n46 259 -1\n46 263 30\n46 270 23\n46 275 34\n46 278 40\n46 323 49\n46 332 18\n46 393 25\n46 403 7\n46 426 43\n46 447 24\n46 478 42\n46 479 19\n46 503 1\n46 513 30\n46 577 35\n46 636 49\n46 704 21\n46 712 12\n46 713 24\n46 727 26\n46 739 20\n46 758 14\n46 771 38\n46 807 46\n46 808 2\n46 839 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19\n48 516 37\n48 534 7\n48 541 6\n48 550 35\n48 554 37\n48 569 35\n48 572 38\n48 581 16\n48 611 20\n48 620 18\n48 666 26\n48 688 1\n48 716 36\n48 790 32\n48 823 24\n48 849 48\n48 871 22\n48 874 17\n48 927 38\n48 957 27\n48 958 18\n48 960 38\n48 986 33\n48 994 46\n49 10 40\n49 19 19\n49 61 2\n49 69 32\n49 73 25\n49 89 45\n49 90 20\n49 96 25\n49 99 15\n49 130 19\n49 141 18\n49 160 20\n49 163 16\n49 186 27\n49 198 45\n49 207 34\n49 211 34\n49 221 25\n49 228 31\n49 230 27\n49 239 4\n49 260 38\n49 309 38\n49 323 42\n49 324 7\n49 341 42\n49 343 6\n49 373 5\n49 407 25\n49 419 -1\n49 435 -2\n49 447 41\n49 491 24\n49 513 -2\n49 523 19\n49 525 5\n49 528 43\n49 561 47\n49 595 38\n49 600 21\n49 608 26\n49 643 32\n49 677 38\n49 800 42\n49 835 11\n49 841 21\n49 851 40\n49 866 3\n49 876 -2\n49 877 35\n49 908 31\n49 944 23\n49 948 40\n49 949 27\n49 950 23\n49 963 16\n49 982 28\n49 996 18\n50 43 31\n50 75 14\n50 91 32\n50 132 33\n50 153 34\n50 167 3\n50 180 -1\n50 192 32\n50 245 17\n50 267 24\n50 280 45\n50 292 39\n50 314 0\n50 319 42\n50 323 7\n50 328 36\n50 350 21\n50 355 32\n50 391 33\n50 392 24\n50 407 6\n50 412 21\n50 429 6\n50 463 41\n50 464 5\n50 479 16\n50 489 26\n50 495 17\n50 496 28\n50 540 33\n50 543 5\n50 563 44\n50 567 17\n50 596 3\n50 613 25\n50 628 -2\n50 640 16\n50 654 2\n50 689 19\n50 700 50\n50 704 42\n50 728 43\n50 746 3\n50 754 12\n50 760 45\n50 779 46\n50 809 10\n50 825 1\n50 855 22\n50 864 36\n50 868 4\n50 994 26\n51 38 7\n51 118 0\n51 131 32\n51 133 28\n51 177 34\n51 185 19\n51 190 41\n51 203 22\n51 206 28\n51 251 43\n51 261 25\n51 270 0\n51 285 36\n51 309 25\n51 322 34\n51 368 36\n51 377 14\n51 507 45\n51 568 38\n51 622 48\n51 648 41\n51 651 40\n51 655 5\n51 689 46\n51 726 -1\n51 729 25\n51 734 26\n51 741 19\n51 747 14\n51 788 9\n51 792 25\n51 802 17\n51 817 37\n51 845 9\n51 876 3\n51 914 30\n51 934 26\n51 974 42\n51 978 49\n51 979 50\n51 981 0\n51 992 14\n52 11 37\n52 38 41\n52 69 24\n52 71 0\n52 73 35\n52 96 26\n52 112 17\n52 127 31\n52 163 42\n52 173 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880 2\n113 895 44\n113 897 45\n113 916 12\n113 921 2\n113 928 6\n113 955 25\n113 996 12\n114 1 12\n114 12 31\n114 29 38\n114 42 42\n114 128 28\n114 154 17\n114 157 31\n114 171 29\n114 173 0\n114 184 3\n114 198 2\n114 200 2\n114 203 9\n114 214 2\n114 240 40\n114 250 47\n114 255 28\n114 262 2\n114 275 15\n114 314 45\n114 362 15\n114 483 9\n114 512 50\n114 526 50\n114 528 18\n114 539 14\n114 556 39\n114 619 34\n114 643 5\n114 644 -2\n114 700 16\n114 704 35\n114 743 12\n114 765 39\n114 799 11\n114 800 13\n114 806 23\n114 809 29\n114 823 13\n114 832 2\n114 895 3\n114 896 47\n114 927 6\n114 947 13\n114 981 31\n115 33 48\n115 43 19\n115 71 30\n115 107 18\n115 110 0\n115 118 18\n115 143 3\n115 147 6\n115 248 40\n115 279 37\n115 295 46\n115 331 43\n115 341 3\n115 373 6\n115 378 25\n115 380 20\n115 408 33\n115 427 29\n115 428 44\n115 484 1\n115 504 32\n115 508 45\n115 517 43\n115 531 35\n115 548 9\n115 577 1\n115 600 40\n115 610 9\n115 642 29\n115 644 29\n115 692 41\n115 703 25\n115 707 13\n115 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1\n120 603 50\n120 630 20\n120 670 4\n120 674 12\n120 688 49\n120 708 7\n120 789 34\n120 797 49\n120 801 8\n120 854 -2\n120 855 41\n120 909 24\n120 912 6\n120 914 33\n120 938 9\n120 946 6\n120 971 0\n120 975 30\n121 31 11\n121 45 6\n121 68 13\n121 79 28\n121 131 41\n121 144 18\n121 201 20\n121 223 43\n121 224 35\n121 254 4\n121 347 0\n121 363 49\n121 376 25\n121 384 46\n121 441 43\n121 459 21\n121 496 48\n121 517 33\n121 538 39\n121 565 -1\n121 626 14\n121 631 22\n121 652 25\n121 658 5\n121 695 3\n121 703 31\n121 772 10\n121 827 9\n121 869 48\n121 874 30\n121 911 29\n121 920 3\n121 939 28\n121 962 19\n121 964 4\n121 979 31\n121 981 15\n121 983 37\n121 991 26\n122 2 14\n122 19 27\n122 22 41\n122 25 49\n122 26 30\n122 33 46\n122 52 40\n122 67 2\n122 69 15\n122 84 7\n122 94 13\n122 107 40\n122 131 18\n122 137 36\n122 144 41\n122 176 20\n122 177 24\n122 212 33\n122 239 -1\n122 253 41\n122 277 25\n122 343 13\n122 364 31\n122 365 21\n122 379 10\n122 383 45\n122 414 26\n122 463 7\n122 469 22\n122 478 32\n122 506 32\n122 532 37\n122 540 5\n122 590 22\n122 615 29\n122 640 16\n122 644 0\n122 654 48\n122 655 23\n122 661 34\n122 662 32\n122 689 49\n122 707 16\n122 710 10\n122 722 44\n122 727 8\n122 755 39\n122 798 22\n122 801 0\n122 834 11\n122 842 31\n122 849 17\n122 868 7\n122 903 -2\n122 920 27\n122 929 18\n122 966 44\n122 979 32\n122 995 1\n123 27 22\n123 44 11\n123 47 47\n123 92 -2\n123 93 21\n123 107 42\n123 128 46\n123 136 38\n123 148 23\n123 211 32\n123 218 32\n123 230 28\n123 249 38\n123 263 30\n123 264 44\n123 272 12\n123 281 28\n123 291 21\n123 297 50\n123 299 45\n123 309 -2\n123 355 15\n123 357 23\n123 375 33\n123 376 15\n123 392 49\n123 398 39\n123 400 48\n123 413 9\n123 464 35\n123 514 9\n123 528 41\n123 586 39\n123 597 15\n123 626 35\n123 656 26\n123 698 18\n123 706 23\n123 709 -1\n123 758 42\n123 779 45\n123 786 40\n123 795 1\n123 814 29\n123 816 24\n123 830 19\n123 873 3\n123 875 49\n123 897 21\n123 929 4\n123 952 19\n123 955 2\n124 50 37\n124 76 49\n124 84 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7\n125 964 -2\n125 988 21\n125 989 15\n126 6 24\n126 25 25\n126 93 10\n126 96 11\n126 102 15\n126 115 42\n126 216 3\n126 217 40\n126 230 15\n126 263 15\n126 293 3\n126 328 9\n126 365 34\n126 377 40\n126 389 49\n126 407 20\n126 417 47\n126 426 21\n126 435 24\n126 441 33\n126 516 47\n126 530 13\n126 580 44\n126 590 35\n126 596 36\n126 610 24\n126 612 39\n126 647 8\n126 651 21\n126 675 13\n126 723 17\n126 732 31\n126 746 11\n126 758 8\n126 782 20\n126 793 34\n126 794 15\n126 805 -2\n126 806 1\n126 815 43\n126 828 41\n126 832 35\n126 854 5\n126 872 16\n126 874 9\n126 886 43\n126 903 23\n126 945 10\n126 955 38\n126 960 42\n126 962 45\n127 4 40\n127 16 46\n127 19 41\n127 24 43\n127 34 21\n127 40 43\n127 42 12\n127 47 47\n127 69 45\n127 77 41\n127 90 13\n127 97 31\n127 108 18\n127 119 -2\n127 123 39\n127 136 24\n127 138 0\n127 162 2\n127 169 10\n127 211 20\n127 285 39\n127 293 36\n127 298 50\n127 325 25\n127 381 38\n127 409 7\n127 426 49\n127 432 39\n127 438 9\n127 481 50\n127 496 3\n127 513 25\n127 567 45\n127 599 43\n127 611 23\n127 630 43\n127 639 8\n127 660 38\n127 690 19\n127 698 28\n127 709 25\n127 716 13\n127 725 35\n127 737 3\n127 744 31\n127 751 39\n127 753 18\n127 759 43\n127 763 7\n127 766 25\n127 786 32\n127 807 16\n127 809 1\n127 812 43\n127 814 11\n127 826 49\n127 860 41\n127 919 48\n127 928 22\n127 930 18\n127 938 16\n127 943 47\n127 968 4\n127 979 38\n128 77 9\n128 85 30\n128 89 27\n128 90 28\n128 113 32\n128 139 34\n128 144 -1\n128 155 17\n128 167 31\n128 177 43\n128 255 39\n128 261 5\n128 269 38\n128 315 38\n128 373 25\n128 376 8\n128 382 9\n128 389 -1\n128 390 43\n128 398 48\n128 400 44\n128 410 41\n128 414 -1\n128 432 33\n128 441 5\n128 453 -2\n128 466 33\n128 538 22\n128 544 36\n128 550 8\n128 563 7\n128 588 43\n128 609 -1\n128 611 3\n128 614 35\n128 648 26\n128 660 9\n128 662 10\n128 669 9\n128 714 27\n128 765 4\n128 859 22\n128 884 14\n128 899 7\n128 900 40\n128 917 7\n128 931 14\n128 965 34\n128 982 9\n128 1000 22\n129 28 10\n129 38 17\n129 43 45\n129 92 8\n129 123 8\n129 156 28\n129 183 11\n129 184 16\n129 193 13\n129 273 31\n129 296 48\n129 340 6\n129 352 32\n129 364 35\n129 374 14\n129 391 39\n129 400 19\n129 409 38\n129 423 32\n129 441 19\n129 454 43\n129 492 25\n129 497 35\n129 535 14\n129 556 24\n129 559 22\n129 585 50\n129 647 13\n129 708 22\n129 729 36\n129 739 4\n129 777 36\n129 781 23\n129 782 8\n129 785 12\n129 793 22\n129 810 17\n129 816 47\n129 828 0\n129 833 -2\n129 851 42\n129 863 41\n129 886 17\n129 898 5\n129 915 21\n129 916 37\n129 945 31\n129 956 6\n129 980 12\n129 984 48\n130 14 16\n130 50 27\n130 53 36\n130 71 22\n130 119 31\n130 143 43\n130 147 7\n130 160 28\n130 191 37\n130 200 23\n130 216 18\n130 231 37\n130 233 46\n130 246 6\n130 259 5\n130 269 22\n130 279 38\n130 315 35\n130 336 7\n130 347 35\n130 351 41\n130 376 4\n130 406 45\n130 451 4\n130 455 35\n130 463 16\n130 468 6\n130 499 36\n130 507 7\n130 511 46\n130 529 32\n130 549 17\n130 561 35\n130 586 11\n130 591 46\n130 609 39\n130 646 21\n130 663 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399 38\n132 405 43\n132 409 40\n132 416 32\n132 443 28\n132 573 49\n132 582 32\n132 612 9\n132 637 19\n132 685 41\n132 743 49\n132 755 5\n132 769 15\n132 788 13\n132 801 24\n132 815 33\n132 837 23\n132 856 21\n132 866 15\n132 884 2\n132 887 26\n132 890 28\n132 934 -1\n132 942 46\n132 956 27\n133 4 38\n133 11 29\n133 50 18\n133 78 16\n133 94 24\n133 99 43\n133 102 23\n133 140 31\n133 167 49\n133 178 40\n133 196 27\n133 207 5\n133 234 47\n133 249 -2\n133 275 26\n133 289 23\n133 329 46\n133 330 29\n133 361 47\n133 403 31\n133 473 43\n133 487 -1\n133 499 38\n133 505 45\n133 514 11\n133 521 1\n133 549 5\n133 560 47\n133 619 2\n133 627 37\n133 637 2\n133 658 46\n133 661 16\n133 670 15\n133 678 26\n133 681 24\n133 691 28\n133 693 50\n133 700 23\n133 705 27\n133 718 41\n133 748 40\n133 775 -2\n133 780 9\n133 812 48\n133 814 36\n133 843 30\n133 858 12\n133 870 27\n133 873 38\n133 911 38\n133 921 47\n133 930 41\n133 935 37\n133 942 18\n133 946 48\n133 947 -2\n133 950 33\n133 970 35\n133 984 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983 17\n135 987 40\n135 993 23\n135 1000 41\n136 38 6\n136 47 5\n136 65 25\n136 82 2\n136 123 3\n136 124 33\n136 126 49\n136 133 20\n136 139 5\n136 141 3\n136 167 24\n136 208 33\n136 218 12\n136 219 11\n136 221 21\n136 230 21\n136 242 10\n136 253 28\n136 263 3\n136 311 -2\n136 314 22\n136 324 28\n136 331 -1\n136 344 41\n136 348 39\n136 352 25\n136 389 14\n136 395 39\n136 442 41\n136 448 49\n136 458 46\n136 472 32\n136 486 20\n136 515 34\n136 524 22\n136 575 27\n136 605 38\n136 633 26\n136 648 32\n136 699 20\n136 712 6\n136 720 4\n136 809 42\n136 860 16\n136 876 35\n136 898 34\n136 908 41\n136 916 13\n136 918 8\n136 926 44\n136 964 25\n136 976 19\n137 31 22\n137 44 4\n137 51 36\n137 84 26\n137 148 24\n137 149 25\n137 168 20\n137 191 -1\n137 193 5\n137 204 8\n137 239 42\n137 279 10\n137 280 37\n137 291 48\n137 312 41\n137 328 41\n137 348 21\n137 370 49\n137 421 37\n137 459 48\n137 475 41\n137 490 28\n137 494 37\n137 511 8\n137 523 5\n137 554 10\n137 564 45\n137 566 1\n137 649 20\n137 714 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263 19\n141 282 1\n141 309 47\n141 335 32\n141 337 2\n141 345 14\n141 351 3\n141 369 44\n141 382 13\n141 408 22\n141 478 4\n141 486 27\n141 499 -1\n141 510 22\n141 513 50\n141 518 46\n141 521 32\n141 544 42\n141 563 32\n141 571 5\n141 590 13\n141 608 12\n141 612 49\n141 616 12\n141 629 20\n141 633 21\n141 644 24\n141 655 -2\n141 667 46\n141 676 50\n141 705 0\n141 721 49\n141 725 34\n141 763 7\n141 764 43\n141 776 25\n141 785 28\n141 786 44\n141 805 41\n141 806 1\n141 819 28\n141 820 43\n141 826 10\n141 844 18\n141 857 29\n141 871 49\n141 899 31\n141 916 47\n141 948 1\n141 963 40\n141 972 49\n141 979 49\n142 8 11\n142 35 19\n142 48 14\n142 49 40\n142 83 18\n142 97 45\n142 108 27\n142 115 36\n142 129 25\n142 139 38\n142 143 47\n142 150 42\n142 163 4\n142 201 6\n142 203 30\n142 215 48\n142 277 8\n142 303 13\n142 311 42\n142 312 -2\n142 332 38\n142 383 48\n142 385 12\n142 417 11\n142 433 39\n142 434 43\n142 437 42\n142 442 14\n142 449 9\n142 466 37\n142 482 18\n142 485 15\n142 488 20\n142 556 27\n142 570 14\n142 572 39\n142 596 31\n142 607 30\n142 614 10\n142 653 47\n142 663 13\n142 685 31\n142 686 23\n142 695 7\n142 710 15\n142 721 31\n142 730 17\n142 732 49\n142 746 0\n142 755 48\n142 811 35\n142 822 41\n142 831 16\n142 865 43\n142 868 20\n142 900 18\n142 925 42\n142 933 1\n142 934 13\n142 941 46\n142 945 24\n142 970 12\n142 974 30\n142 998 26\n143 17 42\n143 36 5\n143 57 41\n143 118 33\n143 159 38\n143 170 43\n143 175 16\n143 177 50\n143 186 5\n143 195 17\n143 208 44\n143 211 27\n143 223 21\n143 226 26\n143 255 18\n143 259 6\n143 287 28\n143 288 15\n143 333 0\n143 352 46\n143 381 20\n143 400 20\n143 443 24\n143 448 41\n143 457 13\n143 467 27\n143 470 32\n143 479 44\n143 516 4\n143 535 22\n143 551 24\n143 555 45\n143 587 48\n143 600 31\n143 643 17\n143 645 4\n143 696 22\n143 703 11\n143 719 20\n143 760 43\n143 765 29\n143 804 35\n143 806 50\n143 890 49\n143 894 6\n143 901 38\n143 910 15\n143 922 12\n143 924 34\n143 931 -1\n143 958 39\n143 993 16\n143 995 32\n144 1 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814 47\n145 823 33\n145 830 31\n145 832 9\n145 839 50\n145 842 13\n145 846 14\n145 873 1\n145 878 36\n145 879 24\n145 881 39\n145 918 31\n145 931 25\n145 933 23\n145 950 19\n145 962 49\n145 996 5\n146 8 42\n146 12 -1\n146 19 21\n146 22 37\n146 25 27\n146 34 49\n146 36 21\n146 42 34\n146 84 22\n146 126 5\n146 151 18\n146 162 9\n146 183 29\n146 193 7\n146 202 5\n146 275 30\n146 281 14\n146 310 6\n146 329 6\n146 355 13\n146 390 9\n146 414 43\n146 419 17\n146 425 9\n146 467 46\n146 482 47\n146 500 8\n146 533 14\n146 561 40\n146 587 50\n146 621 6\n146 664 33\n146 680 38\n146 684 17\n146 699 10\n146 716 2\n146 741 24\n146 743 27\n146 827 33\n146 845 48\n146 847 28\n146 853 28\n146 874 6\n146 883 39\n146 886 29\n146 891 6\n146 904 0\n146 907 43\n146 915 20\n146 966 20\n146 968 20\n146 978 19\n146 988 27\n146 998 36\n147 30 48\n147 51 32\n147 58 38\n147 80 34\n147 82 5\n147 92 17\n147 106 33\n147 115 19\n147 125 0\n147 130 40\n147 193 47\n147 201 41\n147 205 19\n147 212 7\n147 231 15\n147 252 22\n147 257 24\n147 295 -1\n147 305 34\n147 320 10\n147 329 18\n147 353 6\n147 397 9\n147 401 36\n147 416 27\n147 423 46\n147 424 35\n147 460 1\n147 466 18\n147 468 10\n147 479 18\n147 496 1\n147 522 1\n147 582 35\n147 603 13\n147 635 39\n147 638 20\n147 644 25\n147 647 50\n147 664 9\n147 676 1\n147 715 13\n147 721 49\n147 727 10\n147 750 40\n147 756 48\n147 769 17\n147 778 36\n147 786 33\n147 831 18\n147 847 4\n147 849 1\n147 870 37\n147 881 35\n147 898 43\n147 899 5\n147 907 19\n147 943 32\n147 949 26\n147 972 47\n148 6 14\n148 133 26\n148 151 27\n148 208 46\n148 231 12\n148 233 4\n148 302 34\n148 310 47\n148 378 23\n148 392 43\n148 408 8\n148 409 33\n148 426 -1\n148 436 2\n148 448 31\n148 479 0\n148 515 26\n148 518 20\n148 519 27\n148 550 16\n148 563 20\n148 590 12\n148 602 24\n148 644 37\n148 652 28\n148 669 24\n148 713 36\n148 743 -1\n148 815 6\n148 834 8\n148 855 31\n148 907 43\n148 931 5\n148 974 12\n149 42 13\n149 44 11\n149 45 29\n149 59 36\n149 85 5\n149 173 29\n149 174 48\n149 217 21\n149 234 3\n149 272 27\n149 295 35\n149 319 24\n149 331 38\n149 338 27\n149 348 2\n149 379 -2\n149 434 10\n149 449 48\n149 451 8\n149 521 17\n149 550 4\n149 553 30\n149 575 5\n149 582 28\n149 583 6\n149 590 9\n149 593 23\n149 611 46\n149 614 24\n149 688 4\n149 698 13\n149 700 30\n149 721 8\n149 762 40\n149 768 13\n149 772 3\n149 789 49\n149 841 13\n149 865 36\n149 876 5\n149 914 31\n149 923 45\n149 927 14\n149 953 30\n149 954 -1\n150 6 31\n150 26 4\n150 29 31\n150 35 14\n150 36 30\n150 37 6\n150 76 45\n150 79 29\n150 97 21\n150 98 19\n150 103 8\n150 125 48\n150 145 4\n150 153 16\n150 195 23\n150 237 9\n150 272 19\n150 277 31\n150 286 15\n150 292 2\n150 308 23\n150 310 14\n150 312 46\n150 321 2\n150 355 3\n150 360 -2\n150 362 42\n150 397 33\n150 400 0\n150 402 40\n150 445 28\n150 471 50\n150 523 8\n150 526 4\n150 532 7\n150 535 16\n150 556 1\n150 563 27\n150 579 -1\n150 586 27\n150 627 44\n150 655 47\n150 672 25\n150 687 11\n150 693 21\n150 715 34\n150 752 6\n150 755 37\n150 756 21\n150 764 42\n150 772 48\n150 774 39\n150 860 17\n150 868 29\n150 880 9\n150 913 -2\n150 914 20\n150 932 34\n150 971 35\n150 992 21\n150 999 16\n151 40 26\n151 58 -2\n151 78 27\n151 93 10\n151 139 6\n151 197 41\n151 202 20\n151 235 45\n151 248 31\n151 250 27\n151 259 44\n151 286 34\n151 369 24\n151 415 17\n151 424 7\n151 448 23\n151 462 -2\n151 523 20\n151 544 49\n151 557 41\n151 564 25\n151 569 46\n151 602 8\n151 621 40\n151 648 15\n151 663 -1\n151 668 8\n151 670 17\n151 672 32\n151 728 34\n151 792 43\n151 805 -2\n151 810 4\n151 811 31\n151 821 22\n151 831 46\n151 848 50\n151 868 21\n151 937 29\n151 940 39\n151 951 16\n151 954 49\n151 990 12\n152 1 42\n152 26 -2\n152 33 3\n152 69 23\n152 78 11\n152 112 10\n152 115 16\n152 116 37\n152 128 38\n152 131 49\n152 135 47\n152 171 9\n152 239 26\n152 244 40\n152 277 5\n152 304 42\n152 348 2\n152 391 13\n152 439 18\n152 450 7\n152 480 15\n152 510 14\n152 537 47\n152 549 15\n152 556 24\n152 647 37\n152 661 44\n152 662 5\n152 667 23\n152 705 22\n152 724 46\n152 732 49\n152 735 37\n152 768 2\n152 772 -2\n152 812 43\n152 834 42\n152 875 7\n152 889 -1\n152 896 6\n152 897 -1\n152 921 13\n152 951 20\n152 957 37\n153 19 49\n153 27 7\n153 60 13\n153 77 24\n153 97 33\n153 110 0\n153 126 9\n153 129 42\n153 146 22\n153 151 14\n153 185 15\n153 201 33\n153 223 13\n153 254 10\n153 263 14\n153 286 44\n153 301 24\n153 304 18\n153 305 34\n153 332 46\n153 363 21\n153 364 3\n153 366 11\n153 408 49\n153 410 19\n153 426 -2\n153 439 34\n153 448 3\n153 452 15\n153 455 13\n153 466 17\n153 470 37\n153 500 3\n153 511 7\n153 525 33\n153 548 19\n153 574 33\n153 586 2\n153 596 22\n153 606 4\n153 607 38\n153 624 13\n153 695 44\n153 697 15\n153 732 33\n153 746 30\n153 751 41\n153 753 32\n153 765 35\n153 782 16\n153 819 32\n153 842 25\n153 855 18\n153 857 41\n153 869 20\n153 889 25\n153 894 14\n153 910 32\n153 928 34\n153 935 24\n153 949 22\n153 984 6\n153 996 2\n154 16 17\n154 41 21\n154 44 6\n154 51 7\n154 61 29\n154 65 25\n154 111 35\n154 134 45\n154 153 5\n154 185 25\n154 215 42\n154 230 42\n154 231 7\n154 244 22\n154 247 -1\n154 249 16\n154 257 35\n154 307 0\n154 341 8\n154 357 32\n154 361 10\n154 375 16\n154 382 17\n154 389 33\n154 401 48\n154 403 0\n154 412 29\n154 418 12\n154 453 30\n154 576 24\n154 584 10\n154 624 33\n154 635 43\n154 660 37\n154 673 29\n154 680 5\n154 684 5\n154 687 21\n154 695 29\n154 710 38\n154 715 19\n154 717 24\n154 765 7\n154 788 22\n154 790 22\n154 793 14\n154 831 46\n154 857 12\n154 877 40\n154 878 45\n154 900 12\n154 917 33\n154 935 33\n154 954 22\n154 966 7\n154 993 26\n155 11 10\n155 31 7\n155 33 16\n155 74 41\n155 89 44\n155 96 45\n155 108 4\n155 111 18\n155 136 24\n155 138 48\n155 217 13\n155 229 2\n155 236 7\n155 265 47\n155 294 45\n155 305 10\n155 306 34\n155 326 33\n155 350 48\n155 362 8\n155 381 28\n155 399 15\n155 427 8\n155 432 47\n155 454 10\n155 479 46\n155 510 34\n155 530 13\n155 549 22\n155 550 24\n155 597 19\n155 623 32\n155 628 4\n155 647 22\n155 658 45\n155 659 19\n155 681 1\n155 706 2\n155 715 14\n155 716 31\n155 722 1\n155 724 45\n155 739 13\n155 761 9\n155 763 1\n155 776 17\n155 783 -2\n155 835 40\n155 846 33\n155 867 5\n155 876 12\n155 892 48\n155 906 -1\n155 911 35\n155 914 25\n155 918 47\n155 919 22\n155 924 43\n155 927 38\n155 968 -2\n155 983 23\n156 27 13\n156 76 31\n156 98 36\n156 103 14\n156 144 20\n156 167 41\n156 179 1\n156 195 48\n156 237 26\n156 242 9\n156 248 13\n156 262 20\n156 284 45\n156 286 37\n156 287 33\n156 290 21\n156 303 17\n156 314 40\n156 321 44\n156 378 32\n156 379 20\n156 409 34\n156 416 26\n156 452 27\n156 474 28\n156 523 15\n156 525 4\n156 560 8\n156 595 9\n156 597 18\n156 621 24\n156 645 23\n156 689 30\n156 701 42\n156 707 44\n156 723 17\n156 724 24\n156 729 22\n156 768 25\n156 777 24\n156 781 21\n156 784 29\n156 791 41\n156 797 42\n156 806 47\n156 814 23\n156 829 0\n156 830 20\n156 835 16\n156 855 40\n156 856 18\n156 883 5\n156 884 44\n156 894 33\n156 897 44\n156 903 10\n156 926 43\n156 927 42\n156 931 11\n156 932 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14\n165 597 46\n165 613 43\n165 623 40\n165 658 2\n165 668 48\n165 715 25\n165 735 17\n165 752 10\n165 753 33\n165 778 30\n165 781 10\n165 806 41\n165 850 30\n165 877 12\n165 893 8\n165 914 50\n165 928 10\n165 944 50\n165 946 13\n165 958 19\n165 974 28\n166 21 7\n166 25 0\n166 30 21\n166 105 16\n166 108 21\n166 122 45\n166 147 17\n166 209 8\n166 215 44\n166 256 11\n166 336 21\n166 343 36\n166 368 42\n166 399 42\n166 453 3\n166 487 39\n166 496 19\n166 529 13\n166 530 36\n166 553 1\n166 571 3\n166 580 -2\n166 611 18\n166 617 29\n166 667 24\n166 668 32\n166 691 33\n166 717 44\n166 722 23\n166 723 46\n166 736 33\n166 755 6\n166 783 34\n166 808 30\n166 827 0\n166 828 1\n166 842 -2\n166 850 33\n166 854 27\n166 856 44\n166 865 31\n166 880 20\n166 883 25\n166 928 47\n166 957 20\n167 57 16\n167 107 12\n167 115 25\n167 126 1\n167 158 2\n167 165 48\n167 195 39\n167 200 44\n167 230 -2\n167 235 16\n167 253 8\n167 284 5\n167 288 14\n167 317 40\n167 339 31\n167 373 14\n167 376 31\n167 388 21\n167 400 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1\n170 952 24\n170 982 27\n171 41 36\n171 43 8\n171 47 21\n171 55 -2\n171 62 48\n171 74 29\n171 76 6\n171 82 22\n171 92 31\n171 106 42\n171 154 9\n171 157 37\n171 159 29\n171 187 24\n171 225 17\n171 249 28\n171 273 46\n171 298 36\n171 303 28\n171 339 28\n171 362 15\n171 366 4\n171 386 38\n171 411 26\n171 423 48\n171 426 15\n171 434 14\n171 460 -1\n171 478 47\n171 552 50\n171 584 47\n171 615 -2\n171 670 37\n171 680 35\n171 682 6\n171 698 -2\n171 709 26\n171 777 27\n171 781 37\n171 793 42\n171 804 22\n171 810 -2\n171 862 7\n171 872 30\n171 883 31\n171 889 41\n171 908 42\n171 917 11\n171 927 8\n171 932 15\n171 936 45\n171 968 47\n171 969 43\n171 972 30\n171 981 47\n172 17 37\n172 29 14\n172 38 21\n172 50 -1\n172 54 8\n172 58 42\n172 63 19\n172 69 50\n172 81 18\n172 104 8\n172 112 26\n172 115 41\n172 159 45\n172 169 11\n172 177 5\n172 182 48\n172 183 35\n172 270 11\n172 359 14\n172 423 35\n172 424 0\n172 441 40\n172 501 13\n172 510 33\n172 530 35\n172 562 9\n172 569 15\n172 585 5\n172 593 14\n172 614 47\n172 619 28\n172 630 22\n172 634 13\n172 686 48\n172 688 -1\n172 729 34\n172 741 8\n172 744 6\n172 777 29\n172 812 27\n172 815 -1\n172 818 10\n172 877 30\n172 884 -1\n172 893 24\n172 897 27\n172 916 16\n172 954 19\n172 957 8\n173 14 25\n173 22 7\n173 40 48\n173 74 48\n173 76 41\n173 99 20\n173 101 5\n173 105 24\n173 108 35\n173 119 9\n173 135 43\n173 183 22\n173 239 39\n173 242 7\n173 254 42\n173 268 38\n173 282 9\n173 291 42\n173 320 30\n173 334 41\n173 338 2\n173 377 13\n173 405 8\n173 413 -2\n173 423 18\n173 426 -1\n173 456 -2\n173 457 2\n173 463 34\n173 496 40\n173 497 -1\n173 504 47\n173 513 19\n173 530 6\n173 535 24\n173 551 0\n173 584 49\n173 595 14\n173 598 4\n173 619 20\n173 623 35\n173 626 32\n173 694 6\n173 700 3\n173 716 0\n173 718 5\n173 748 37\n173 805 23\n173 822 26\n173 836 34\n173 842 43\n173 877 10\n173 900 14\n173 928 9\n173 943 41\n173 966 13\n173 974 5\n174 22 37\n174 39 38\n174 40 10\n174 76 44\n174 123 35\n174 126 6\n174 138 28\n174 145 21\n174 158 34\n174 192 16\n174 206 0\n174 248 46\n174 251 37\n174 254 7\n174 265 13\n174 273 11\n174 293 20\n174 297 17\n174 325 36\n174 394 32\n174 488 24\n174 501 6\n174 502 0\n174 518 27\n174 544 15\n174 554 10\n174 591 15\n174 596 35\n174 597 18\n174 601 47\n174 626 7\n174 659 36\n174 694 35\n174 703 6\n174 706 39\n174 718 35\n174 738 34\n174 770 -1\n174 771 12\n174 800 27\n174 818 23\n174 836 10\n174 918 12\n174 976 13\n174 990 3\n174 997 44\n175 1 24\n175 4 9\n175 34 40\n175 41 45\n175 106 37\n175 149 26\n175 163 19\n175 165 12\n175 176 20\n175 177 0\n175 205 22\n175 227 28\n175 237 10\n175 247 38\n175 251 36\n175 300 45\n175 310 8\n175 332 26\n175 349 6\n175 363 18\n175 405 36\n175 446 12\n175 469 32\n175 510 41\n175 547 17\n175 561 45\n175 587 22\n175 593 39\n175 595 30\n175 599 -2\n175 620 3\n175 674 34\n175 719 15\n175 755 8\n175 770 33\n175 785 40\n175 789 45\n175 836 13\n175 888 37\n175 917 22\n175 931 9\n175 940 37\n175 951 5\n175 984 26\n176 23 9\n176 41 38\n176 55 0\n176 69 15\n176 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3\n177 705 24\n177 715 45\n177 758 47\n177 763 40\n177 765 22\n177 784 47\n177 790 25\n177 835 29\n177 837 33\n177 864 38\n177 890 38\n178 64 40\n178 75 34\n178 108 5\n178 120 -1\n178 127 16\n178 136 37\n178 198 12\n178 214 41\n178 217 27\n178 225 28\n178 251 15\n178 305 23\n178 326 17\n178 353 19\n178 398 11\n178 404 33\n178 465 48\n178 468 33\n178 470 2\n178 482 19\n178 488 1\n178 523 -1\n178 578 20\n178 579 48\n178 587 5\n178 741 35\n178 750 15\n178 766 42\n178 769 2\n178 770 34\n178 801 42\n178 806 45\n178 820 27\n178 864 30\n178 911 32\n179 27 2\n179 33 22\n179 34 7\n179 63 28\n179 68 23\n179 71 26\n179 145 14\n179 153 3\n179 165 22\n179 171 11\n179 191 34\n179 194 1\n179 201 26\n179 226 40\n179 266 26\n179 280 6\n179 282 35\n179 284 35\n179 293 33\n179 295 2\n179 306 40\n179 309 48\n179 339 0\n179 370 28\n179 378 1\n179 381 41\n179 390 27\n179 440 16\n179 466 33\n179 488 18\n179 524 22\n179 603 20\n179 612 32\n179 618 35\n179 692 21\n179 703 41\n179 732 8\n179 759 9\n179 877 17\n179 900 16\n179 918 18\n179 929 10\n179 948 21\n179 991 24\n180 7 20\n180 9 31\n180 25 2\n180 27 26\n180 36 10\n180 40 14\n180 43 32\n180 55 16\n180 77 10\n180 96 34\n180 118 12\n180 140 46\n180 146 1\n180 151 27\n180 156 50\n180 193 30\n180 195 19\n180 204 21\n180 213 15\n180 255 27\n180 266 23\n180 293 14\n180 298 44\n180 345 35\n180 362 11\n180 363 35\n180 424 6\n180 432 39\n180 436 30\n180 439 34\n180 457 45\n180 485 28\n180 493 15\n180 507 46\n180 516 37\n180 530 50\n180 545 24\n180 550 4\n180 586 12\n180 595 3\n180 597 30\n180 599 27\n180 606 33\n180 619 21\n180 661 5\n180 678 41\n180 684 23\n180 707 1\n180 717 27\n180 732 41\n180 733 18\n180 755 36\n180 765 28\n180 805 45\n180 808 22\n180 818 5\n180 820 13\n180 836 33\n180 848 20\n180 852 33\n180 857 28\n180 976 10\n180 991 25\n181 38 39\n181 39 9\n181 58 39\n181 59 27\n181 68 41\n181 91 46\n181 136 43\n181 146 41\n181 163 8\n181 251 40\n181 289 11\n181 346 22\n181 363 18\n181 364 11\n181 369 5\n181 373 16\n181 374 23\n181 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19 47\n183 126 50\n183 128 48\n183 135 4\n183 141 37\n183 146 20\n183 163 4\n183 190 15\n183 207 9\n183 210 19\n183 221 -1\n183 235 14\n183 255 21\n183 260 34\n183 271 19\n183 310 43\n183 356 30\n183 390 24\n183 397 47\n183 443 10\n183 482 20\n183 498 17\n183 500 0\n183 512 10\n183 544 40\n183 557 0\n183 567 23\n183 569 30\n183 616 3\n183 622 16\n183 630 13\n183 638 36\n183 641 9\n183 642 11\n183 659 32\n183 664 39\n183 670 24\n183 696 6\n183 729 -2\n183 773 44\n183 783 34\n183 786 49\n183 861 7\n183 876 23\n183 900 43\n183 921 7\n183 922 37\n183 936 0\n183 941 41\n183 946 9\n184 32 41\n184 33 22\n184 39 42\n184 59 37\n184 70 12\n184 118 28\n184 136 13\n184 146 39\n184 163 5\n184 169 7\n184 173 43\n184 215 11\n184 249 50\n184 284 21\n184 288 7\n184 316 10\n184 329 1\n184 354 29\n184 367 41\n184 370 15\n184 372 28\n184 373 -1\n184 375 42\n184 381 44\n184 403 33\n184 415 3\n184 429 23\n184 430 17\n184 432 24\n184 455 46\n184 460 38\n184 467 50\n184 498 19\n184 521 23\n184 559 45\n184 581 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595 28\n187 596 15\n187 614 18\n187 621 9\n187 646 6\n187 665 48\n187 708 29\n187 712 24\n187 751 2\n187 756 42\n187 781 39\n187 788 20\n187 793 25\n187 818 7\n187 844 30\n187 850 -2\n187 873 40\n187 881 20\n187 898 3\n187 929 40\n187 982 10\n188 12 10\n188 19 32\n188 22 49\n188 27 -2\n188 41 50\n188 54 41\n188 55 26\n188 61 29\n188 68 2\n188 83 48\n188 126 12\n188 130 42\n188 131 18\n188 181 49\n188 206 34\n188 227 2\n188 243 39\n188 295 12\n188 310 29\n188 331 41\n188 370 35\n188 373 13\n188 385 18\n188 403 19\n188 426 38\n188 439 19\n188 455 20\n188 461 23\n188 464 5\n188 492 15\n188 503 17\n188 511 5\n188 522 46\n188 526 28\n188 532 18\n188 574 11\n188 585 22\n188 588 26\n188 608 46\n188 622 39\n188 646 15\n188 673 50\n188 746 28\n188 757 11\n188 768 42\n188 777 26\n188 789 0\n188 800 35\n188 825 24\n188 827 37\n188 833 13\n188 842 14\n188 867 -1\n188 871 18\n188 887 12\n188 891 4\n188 938 0\n188 940 -2\n188 947 3\n188 972 3\n189 23 17\n189 62 17\n189 82 37\n189 111 35\n189 160 14\n189 205 10\n189 209 18\n189 224 45\n189 274 49\n189 291 1\n189 308 29\n189 368 42\n189 372 18\n189 385 24\n189 395 23\n189 425 10\n189 446 12\n189 449 8\n189 450 24\n189 472 16\n189 479 22\n189 505 11\n189 548 31\n189 573 20\n189 581 3\n189 584 16\n189 597 17\n189 604 47\n189 612 37\n189 625 25\n189 638 8\n189 641 47\n189 642 49\n189 661 13\n189 670 47\n189 744 28\n189 749 16\n189 750 49\n189 765 28\n189 802 11\n189 809 6\n189 813 49\n189 817 7\n189 896 31\n189 909 43\n189 925 29\n189 956 19\n189 999 19\n190 3 5\n190 5 29\n190 6 30\n190 12 46\n190 27 35\n190 30 16\n190 123 34\n190 185 34\n190 233 41\n190 248 45\n190 279 46\n190 282 43\n190 292 46\n190 321 27\n190 328 37\n190 335 15\n190 365 20\n190 373 2\n190 397 31\n190 408 15\n190 417 12\n190 451 20\n190 463 14\n190 512 46\n190 535 39\n190 546 23\n190 565 41\n190 578 24\n190 579 49\n190 597 39\n190 599 12\n190 642 36\n190 663 20\n190 727 26\n190 733 36\n190 768 0\n190 779 27\n190 820 11\n190 840 18\n190 911 34\n190 924 33\n190 943 25\n190 983 24\n191 55 43\n191 86 38\n191 125 28\n191 131 46\n191 152 41\n191 158 18\n191 173 44\n191 179 46\n191 194 24\n191 224 49\n191 230 46\n191 244 19\n191 246 6\n191 254 14\n191 285 19\n191 330 31\n191 331 12\n191 344 -2\n191 383 3\n191 397 33\n191 439 47\n191 454 50\n191 462 17\n191 533 8\n191 563 15\n191 592 28\n191 595 19\n191 605 46\n191 620 27\n191 641 32\n191 677 25\n191 692 33\n191 721 8\n191 736 36\n191 739 43\n191 761 11\n191 764 2\n191 772 6\n191 785 42\n191 796 4\n191 804 25\n191 819 25\n191 827 2\n191 871 4\n191 933 14\n191 999 7\n192 18 22\n192 35 35\n192 74 43\n192 76 19\n192 93 9\n192 108 3\n192 145 4\n192 148 30\n192 152 8\n192 161 40\n192 181 14\n192 224 5\n192 251 7\n192 278 17\n192 298 31\n192 305 23\n192 338 25\n192 355 19\n192 358 36\n192 371 17\n192 378 46\n192 389 33\n192 454 17\n192 489 16\n192 492 45\n192 496 14\n192 523 20\n192 533 50\n192 536 15\n192 538 32\n192 541 3\n192 545 20\n192 592 13\n192 639 32\n192 654 41\n192 684 41\n192 699 10\n192 703 9\n192 719 3\n192 725 19\n192 731 -1\n192 806 22\n192 811 7\n192 835 3\n192 876 22\n192 943 10\n192 962 42\n192 963 39\n192 975 42\n192 999 6\n193 1 14\n193 21 -2\n193 31 44\n193 54 12\n193 58 0\n193 86 32\n193 115 47\n193 140 45\n193 170 3\n193 225 18\n193 230 16\n193 235 24\n193 241 30\n193 243 2\n193 286 5\n193 288 44\n193 318 5\n193 358 16\n193 364 49\n193 365 16\n193 373 28\n193 386 26\n193 393 25\n193 401 2\n193 432 27\n193 440 19\n193 461 24\n193 464 40\n193 470 25\n193 515 8\n193 549 15\n193 631 25\n193 639 2\n193 641 27\n193 643 26\n193 736 0\n193 762 16\n193 764 12\n193 787 22\n193 822 33\n193 839 47\n193 882 39\n193 888 18\n193 945 0\n193 952 50\n193 954 34\n193 964 1\n193 969 41\n194 32 22\n194 61 42\n194 75 10\n194 161 30\n194 170 17\n194 180 6\n194 195 37\n194 217 0\n194 245 24\n194 279 5\n194 292 31\n194 350 -2\n194 352 -1\n194 376 10\n194 403 2\n194 410 50\n194 423 -1\n194 492 1\n194 515 30\n194 519 39\n194 533 20\n194 536 27\n194 556 33\n194 561 1\n194 563 -1\n194 643 -1\n194 644 40\n194 686 43\n194 690 34\n194 713 24\n194 762 0\n194 773 42\n194 809 18\n194 859 11\n194 918 8\n194 925 22\n194 961 18\n194 991 32\n195 9 46\n195 46 48\n195 52 42\n195 74 19\n195 89 16\n195 135 38\n195 138 8\n195 159 11\n195 163 39\n195 184 5\n195 243 20\n195 305 39\n195 343 3\n195 364 20\n195 376 49\n195 377 28\n195 392 7\n195 397 42\n195 405 16\n195 485 35\n195 489 29\n195 510 33\n195 546 43\n195 556 14\n195 578 39\n195 621 15\n195 647 18\n195 672 38\n195 730 12\n195 736 39\n195 738 18\n195 811 49\n195 899 43\n195 983 18\n196 31 3\n196 40 1\n196 57 14\n196 69 32\n196 77 28\n196 129 46\n196 148 39\n196 150 43\n196 160 39\n196 165 43\n196 215 37\n196 258 19\n196 286 -2\n196 292 15\n196 319 17\n196 328 0\n196 342 29\n196 343 0\n196 370 30\n196 418 37\n196 442 19\n196 488 8\n196 502 1\n196 506 31\n196 528 36\n196 533 -2\n196 535 12\n196 542 36\n196 558 49\n196 586 7\n196 603 14\n196 605 31\n196 622 -1\n196 636 20\n196 659 10\n196 702 3\n196 719 1\n196 752 17\n196 755 37\n196 773 26\n196 784 37\n196 805 19\n196 806 27\n196 826 25\n196 833 41\n196 845 33\n196 886 12\n196 899 -2\n196 903 36\n196 914 18\n196 920 16\n196 957 35\n196 996 15\n197 66 49\n197 93 10\n197 141 10\n197 158 -1\n197 206 19\n197 221 40\n197 256 44\n197 274 35\n197 309 42\n197 327 43\n197 328 24\n197 332 32\n197 348 4\n197 386 2\n197 450 49\n197 451 6\n197 455 42\n197 477 -2\n197 486 35\n197 491 44\n197 506 10\n197 521 49\n197 529 27\n197 534 37\n197 540 12\n197 564 28\n197 591 4\n197 609 -1\n197 647 32\n197 668 34\n197 671 3\n197 690 42\n197 691 7\n197 700 47\n197 702 19\n197 707 19\n197 710 5\n197 739 17\n197 793 39\n197 835 3\n197 836 5\n197 846 3\n197 882 -1\n197 896 19\n197 938 21\n197 991 29\n198 10 27\n198 56 49\n198 58 27\n198 61 19\n198 65 1\n198 142 36\n198 200 22\n198 242 29\n198 254 34\n198 262 42\n198 276 24\n198 292 12\n198 293 27\n198 315 -1\n198 322 28\n198 328 0\n198 337 45\n198 400 8\n198 401 38\n198 412 36\n198 415 10\n198 443 20\n198 445 3\n198 459 9\n198 465 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12\n201 938 13\n201 961 7\n201 982 14\n201 993 9\n202 1 41\n202 42 2\n202 44 38\n202 62 31\n202 74 50\n202 104 15\n202 111 32\n202 117 27\n202 125 47\n202 150 21\n202 197 36\n202 211 22\n202 244 45\n202 246 25\n202 249 24\n202 267 43\n202 293 19\n202 300 38\n202 303 48\n202 339 29\n202 373 32\n202 377 -1\n202 393 19\n202 396 29\n202 401 0\n202 420 21\n202 425 24\n202 456 30\n202 468 7\n202 480 1\n202 481 0\n202 485 42\n202 508 3\n202 526 0\n202 535 19\n202 539 4\n202 618 1\n202 639 27\n202 658 6\n202 676 10\n202 679 12\n202 691 34\n202 713 32\n202 719 17\n202 720 27\n202 730 31\n202 742 1\n202 775 29\n202 798 31\n202 849 29\n202 861 34\n202 873 4\n202 881 20\n202 931 20\n202 951 39\n202 959 17\n202 996 45\n203 13 9\n203 30 28\n203 34 5\n203 46 24\n203 49 27\n203 71 -1\n203 80 45\n203 97 44\n203 135 12\n203 148 15\n203 170 19\n203 177 22\n203 211 21\n203 230 48\n203 246 34\n203 252 15\n203 268 8\n203 287 46\n203 361 21\n203 373 23\n203 391 12\n203 434 17\n203 447 6\n203 486 9\n203 487 17\n203 489 32\n203 499 3\n203 502 6\n203 541 40\n203 556 21\n203 628 42\n203 649 36\n203 660 13\n203 665 3\n203 702 0\n203 714 49\n203 726 41\n203 735 0\n203 736 22\n203 762 49\n203 777 16\n203 784 16\n203 790 26\n203 793 41\n203 798 27\n203 835 8\n203 843 31\n203 846 30\n203 854 44\n203 885 15\n203 888 39\n203 916 8\n203 928 49\n204 3 11\n204 15 11\n204 30 50\n204 44 17\n204 72 36\n204 87 37\n204 110 36\n204 112 21\n204 171 17\n204 178 15\n204 184 25\n204 220 40\n204 223 22\n204 235 43\n204 236 4\n204 238 7\n204 251 4\n204 275 50\n204 309 35\n204 337 17\n204 350 45\n204 374 46\n204 382 25\n204 418 23\n204 441 7\n204 461 26\n204 541 37\n204 543 42\n204 580 22\n204 596 31\n204 610 30\n204 619 27\n204 660 23\n204 676 3\n204 678 14\n204 750 21\n204 756 34\n204 844 24\n204 857 19\n204 971 8\n204 972 42\n204 976 16\n204 985 14\n205 53 14\n205 71 30\n205 106 6\n205 122 32\n205 130 21\n205 136 36\n205 138 6\n205 143 32\n205 157 8\n205 178 37\n205 230 36\n205 241 25\n205 336 26\n205 343 29\n205 346 18\n205 367 35\n205 369 46\n205 390 25\n205 409 6\n205 429 19\n205 445 1\n205 473 41\n205 493 38\n205 509 32\n205 559 7\n205 560 38\n205 607 25\n205 619 46\n205 690 19\n205 716 37\n205 755 9\n205 798 37\n205 804 9\n205 807 20\n205 813 25\n205 821 30\n205 829 34\n205 843 21\n205 866 47\n205 971 41\n206 39 7\n206 54 29\n206 77 19\n206 105 32\n206 109 28\n206 128 47\n206 132 45\n206 139 10\n206 154 30\n206 161 41\n206 165 25\n206 169 10\n206 209 15\n206 221 5\n206 246 33\n206 256 48\n206 265 33\n206 287 32\n206 307 45\n206 320 25\n206 330 7\n206 358 48\n206 395 45\n206 446 14\n206 502 18\n206 518 25\n206 525 12\n206 529 3\n206 534 37\n206 542 31\n206 582 11\n206 624 16\n206 642 50\n206 667 22\n206 670 37\n206 672 19\n206 691 30\n206 696 8\n206 699 0\n206 719 48\n206 734 48\n206 787 14\n206 794 2\n206 803 35\n206 805 21\n206 810 33\n206 835 0\n206 854 21\n206 920 15\n206 924 45\n206 965 36\n206 989 20\n206 991 31\n207 9 47\n207 65 35\n207 106 23\n207 135 19\n207 142 23\n207 175 44\n207 181 15\n207 199 45\n207 201 42\n207 224 21\n207 374 35\n207 381 12\n207 391 32\n207 403 27\n207 418 23\n207 463 10\n207 464 30\n207 527 27\n207 564 13\n207 600 29\n207 617 4\n207 671 38\n207 679 47\n207 771 24\n207 782 5\n207 809 39\n207 812 34\n207 858 49\n207 895 15\n207 912 12\n207 920 25\n207 947 19\n207 952 50\n207 960 18\n207 969 22\n208 5 10\n208 8 18\n208 48 30\n208 84 44\n208 100 3\n208 111 15\n208 134 11\n208 139 18\n208 163 43\n208 170 14\n208 181 22\n208 210 39\n208 214 26\n208 221 1\n208 226 38\n208 232 44\n208 244 22\n208 302 3\n208 348 28\n208 389 11\n208 417 2\n208 430 10\n208 440 36\n208 455 23\n208 476 3\n208 487 45\n208 489 41\n208 531 4\n208 566 34\n208 690 39\n208 723 29\n208 736 37\n208 740 14\n208 809 7\n208 824 41\n208 834 20\n208 847 31\n208 863 7\n208 875 41\n208 882 36\n208 914 50\n208 969 -1\n209 3 18\n209 26 42\n209 42 40\n209 65 47\n209 80 -2\n209 83 41\n209 129 23\n209 131 45\n209 133 20\n209 163 45\n209 171 19\n209 185 16\n209 213 27\n209 244 17\n209 276 41\n209 435 7\n209 438 3\n209 450 7\n209 476 14\n209 511 12\n209 537 48\n209 569 35\n209 594 36\n209 598 0\n209 611 49\n209 636 21\n209 692 39\n209 702 47\n209 739 48\n209 799 9\n209 800 10\n209 804 45\n209 814 24\n209 898 48\n209 908 45\n209 910 21\n209 914 17\n209 930 46\n209 931 30\n209 970 40\n209 980 5\n209 983 22\n209 996 46\n210 5 46\n210 21 13\n210 38 5\n210 71 5\n210 110 -2\n210 113 36\n210 152 4\n210 156 25\n210 191 8\n210 194 24\n210 202 44\n210 212 31\n210 215 35\n210 227 15\n210 285 23\n210 303 16\n210 365 37\n210 393 36\n210 408 44\n210 460 26\n210 469 25\n210 481 41\n210 510 48\n210 520 13\n210 525 25\n210 535 38\n210 621 27\n210 643 12\n210 762 38\n210 787 48\n210 839 46\n210 844 1\n210 855 50\n210 889 25\n210 915 36\n210 921 -2\n210 929 2\n210 991 50\n211 3 41\n211 6 11\n211 14 34\n211 31 38\n211 42 5\n211 70 47\n211 117 3\n211 119 10\n211 148 -2\n211 171 -2\n211 187 14\n211 198 21\n211 224 26\n211 232 16\n211 264 -1\n211 267 47\n211 284 37\n211 287 17\n211 301 40\n211 323 19\n211 328 42\n211 353 32\n211 358 -1\n211 388 -1\n211 410 18\n211 446 0\n211 460 43\n211 461 45\n211 509 30\n211 557 9\n211 570 21\n211 593 48\n211 608 9\n211 619 27\n211 634 50\n211 655 1\n211 658 21\n211 660 39\n211 685 13\n211 763 46\n211 768 14\n211 769 -1\n211 850 36\n211 853 2\n211 886 3\n211 913 7\n211 917 33\n211 938 34\n211 941 45\n211 980 44\n212 35 6\n212 61 31\n212 63 18\n212 79 19\n212 82 7\n212 106 45\n212 109 42\n212 131 22\n212 142 -1\n212 162 31\n212 164 -1\n212 235 29\n212 239 -2\n212 246 10\n212 254 35\n212 264 23\n212 273 25\n212 283 35\n212 312 10\n212 334 46\n212 356 33\n212 358 -1\n212 374 32\n212 448 12\n212 452 3\n212 457 27\n212 473 20\n212 479 15\n212 484 15\n212 555 26\n212 567 48\n212 626 39\n212 631 19\n212 672 41\n212 675 28\n212 687 16\n212 723 28\n212 730 50\n212 792 32\n212 803 50\n212 838 17\n212 911 45\n212 925 9\n213 17 12\n213 24 20\n213 26 39\n213 61 5\n213 81 7\n213 106 42\n213 107 33\n213 116 9\n213 142 5\n213 156 39\n213 200 41\n213 215 5\n213 248 31\n213 275 4\n213 281 26\n213 293 11\n213 315 15\n213 389 17\n213 426 -1\n213 429 47\n213 430 16\n213 536 30\n213 546 33\n213 566 30\n213 574 2\n213 576 6\n213 581 29\n213 591 30\n213 630 48\n213 635 20\n213 656 31\n213 674 24\n213 719 35\n213 738 48\n213 741 10\n213 769 4\n213 791 30\n213 803 14\n213 843 39\n213 902 10\n213 904 26\n213 926 31\n213 936 25\n213 964 27\n213 989 29\n213 994 50\n214 6 10\n214 13 11\n214 36 -2\n214 40 48\n214 52 22\n214 61 21\n214 74 42\n214 81 50\n214 123 46\n214 124 17\n214 140 35\n214 146 13\n214 158 19\n214 181 6\n214 193 15\n214 199 31\n214 226 17\n214 244 48\n214 290 10\n214 324 32\n214 358 48\n214 383 2\n214 405 26\n214 417 10\n214 433 21\n214 461 6\n214 479 44\n214 487 2\n214 498 -2\n214 518 20\n214 521 4\n214 541 48\n214 550 9\n214 551 33\n214 577 12\n214 586 19\n214 589 25\n214 617 42\n214 634 36\n214 661 28\n214 664 36\n214 677 42\n214 682 50\n214 688 26\n214 699 4\n214 715 8\n214 742 37\n214 748 38\n214 752 19\n214 859 34\n214 863 30\n214 885 5\n214 891 29\n214 910 42\n214 922 11\n214 953 35\n214 989 42\n215 37 13\n215 38 22\n215 40 15\n215 47 19\n215 101 38\n215 120 23\n215 136 9\n215 140 31\n215 153 38\n215 161 23\n215 168 -2\n215 179 -1\n215 210 5\n215 237 15\n215 272 47\n215 277 40\n215 279 27\n215 292 38\n215 312 9\n215 354 21\n215 389 10\n215 440 37\n215 443 17\n215 458 18\n215 462 17\n215 485 20\n215 494 22\n215 507 31\n215 532 -2\n215 556 21\n215 594 4\n215 603 50\n215 637 18\n215 641 7\n215 645 44\n215 658 49\n215 663 0\n215 664 1\n215 680 43\n215 689 9\n215 731 22\n215 795 42\n215 813 42\n215 839 39\n215 875 12\n215 900 16\n215 942 7\n215 973 23\n216 19 26\n216 45 13\n216 50 -1\n216 155 37\n216 192 36\n216 201 33\n216 214 6\n216 244 7\n216 247 41\n216 258 25\n216 270 44\n216 276 33\n216 280 47\n216 290 50\n216 307 10\n216 341 10\n216 351 9\n216 363 6\n216 375 48\n216 389 18\n216 425 23\n216 472 25\n216 476 28\n216 579 12\n216 582 38\n216 586 12\n216 605 3\n216 613 29\n216 618 30\n216 661 21\n216 670 45\n216 692 31\n216 700 16\n216 715 6\n216 772 42\n216 776 16\n216 794 43\n216 804 44\n216 852 5\n216 890 11\n216 903 47\n216 912 44\n216 923 43\n216 927 46\n216 930 23\n216 957 16\n216 962 10\n216 971 48\n217 5 37\n217 28 2\n217 42 33\n217 48 35\n217 51 12\n217 125 15\n217 161 18\n217 202 9\n217 214 1\n217 218 24\n217 231 1\n217 238 16\n217 250 31\n217 266 9\n217 269 20\n217 274 27\n217 285 30\n217 295 6\n217 349 24\n217 388 14\n217 406 47\n217 409 38\n217 471 2\n217 476 48\n217 484 43\n217 504 18\n217 506 8\n217 533 46\n217 535 15\n217 536 41\n217 547 8\n217 564 22\n217 586 23\n217 604 13\n217 606 27\n217 629 38\n217 634 11\n217 638 30\n217 656 1\n217 687 11\n217 719 2\n217 750 43\n217 751 40\n217 766 28\n217 805 2\n217 813 38\n217 839 16\n217 844 50\n217 877 3\n217 892 10\n217 894 7\n217 917 30\n217 964 40\n217 969 47\n217 973 9\n217 977 50\n217 988 40\n218 47 49\n218 60 7\n218 69 31\n218 100 14\n218 155 36\n218 168 0\n218 197 22\n218 253 15\n218 277 44\n218 324 17\n218 398 44\n218 404 25\n218 442 23\n218 469 1\n218 495 3\n218 505 37\n218 518 7\n218 529 29\n218 536 22\n218 540 7\n218 543 47\n218 567 50\n218 568 27\n218 577 11\n218 589 40\n218 609 48\n218 611 33\n218 633 40\n218 668 28\n218 677 29\n218 702 26\n218 712 4\n218 780 9\n218 809 7\n218 820 31\n218 826 46\n218 827 11\n218 846 1\n218 860 13\n218 889 8\n218 891 39\n218 911 20\n218 917 2\n218 925 6\n218 930 4\n218 932 44\n218 959 25\n218 978 12\n219 26 44\n219 61 50\n219 65 48\n219 72 12\n219 101 26\n219 103 2\n219 127 48\n219 128 9\n219 148 18\n219 179 14\n219 218 22\n219 224 32\n219 237 49\n219 243 4\n219 254 38\n219 308 11\n219 329 49\n219 349 44\n219 355 48\n219 374 19\n219 401 17\n219 442 41\n219 458 7\n219 489 26\n219 540 10\n219 543 40\n219 567 27\n219 591 27\n219 633 23\n219 679 37\n219 699 49\n219 713 3\n219 750 42\n219 770 23\n219 777 21\n219 794 19\n219 802 -2\n219 813 30\n219 856 26\n219 924 42\n219 937 36\n219 943 8\n219 960 2\n219 972 37\n220 5 -2\n220 43 37\n220 58 22\n220 65 38\n220 88 23\n220 100 40\n220 105 5\n220 197 12\n220 200 25\n220 226 8\n220 246 50\n220 279 45\n220 306 14\n220 406 11\n220 446 40\n220 453 29\n220 512 15\n220 522 0\n220 580 37\n220 595 -2\n220 601 1\n220 609 35\n220 688 26\n220 736 28\n220 765 4\n220 767 9\n220 773 41\n220 802 6\n220 837 2\n220 864 48\n220 865 6\n220 872 27\n220 880 -2\n220 891 45\n220 892 0\n220 923 48\n220 924 13\n220 935 17\n220 957 39\n220 976 38\n220 998 34\n221 4 40\n221 63 26\n221 67 22\n221 77 1\n221 79 11\n221 86 12\n221 90 42\n221 93 8\n221 124 7\n221 131 49\n221 157 30\n221 169 13\n221 179 30\n221 209 50\n221 259 18\n221 296 -2\n221 317 16\n221 331 33\n221 338 46\n221 350 34\n221 400 12\n221 409 48\n221 434 10\n221 439 50\n221 452 28\n221 481 19\n221 489 12\n221 504 4\n221 552 36\n221 564 1\n221 588 32\n221 605 28\n221 610 27\n221 640 30\n221 668 14\n221 673 3\n221 708 3\n221 788 21\n221 823 -2\n221 830 32\n221 840 30\n221 853 13\n221 869 50\n221 894 2\n221 929 15\n221 931 50\n221 935 25\n221 949 46\n221 965 39\n222 10 23\n222 11 16\n222 40 19\n222 48 8\n222 97 6\n222 108 31\n222 121 18\n222 137 14\n222 177 26\n222 194 43\n222 240 40\n222 273 44\n222 275 20\n222 276 48\n222 320 30\n222 335 10\n222 338 44\n222 366 8\n222 410 25\n222 436 41\n222 462 30\n222 472 40\n222 475 13\n222 476 24\n222 534 3\n222 544 25\n222 546 38\n222 575 29\n222 591 22\n222 600 32\n222 618 30\n222 637 16\n222 644 38\n222 659 22\n222 662 29\n222 697 10\n222 713 19\n222 744 38\n222 758 33\n222 764 13\n222 780 35\n222 785 24\n222 812 20\n222 814 16\n222 834 45\n222 838 13\n222 859 28\n222 872 31\n222 873 32\n222 904 47\n222 930 1\n222 936 50\n222 943 33\n222 950 14\n222 964 37\n222 996 24\n223 14 17\n223 19 22\n223 24 13\n223 33 10\n223 54 8\n223 55 24\n223 94 29\n223 103 38\n223 108 36\n223 113 11\n223 179 0\n223 183 43\n223 214 7\n223 262 0\n223 293 1\n223 360 18\n223 364 -2\n223 366 9\n223 401 -2\n223 423 17\n223 445 23\n223 454 40\n223 470 15\n223 480 49\n223 490 39\n223 502 14\n223 533 36\n223 567 40\n223 570 14\n223 619 41\n223 635 29\n223 648 20\n223 675 33\n223 722 27\n223 728 24\n223 742 40\n223 762 15\n223 781 16\n223 787 40\n223 849 2\n223 858 0\n223 866 20\n223 895 22\n223 928 0\n223 968 41\n223 981 2\n223 984 18\n223 1000 15\n224 17 19\n224 34 40\n224 89 23\n224 111 43\n224 167 -2\n224 182 35\n224 203 49\n224 279 45\n224 287 49\n224 290 31\n224 300 39\n224 346 30\n224 372 49\n224 378 38\n224 391 7\n224 402 29\n224 409 -1\n224 412 10\n224 426 34\n224 431 38\n224 447 39\n224 449 33\n224 466 20\n224 489 26\n224 507 22\n224 582 25\n224 603 4\n224 611 13\n224 616 48\n224 629 45\n224 633 11\n224 641 12\n224 679 45\n224 724 11\n224 731 -2\n224 744 46\n224 764 40\n224 766 13\n224 772 15\n224 793 27\n224 845 16\n224 916 36\n224 934 5\n224 953 1\n224 966 -2\n224 976 40\n224 986 6\n225 18 48\n225 41 48\n225 48 12\n225 72 29\n225 102 41\n225 119 50\n225 120 40\n225 127 0\n225 132 45\n225 146 14\n225 176 14\n225 183 0\n225 198 29\n225 230 -2\n225 249 36\n225 258 31\n225 260 41\n225 302 35\n225 348 42\n225 366 43\n225 379 -1\n225 385 14\n225 412 49\n225 451 43\n225 457 29\n225 479 13\n225 482 48\n225 509 6\n225 525 41\n225 532 28\n225 544 25\n225 561 38\n225 616 3\n225 677 41\n225 684 31\n225 724 30\n225 731 4\n225 764 11\n225 781 3\n225 797 14\n225 829 46\n225 832 14\n225 848 3\n225 852 37\n225 890 17\n225 892 1\n225 913 31\n225 919 30\n225 954 11\n225 960 50\n225 987 34\n226 3 22\n226 36 49\n226 39 32\n226 46 13\n226 51 22\n226 62 18\n226 68 10\n226 96 14\n226 128 45\n226 142 1\n226 151 4\n226 170 26\n226 191 50\n226 196 7\n226 198 25\n226 213 33\n226 239 26\n226 246 11\n226 269 44\n226 340 21\n226 344 47\n226 345 1\n226 357 27\n226 413 24\n226 432 34\n226 456 13\n226 484 40\n226 506 4\n226 557 13\n226 564 11\n226 594 -1\n226 597 47\n226 625 36\n226 631 49\n226 642 39\n226 652 32\n226 656 42\n226 678 -2\n226 688 6\n226 705 29\n226 710 27\n226 713 48\n226 734 49\n226 758 8\n226 797 26\n226 803 7\n226 810 14\n226 845 41\n226 857 24\n226 879 35\n226 902 8\n226 935 1\n226 956 7\n226 960 38\n227 8 -1\n227 47 21\n227 53 9\n227 86 25\n227 101 0\n227 102 40\n227 105 9\n227 109 38\n227 121 7\n227 172 10\n227 190 31\n227 192 37\n227 203 30\n227 207 40\n227 235 32\n227 245 28\n227 254 30\n227 289 40\n227 303 20\n227 307 39\n227 309 2\n227 321 17\n227 322 28\n227 353 13\n227 383 48\n227 393 49\n227 446 0\n227 448 10\n227 450 47\n227 465 45\n227 485 34\n227 489 31\n227 496 3\n227 551 24\n227 560 47\n227 584 27\n227 600 11\n227 628 27\n227 634 42\n227 691 37\n227 695 48\n227 749 44\n227 785 45\n227 791 27\n227 793 46\n227 796 36\n227 803 5\n227 819 21\n227 846 19\n227 872 46\n227 877 38\n227 884 19\n227 893 1\n227 919 39\n227 922 0\n227 934 33\n227 952 45\n227 957 23\n227 961 40\n227 966 46\n227 969 -2\n228 4 -2\n228 27 44\n228 52 18\n228 79 10\n228 118 30\n228 125 13\n228 129 9\n228 210 13\n228 216 0\n228 223 15\n228 253 15\n228 294 20\n228 322 50\n228 372 12\n228 502 17\n228 536 50\n228 550 46\n228 558 41\n228 559 16\n228 562 8\n228 570 43\n228 573 13\n228 594 7\n228 608 14\n228 644 17\n228 648 25\n228 677 33\n228 682 42\n228 689 47\n228 699 49\n228 700 43\n228 704 23\n228 715 22\n228 728 13\n228 739 6\n228 759 42\n228 763 27\n228 778 24\n228 788 -2\n228 845 21\n228 849 39\n228 851 12\n228 902 47\n228 928 41\n228 984 23\n228 999 50\n229 20 16\n229 24 10\n229 31 22\n229 35 19\n229 73 1\n229 97 12\n229 106 -2\n229 115 17\n229 126 50\n229 176 7\n229 232 27\n229 270 43\n229 273 27\n229 290 16\n229 311 38\n229 314 38\n229 322 0\n229 347 37\n229 370 9\n229 380 33\n229 385 24\n229 420 19\n229 440 -1\n229 493 26\n229 528 40\n229 608 -1\n229 609 6\n229 654 39\n229 663 -2\n229 671 48\n229 741 10\n229 754 44\n229 789 18\n229 821 15\n229 887 23\n229 971 39\n229 977 2\n230 35 24\n230 43 2\n230 79 -2\n230 86 36\n230 110 23\n230 139 37\n230 164 42\n230 248 46\n230 274 36\n230 333 27\n230 347 44\n230 380 45\n230 381 3\n230 404 46\n230 413 10\n230 428 0\n230 438 4\n230 442 38\n230 455 42\n230 506 31\n230 507 5\n230 516 23\n230 532 8\n230 538 32\n230 579 46\n230 583 4\n230 596 38\n230 618 20\n230 620 16\n230 625 23\n230 631 17\n230 633 39\n230 638 49\n230 651 6\n230 687 15\n230 701 47\n230 775 27\n230 802 40\n230 861 32\n230 865 34\n230 880 22\n230 896 29\n230 920 24\n230 922 36\n230 999 34\n231 38 13\n231 76 15\n231 80 45\n231 95 48\n231 122 10\n231 197 20\n231 247 31\n231 261 -2\n231 296 46\n231 317 25\n231 352 21\n231 372 26\n231 377 13\n231 385 19\n231 396 20\n231 408 -2\n231 424 37\n231 452 19\n231 455 1\n231 468 22\n231 478 35\n231 493 20\n231 499 35\n231 546 40\n231 555 34\n231 610 23\n231 647 28\n231 673 48\n231 689 39\n231 717 2\n231 731 20\n231 785 39\n231 793 27\n231 842 17\n231 846 27\n231 883 0\n231 902 37\n231 906 34\n231 909 8\n231 910 7\n231 953 33\n231 966 13\n232 32 5\n232 37 26\n232 45 45\n232 55 36\n232 79 7\n232 101 37\n232 153 22\n232 175 19\n232 197 9\n232 222 33\n232 245 28\n232 301 35\n232 309 38\n232 317 38\n232 331 45\n232 333 7\n232 364 21\n232 371 9\n232 377 8\n232 382 16\n232 392 48\n232 395 26\n232 405 40\n232 406 2\n232 421 33\n232 426 32\n232 432 45\n232 443 47\n232 568 41\n232 599 4\n232 613 29\n232 636 34\n232 660 4\n232 679 33\n232 692 11\n232 698 40\n232 707 43\n232 714 21\n232 719 8\n232 751 34\n232 755 12\n232 756 4\n232 767 32\n232 773 31\n232 789 42\n232 796 33\n232 827 12\n232 857 17\n232 860 14\n232 866 5\n232 906 20\n232 951 18\n232 952 20\n232 976 14\n233 3 13\n233 26 45\n233 47 28\n233 72 28\n233 73 31\n233 99 24\n233 100 27\n233 144 19\n233 151 19\n233 205 3\n233 209 50\n233 223 39\n233 230 46\n233 235 1\n233 291 29\n233 306 33\n233 321 18\n233 324 36\n233 355 24\n233 371 0\n233 376 45\n233 435 16\n233 443 3\n233 463 20\n233 478 18\n233 483 18\n233 490 32\n233 509 20\n233 535 6\n233 577 3\n233 594 39\n233 624 19\n233 625 37\n233 642 49\n233 656 3\n233 677 30\n233 743 6\n233 758 18\n233 768 4\n233 778 16\n233 780 21\n233 899 -2\n233 901 28\n233 932 0\n233 952 30\n233 958 30\n233 961 38\n233 967 30\n233 971 44\n233 975 48\n233 984 3\n234 4 -2\n234 35 17\n234 39 3\n234 60 36\n234 76 -2\n234 130 23\n234 131 33\n234 135 36\n234 181 25\n234 186 8\n234 191 -2\n234 198 38\n234 199 3\n234 217 18\n234 237 20\n234 293 23\n234 310 49\n234 314 2\n234 315 8\n234 354 44\n234 384 26\n234 389 19\n234 400 22\n234 462 25\n234 467 47\n234 483 31\n234 494 18\n234 511 8\n234 590 10\n234 603 21\n234 611 20\n234 627 40\n234 657 28\n234 673 14\n234 681 37\n234 687 36\n234 706 0\n234 751 16\n234 752 22\n234 773 12\n234 796 31\n234 813 0\n234 823 -2\n234 834 47\n234 845 50\n234 854 40\n234 861 12\n234 915 28\n234 947 17\n234 954 28\n234 960 5\n234 963 34\n234 964 39\n234 997 22\n235 12 7\n235 16 13\n235 20 4\n235 29 18\n235 48 3\n235 69 13\n235 91 37\n235 94 46\n235 95 1\n235 102 2\n235 130 6\n235 140 8\n235 197 24\n235 211 3\n235 234 12\n235 251 37\n235 258 11\n235 275 27\n235 287 41\n235 304 42\n235 329 0\n235 337 26\n235 393 50\n235 397 43\n235 437 39\n235 451 39\n235 453 10\n235 493 -2\n235 497 48\n235 531 -2\n235 532 39\n235 539 6\n235 546 -2\n235 597 43\n235 611 48\n235 621 1\n235 625 20\n235 626 28\n235 627 22\n235 635 29\n235 638 41\n235 653 0\n235 777 13\n235 831 37\n235 839 28\n235 844 36\n235 898 22\n235 938 31\n235 959 24\n235 984 8\n235 995 33\n236 5 48\n236 20 40\n236 45 46\n236 50 45\n236 53 31\n236 67 36\n236 90 15\n236 103 35\n236 108 11\n236 109 8\n236 127 29\n236 163 -2\n236 184 41\n236 188 31\n236 218 37\n236 254 36\n236 261 44\n236 264 24\n236 273 20\n236 281 26\n236 292 6\n236 308 22\n236 348 10\n236 361 48\n236 397 13\n236 431 9\n236 482 28\n236 490 48\n236 507 9\n236 508 22\n236 534 28\n236 562 20\n236 572 21\n236 575 12\n236 612 22\n236 666 29\n236 679 24\n236 689 38\n236 724 30\n236 754 13\n236 760 -1\n236 763 42\n236 765 18\n236 770 39\n236 777 -2\n236 811 28\n236 823 34\n236 837 6\n236 858 3\n236 892 50\n236 909 48\n236 912 40\n236 942 41\n236 945 16\n236 979 8\n236 983 23\n237 24 5\n237 49 44\n237 63 24\n237 79 44\n237 93 25\n237 116 38\n237 130 30\n237 136 24\n237 141 4\n237 143 2\n237 147 27\n237 191 39\n237 193 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34\n238 809 24\n238 814 26\n238 826 33\n238 866 44\n238 896 42\n238 900 47\n238 912 50\n238 927 39\n238 952 20\n238 962 28\n238 975 10\n238 982 19\n238 992 21\n238 994 16\n239 14 17\n239 19 27\n239 43 4\n239 68 36\n239 72 50\n239 129 6\n239 139 49\n239 168 21\n239 174 10\n239 190 14\n239 211 48\n239 260 25\n239 276 13\n239 297 5\n239 329 4\n239 343 10\n239 356 35\n239 371 32\n239 379 33\n239 386 27\n239 486 7\n239 525 0\n239 551 0\n239 578 20\n239 584 46\n239 590 16\n239 596 12\n239 620 37\n239 677 5\n239 682 28\n239 684 3\n239 723 0\n239 741 3\n239 813 18\n239 851 7\n239 911 23\n239 994 39\n240 6 50\n240 22 9\n240 30 24\n240 53 25\n240 55 47\n240 67 13\n240 121 6\n240 122 43\n240 128 30\n240 138 0\n240 152 45\n240 160 38\n240 193 40\n240 225 48\n240 265 0\n240 281 19\n240 341 30\n240 378 25\n240 387 27\n240 395 17\n240 425 10\n240 469 9\n240 489 45\n240 498 3\n240 592 18\n240 608 16\n240 652 18\n240 686 37\n240 703 12\n240 735 -1\n240 804 34\n240 840 45\n240 873 10\n240 896 4\n240 924 9\n240 930 32\n241 38 43\n241 53 40\n241 56 2\n241 57 21\n241 66 43\n241 74 -2\n241 98 5\n241 158 37\n241 159 2\n241 199 7\n241 204 18\n241 212 14\n241 231 49\n241 259 23\n241 266 8\n241 269 33\n241 330 37\n241 351 25\n241 372 48\n241 383 5\n241 398 42\n241 399 36\n241 414 28\n241 418 46\n241 422 49\n241 429 39\n241 490 7\n241 509 24\n241 510 5\n241 549 50\n241 587 6\n241 603 0\n241 633 35\n241 650 21\n241 660 39\n241 765 10\n241 804 3\n241 825 -2\n241 828 15\n241 856 3\n241 860 16\n241 874 11\n241 908 20\n241 918 47\n241 955 37\n241 956 5\n241 958 8\n241 978 36\n242 3 47\n242 100 32\n242 111 1\n242 112 47\n242 115 14\n242 133 8\n242 149 30\n242 248 36\n242 249 39\n242 253 20\n242 260 37\n242 262 19\n242 273 39\n242 282 29\n242 297 37\n242 368 44\n242 382 14\n242 387 22\n242 397 30\n242 401 49\n242 408 10\n242 411 19\n242 487 20\n242 525 13\n242 560 25\n242 566 45\n242 578 8\n242 592 16\n242 596 29\n242 604 36\n242 625 24\n242 637 42\n242 655 31\n242 674 3\n242 711 4\n242 717 1\n242 726 46\n242 730 6\n242 734 44\n242 796 48\n242 819 22\n242 841 -1\n242 861 35\n242 883 33\n242 905 34\n242 912 23\n242 966 6\n242 967 30\n243 7 37\n243 8 25\n243 22 5\n243 26 17\n243 37 30\n243 68 0\n243 84 6\n243 93 9\n243 95 5\n243 122 7\n243 142 29\n243 165 0\n243 170 12\n243 182 33\n243 201 5\n243 207 12\n243 227 19\n243 230 41\n243 245 37\n243 248 39\n243 259 9\n243 272 19\n243 282 2\n243 283 18\n243 299 8\n243 313 17\n243 317 23\n243 358 8\n243 359 25\n243 367 1\n243 377 7\n243 455 41\n243 469 5\n243 485 26\n243 500 36\n243 507 18\n243 537 50\n243 558 49\n243 612 27\n243 620 3\n243 644 49\n243 698 -2\n243 743 24\n243 780 13\n243 804 2\n243 864 12\n243 898 19\n243 925 33\n243 937 18\n243 938 43\n243 950 6\n243 961 15\n243 972 19\n243 989 40\n244 19 17\n244 52 8\n244 68 12\n244 75 43\n244 79 3\n244 84 -1\n244 94 17\n244 96 18\n244 100 40\n244 136 28\n244 150 45\n244 156 24\n244 164 31\n244 194 0\n244 225 17\n244 237 4\n244 269 48\n244 273 26\n244 291 31\n244 354 4\n244 360 40\n244 369 3\n244 394 -2\n244 404 5\n244 405 30\n244 462 20\n244 473 21\n244 475 45\n244 490 43\n244 493 32\n244 532 42\n244 546 34\n244 556 32\n244 566 27\n244 603 41\n244 656 50\n244 661 21\n244 732 39\n244 745 15\n244 754 18\n244 755 7\n244 759 0\n244 765 0\n244 777 46\n244 800 21\n244 811 15\n244 829 36\n244 848 42\n244 878 18\n244 934 48\n244 936 10\n245 9 21\n245 21 8\n245 53 1\n245 74 31\n245 125 49\n245 142 3\n245 148 28\n245 161 23\n245 165 22\n245 212 0\n245 237 7\n245 262 50\n245 263 28\n245 266 25\n245 278 15\n245 308 9\n245 309 40\n245 319 1\n245 336 5\n245 404 12\n245 410 1\n245 420 10\n245 448 20\n245 450 7\n245 454 0\n245 475 -2\n245 499 9\n245 521 10\n245 544 5\n245 545 20\n245 570 48\n245 624 25\n245 656 21\n245 662 33\n245 669 15\n245 671 24\n245 688 41\n245 700 38\n245 703 -2\n245 716 35\n245 730 30\n245 761 21\n245 767 17\n245 804 38\n245 854 14\n245 869 4\n245 894 33\n245 928 7\n245 964 36\n245 972 41\n246 3 8\n246 14 30\n246 16 6\n246 22 38\n246 34 8\n246 64 46\n246 150 21\n246 160 18\n246 177 26\n246 206 12\n246 229 6\n246 236 4\n246 266 18\n246 281 27\n246 356 2\n246 360 19\n246 434 47\n246 442 45\n246 455 4\n246 462 9\n246 485 13\n246 488 49\n246 560 48\n246 568 -1\n246 584 31\n246 594 16\n246 621 32\n246 632 4\n246 662 8\n246 691 21\n246 692 7\n246 713 7\n246 725 33\n246 753 14\n246 762 22\n246 781 16\n246 790 5\n246 801 17\n246 807 5\n246 820 37\n246 834 43\n246 842 44\n246 843 44\n246 847 32\n246 858 22\n246 864 31\n246 873 7\n246 918 25\n246 930 6\n246 941 8\n246 958 34\n246 969 -1\n246 975 3\n246 978 45\n246 979 3\n247 13 49\n247 30 24\n247 53 20\n247 54 14\n247 59 44\n247 71 31\n247 86 15\n247 89 50\n247 100 48\n247 152 26\n247 221 39\n247 239 15\n247 369 5\n247 370 41\n247 372 29\n247 377 39\n247 381 45\n247 399 32\n247 426 37\n247 433 36\n247 444 48\n247 447 15\n247 463 24\n247 510 10\n247 521 34\n247 539 20\n247 637 35\n247 655 41\n247 667 24\n247 669 1\n247 686 26\n247 698 42\n247 710 4\n247 718 44\n247 732 3\n247 734 34\n247 747 27\n247 750 4\n247 831 20\n247 833 50\n247 835 35\n247 854 33\n247 907 49\n247 915 28\n247 927 21\n247 934 31\n247 937 39\n247 940 33\n247 950 42\n247 957 24\n247 991 21\n248 16 3\n248 33 34\n248 65 18\n248 100 24\n248 132 19\n248 209 27\n248 221 12\n248 227 16\n248 245 -1\n248 247 4\n248 257 27\n248 263 14\n248 341 17\n248 395 7\n248 405 0\n248 415 24\n248 427 45\n248 463 30\n248 534 14\n248 547 49\n248 561 25\n248 569 30\n248 572 29\n248 597 38\n248 605 49\n248 613 3\n248 620 28\n248 630 12\n248 656 18\n248 659 36\n248 674 7\n248 687 17\n248 701 15\n248 732 36\n248 752 33\n248 775 32\n248 777 18\n248 854 20\n248 866 10\n248 870 42\n248 879 45\n248 881 1\n248 887 41\n248 892 42\n248 906 19\n248 940 17\n248 958 31\n248 989 45\n248 999 44\n249 83 10\n249 100 36\n249 116 42\n249 118 2\n249 129 31\n249 130 11\n249 134 26\n249 155 16\n249 173 10\n249 180 7\n249 194 30\n249 206 17\n249 226 45\n249 232 16\n249 253 12\n249 259 42\n249 283 44\n249 292 50\n249 298 13\n249 313 41\n249 373 37\n249 403 4\n249 413 6\n249 431 8\n249 450 38\n249 467 -1\n249 489 14\n249 528 34\n249 615 -2\n249 627 11\n249 662 1\n249 707 16\n249 732 39\n249 768 28\n249 809 18\n249 817 15\n249 899 21\n249 913 38\n249 929 31\n249 979 21\n249 991 47\n250 6 40\n250 10 32\n250 61 8\n250 85 37\n250 90 11\n250 91 37\n250 93 14\n250 108 14\n250 143 50\n250 145 37\n250 150 -2\n250 159 9\n250 161 27\n250 178 12\n250 192 29\n250 199 10\n250 232 28\n250 246 40\n250 256 36\n250 295 18\n250 307 9\n250 326 33\n250 359 -2\n250 384 39\n250 385 27\n250 397 27\n250 421 45\n250 460 35\n250 462 3\n250 473 43\n250 477 7\n250 520 39\n250 524 30\n250 527 50\n250 530 39\n250 538 41\n250 559 26\n250 625 43\n250 634 29\n250 639 4\n250 661 10\n250 698 14\n250 708 -1\n250 728 18\n250 735 17\n250 770 5\n250 773 50\n250 792 10\n250 839 49\n250 857 4\n250 865 34\n250 884 13\n250 915 44\n250 929 46\n250 967 3\n251 13 46\n251 23 11\n251 36 7\n251 46 48\n251 87 40\n251 116 2\n251 195 48\n251 205 23\n251 208 39\n251 261 38\n251 269 18\n251 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921 12\n252 937 27\n252 941 10\n252 972 14\n252 998 31\n253 14 34\n253 39 3\n253 51 0\n253 53 8\n253 57 44\n253 58 37\n253 74 0\n253 86 18\n253 89 18\n253 98 33\n253 138 41\n253 179 37\n253 187 2\n253 189 5\n253 191 0\n253 222 6\n253 233 32\n253 282 31\n253 338 1\n253 341 7\n253 360 19\n253 392 18\n253 405 32\n253 407 6\n253 439 42\n253 466 23\n253 469 15\n253 470 18\n253 472 29\n253 481 50\n253 517 24\n253 529 17\n253 591 30\n253 597 25\n253 629 5\n253 632 7\n253 644 22\n253 665 45\n253 683 9\n253 687 33\n253 702 21\n253 735 8\n253 775 37\n253 778 17\n253 781 25\n253 782 19\n253 788 45\n253 808 48\n253 820 19\n253 845 12\n253 846 16\n253 887 30\n253 903 48\n253 934 14\n253 951 26\n253 961 11\n253 978 21\n254 13 14\n254 51 7\n254 152 42\n254 154 35\n254 157 49\n254 160 20\n254 175 22\n254 190 25\n254 195 49\n254 199 11\n254 200 23\n254 248 36\n254 279 14\n254 343 39\n254 355 6\n254 357 45\n254 402 11\n254 417 9\n254 464 18\n254 496 32\n254 550 -1\n254 578 7\n254 594 33\n254 605 -2\n254 678 43\n254 679 22\n254 681 36\n254 691 3\n254 701 4\n254 716 18\n254 729 50\n254 742 10\n254 752 38\n254 759 42\n254 777 1\n254 792 -2\n254 794 36\n254 844 17\n254 857 17\n254 883 46\n254 936 41\n254 947 23\n254 949 18\n254 951 37\n254 953 40\n254 954 26\n254 966 8\n254 986 8\n255 2 44\n255 10 41\n255 15 10\n255 24 5\n255 29 2\n255 42 11\n255 81 2\n255 86 43\n255 89 22\n255 123 44\n255 144 -2\n255 154 43\n255 210 23\n255 223 20\n255 232 18\n255 256 32\n255 268 2\n255 278 14\n255 282 49\n255 307 2\n255 357 5\n255 386 3\n255 413 48\n255 422 35\n255 430 38\n255 467 6\n255 547 5\n255 581 11\n255 593 49\n255 599 3\n255 665 17\n255 678 8\n255 698 41\n255 750 7\n255 755 11\n255 757 42\n255 760 44\n255 772 24\n255 811 -1\n255 823 42\n255 846 17\n255 859 6\n255 874 26\n255 875 38\n255 902 2\n255 918 28\n255 933 19\n255 938 36\n255 949 6\n256 1 35\n256 7 20\n256 13 33\n256 24 21\n256 35 28\n256 64 38\n256 65 31\n256 71 -2\n256 85 8\n256 105 16\n256 106 0\n256 127 4\n256 131 10\n256 162 13\n256 188 34\n256 191 50\n256 194 19\n256 230 50\n256 241 40\n256 265 5\n256 309 39\n256 313 -1\n256 340 21\n256 399 33\n256 475 45\n256 486 36\n256 492 34\n256 522 5\n256 585 47\n256 616 16\n256 618 14\n256 632 1\n256 643 17\n256 666 29\n256 675 9\n256 678 33\n256 739 15\n256 764 19\n256 804 21\n256 805 9\n256 807 17\n256 808 35\n256 811 6\n256 826 50\n256 832 -2\n256 894 40\n256 901 25\n256 907 31\n256 917 22\n256 929 45\n256 966 21\n256 967 5\n256 997 26\n256 1000 36\n257 19 42\n257 22 3\n257 39 5\n257 63 42\n257 71 -1\n257 93 10\n257 108 21\n257 135 6\n257 167 23\n257 175 16\n257 185 0\n257 190 40\n257 225 40\n257 232 32\n257 235 40\n257 294 20\n257 318 10\n257 323 48\n257 326 11\n257 335 41\n257 345 21\n257 348 23\n257 350 29\n257 353 27\n257 359 19\n257 379 14\n257 406 22\n257 421 17\n257 458 5\n257 469 21\n257 476 17\n257 485 50\n257 500 5\n257 506 15\n257 513 0\n257 537 41\n257 567 42\n257 595 35\n257 606 6\n257 616 33\n257 655 45\n257 673 22\n257 760 5\n257 769 19\n257 789 9\n257 802 20\n257 829 15\n257 841 3\n257 843 1\n257 870 -2\n257 901 43\n257 915 32\n257 923 33\n257 928 8\n257 956 28\n257 957 46\n257 978 -1\n257 996 29\n258 9 29\n258 10 20\n258 51 40\n258 80 38\n258 107 43\n258 119 0\n258 196 12\n258 203 36\n258 239 3\n258 251 21\n258 297 1\n258 307 25\n258 327 -1\n258 336 20\n258 343 23\n258 352 47\n258 376 -2\n258 398 46\n258 410 -2\n258 448 17\n258 484 44\n258 490 33\n258 520 11\n258 528 9\n258 540 32\n258 548 1\n258 552 20\n258 570 48\n258 582 41\n258 586 27\n258 612 28\n258 643 28\n258 676 17\n258 740 13\n258 747 -2\n258 810 37\n258 843 32\n258 852 3\n258 869 45\n258 870 -2\n258 893 26\n258 898 41\n258 932 3\n258 935 14\n258 937 39\n258 938 13\n258 967 18\n258 985 16\n259 30 13\n259 113 11\n259 115 23\n259 119 14\n259 149 17\n259 156 13\n259 176 23\n259 179 50\n259 191 2\n259 199 8\n259 282 4\n259 285 26\n259 300 12\n259 324 40\n259 385 46\n259 399 13\n259 419 48\n259 441 4\n259 451 39\n259 460 5\n259 466 1\n259 475 11\n259 486 -2\n259 499 18\n259 524 14\n259 531 33\n259 532 3\n259 570 43\n259 594 50\n259 596 34\n259 640 11\n259 643 23\n259 659 23\n259 673 35\n259 690 23\n259 703 -2\n259 732 46\n259 737 34\n259 741 22\n259 746 47\n259 762 46\n259 770 45\n259 772 28\n259 773 6\n259 777 33\n259 801 35\n259 803 38\n259 811 42\n259 833 7\n259 842 13\n259 851 35\n259 855 -2\n259 864 21\n259 872 23\n259 909 40\n259 951 49\n259 969 14\n260 38 9\n260 82 11\n260 145 33\n260 201 12\n260 244 7\n260 252 24\n260 258 30\n260 270 27\n260 281 4\n260 287 27\n260 345 2\n260 490 5\n260 501 22\n260 540 26\n260 550 43\n260 569 5\n260 633 44\n260 639 50\n260 728 27\n260 752 4\n260 754 36\n260 775 27\n260 793 16\n260 798 33\n260 813 40\n260 848 38\n260 875 35\n260 901 21\n260 907 36\n260 918 13\n260 934 3\n260 950 32\n260 956 4\n260 980 -2\n261 10 37\n261 21 37\n261 38 45\n261 92 28\n261 143 30\n261 146 47\n261 168 7\n261 195 20\n261 237 13\n261 240 42\n261 249 18\n261 269 13\n261 272 6\n261 310 9\n261 334 43\n261 336 32\n261 339 9\n261 397 6\n261 453 5\n261 455 45\n261 484 40\n261 534 5\n261 540 32\n261 544 41\n261 568 9\n261 667 44\n261 709 -2\n261 733 36\n261 736 29\n261 746 15\n261 749 15\n261 783 8\n261 808 22\n261 809 35\n261 810 47\n261 842 41\n261 853 41\n261 878 14\n261 902 42\n261 911 22\n261 918 26\n261 924 22\n261 926 8\n261 937 29\n261 973 39\n261 979 26\n262 102 16\n262 114 43\n262 158 29\n262 195 12\n262 232 1\n262 266 12\n262 279 19\n262 290 18\n262 336 23\n262 344 13\n262 345 28\n262 377 22\n262 420 49\n262 443 46\n262 447 44\n262 448 26\n262 461 14\n262 480 13\n262 488 22\n262 502 22\n262 504 25\n262 535 50\n262 603 -1\n262 616 20\n262 659 48\n262 671 11\n262 742 32\n262 759 23\n262 827 19\n262 852 31\n262 859 15\n262 861 37\n262 883 13\n262 900 33\n262 915 35\n262 925 43\n262 928 40\n262 953 31\n262 998 20\n263 20 29\n263 39 25\n263 52 24\n263 58 48\n263 79 17\n263 109 10\n263 112 30\n263 155 41\n263 177 21\n263 278 42\n263 299 46\n263 301 25\n263 325 12\n263 337 48\n263 345 26\n263 366 46\n263 385 33\n263 419 17\n263 444 47\n263 449 13\n263 469 29\n263 504 31\n263 512 49\n263 517 27\n263 522 25\n263 536 11\n263 559 33\n263 578 28\n263 584 -1\n263 617 -1\n263 634 39\n263 685 44\n263 718 27\n263 719 30\n263 738 20\n263 742 32\n263 744 17\n263 753 49\n263 754 44\n263 769 14\n263 789 14\n263 807 46\n263 823 0\n263 854 39\n263 876 18\n263 890 21\n263 933 44\n263 952 50\n263 974 9\n263 977 40\n263 997 18\n264 18 33\n264 32 38\n264 64 17\n264 106 25\n264 109 13\n264 119 0\n264 123 23\n264 128 24\n264 167 32\n264 174 24\n264 206 15\n264 237 17\n264 271 17\n264 278 20\n264 334 -2\n264 344 26\n264 350 33\n264 402 43\n264 433 28\n264 443 38\n264 473 41\n264 474 21\n264 507 13\n264 565 33\n264 627 47\n264 631 34\n264 639 20\n264 662 31\n264 675 17\n264 685 48\n264 706 22\n264 712 50\n264 719 41\n264 721 24\n264 733 5\n264 734 7\n264 735 34\n264 745 7\n264 793 37\n264 867 21\n264 871 4\n264 886 4\n264 923 16\n264 926 5\n264 944 21\n264 978 39\n264 991 -1\n264 993 17\n265 8 11\n265 16 30\n265 19 24\n265 81 29\n265 124 45\n265 133 8\n265 168 27\n265 179 33\n265 184 23\n265 189 2\n265 197 18\n265 220 43\n265 240 24\n265 241 20\n265 258 2\n265 332 49\n265 354 49\n265 375 1\n265 378 32\n265 383 32\n265 411 17\n265 414 15\n265 467 6\n265 476 -2\n265 480 50\n265 493 46\n265 512 18\n265 521 29\n265 532 19\n265 539 26\n265 546 50\n265 557 50\n265 583 28\n265 601 16\n265 648 47\n265 693 44\n265 741 46\n265 752 15\n265 762 14\n265 775 13\n265 815 8\n265 824 44\n265 827 22\n265 828 16\n265 855 12\n265 883 7\n265 884 15\n265 885 36\n265 969 50\n265 999 26\n266 4 24\n266 55 2\n266 105 14\n266 110 21\n266 127 26\n266 198 27\n266 214 7\n266 249 42\n266 269 19\n266 289 16\n266 303 27\n266 308 19\n266 319 38\n266 339 49\n266 362 7\n266 411 31\n266 432 12\n266 456 -2\n266 480 48\n266 493 -1\n266 503 20\n266 513 6\n266 516 -1\n266 522 37\n266 524 28\n266 526 34\n266 550 6\n266 570 30\n266 575 21\n266 593 29\n266 634 0\n266 636 16\n266 651 17\n266 686 39\n266 692 -1\n266 701 26\n266 718 20\n266 754 10\n266 794 5\n266 821 2\n266 841 34\n266 865 45\n266 889 9\n266 932 50\n266 936 46\n266 964 1\n266 970 40\n266 971 50\n267 23 15\n267 29 22\n267 59 10\n267 60 43\n267 72 30\n267 80 44\n267 96 23\n267 132 39\n267 154 19\n267 177 48\n267 194 12\n267 235 39\n267 260 19\n267 315 10\n267 322 17\n267 347 2\n267 392 0\n267 403 44\n267 429 14\n267 435 44\n267 463 33\n267 470 17\n267 487 8\n267 545 33\n267 579 42\n267 591 3\n267 592 33\n267 607 18\n267 677 18\n267 678 50\n267 701 4\n267 707 16\n267 708 15\n267 746 26\n267 763 22\n267 781 40\n267 842 21\n267 862 24\n267 870 17\n267 888 24\n267 892 23\n267 898 12\n267 933 32\n267 946 45\n267 961 -1\n267 964 8\n267 965 11\n267 970 5\n268 13 0\n268 16 18\n268 35 21\n268 50 18\n268 65 10\n268 73 46\n268 102 9\n268 113 25\n268 145 14\n268 146 37\n268 186 -1\n268 193 41\n268 214 19\n268 228 17\n268 246 43\n268 249 21\n268 256 20\n268 290 44\n268 296 43\n268 333 32\n268 396 25\n268 406 5\n268 420 2\n268 421 21\n268 430 27\n268 435 0\n268 476 7\n268 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25\n270 791 14\n270 800 3\n270 803 18\n270 805 8\n270 828 44\n270 873 38\n270 883 42\n270 884 26\n270 931 44\n270 995 33\n271 9 29\n271 14 3\n271 29 30\n271 81 24\n271 83 17\n271 95 40\n271 105 19\n271 154 10\n271 156 33\n271 163 40\n271 166 26\n271 185 9\n271 236 18\n271 237 45\n271 242 -1\n271 277 14\n271 283 29\n271 307 40\n271 313 16\n271 317 24\n271 333 -2\n271 367 38\n271 381 45\n271 389 -1\n271 402 44\n271 406 12\n271 418 30\n271 436 19\n271 448 43\n271 481 14\n271 493 28\n271 581 21\n271 592 20\n271 626 47\n271 652 35\n271 664 35\n271 666 50\n271 679 35\n271 722 33\n271 736 17\n271 763 40\n271 804 6\n271 805 47\n271 818 6\n271 820 16\n271 842 44\n271 850 23\n271 857 36\n271 870 34\n271 904 31\n271 927 16\n271 929 6\n271 936 43\n271 968 13\n271 970 11\n271 991 11\n271 993 36\n272 4 47\n272 30 5\n272 44 -2\n272 48 16\n272 96 -2\n272 99 17\n272 100 40\n272 108 13\n272 134 1\n272 162 43\n272 166 35\n272 168 2\n272 195 16\n272 208 47\n272 209 27\n272 215 28\n272 242 5\n272 246 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18\n278 142 15\n278 148 30\n278 185 42\n278 189 -1\n278 221 35\n278 229 11\n278 248 18\n278 262 22\n278 304 17\n278 308 11\n278 314 -2\n278 315 34\n278 325 4\n278 339 14\n278 347 33\n278 348 37\n278 362 43\n278 369 46\n278 377 32\n278 396 3\n278 397 16\n278 456 6\n278 460 41\n278 472 32\n278 477 10\n278 482 32\n278 498 19\n278 521 28\n278 531 50\n278 534 39\n278 536 40\n278 557 36\n278 574 50\n278 601 8\n278 617 12\n278 631 29\n278 668 18\n278 674 8\n278 697 38\n278 703 46\n278 723 48\n278 768 1\n278 794 46\n278 805 36\n278 866 5\n278 888 45\n278 894 20\n278 911 15\n278 925 15\n278 927 33\n278 946 46\n278 952 32\n278 992 37\n279 43 5\n279 57 32\n279 62 38\n279 68 24\n279 91 39\n279 100 6\n279 106 13\n279 141 49\n279 157 31\n279 186 34\n279 187 29\n279 211 50\n279 238 23\n279 244 27\n279 264 37\n279 324 25\n279 333 20\n279 334 50\n279 346 50\n279 351 30\n279 365 1\n279 372 2\n279 389 9\n279 392 45\n279 421 43\n279 455 20\n279 459 21\n279 514 40\n279 534 10\n279 537 39\n279 538 8\n279 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6\n283 10 36\n283 30 -2\n283 31 1\n283 37 23\n283 46 19\n283 57 33\n283 94 50\n283 96 3\n283 128 21\n283 213 22\n283 223 21\n283 268 21\n283 275 1\n283 287 23\n283 290 -1\n283 291 18\n283 303 14\n283 360 7\n283 382 -2\n283 386 46\n283 447 8\n283 474 35\n283 496 13\n283 557 43\n283 567 -2\n283 572 35\n283 578 34\n283 594 39\n283 614 29\n283 630 6\n283 665 47\n283 672 6\n283 677 30\n283 697 41\n283 700 43\n283 710 29\n283 742 40\n283 744 32\n283 748 5\n283 761 43\n283 773 29\n283 781 43\n283 790 2\n283 835 30\n283 852 42\n283 856 35\n283 861 23\n283 877 24\n283 952 46\n283 977 36\n284 10 1\n284 29 23\n284 35 34\n284 75 10\n284 102 45\n284 110 -1\n284 139 21\n284 167 6\n284 178 13\n284 179 5\n284 183 3\n284 191 15\n284 207 48\n284 215 3\n284 222 2\n284 227 4\n284 282 41\n284 293 47\n284 308 26\n284 315 10\n284 351 6\n284 369 49\n284 403 6\n284 411 14\n284 422 25\n284 429 20\n284 437 32\n284 442 10\n284 456 7\n284 458 46\n284 472 33\n284 474 20\n284 479 15\n284 502 23\n284 517 7\n284 518 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43\n287 970 18\n287 971 16\n287 974 2\n287 979 45\n287 985 17\n287 996 26\n288 28 24\n288 30 31\n288 41 40\n288 50 23\n288 84 21\n288 91 25\n288 94 -1\n288 106 43\n288 134 47\n288 146 2\n288 150 1\n288 168 11\n288 186 32\n288 217 26\n288 254 25\n288 257 18\n288 273 17\n288 287 7\n288 301 44\n288 304 40\n288 342 26\n288 344 19\n288 359 10\n288 373 4\n288 380 7\n288 384 37\n288 399 20\n288 400 23\n288 413 27\n288 463 15\n288 477 23\n288 490 28\n288 492 26\n288 537 22\n288 564 22\n288 668 19\n288 678 30\n288 681 23\n288 682 22\n288 732 34\n288 738 1\n288 754 31\n288 762 36\n288 785 26\n288 813 16\n288 814 46\n288 847 45\n288 855 -2\n288 903 35\n288 916 47\n288 927 6\n288 946 32\n288 947 35\n288 958 7\n288 970 16\n288 990 17\n289 13 27\n289 38 40\n289 41 40\n289 54 20\n289 67 21\n289 68 48\n289 70 11\n289 92 22\n289 94 23\n289 104 24\n289 152 13\n289 213 5\n289 266 12\n289 316 44\n289 324 41\n289 331 48\n289 364 11\n289 368 27\n289 413 2\n289 427 30\n289 430 26\n289 467 16\n289 500 12\n289 526 37\n289 546 47\n289 548 20\n289 566 -2\n289 569 6\n289 623 24\n289 637 10\n289 638 46\n289 642 3\n289 645 42\n289 651 4\n289 653 37\n289 661 11\n289 696 12\n289 713 39\n289 720 26\n289 744 29\n289 750 37\n289 767 39\n289 781 46\n289 783 36\n289 785 -1\n289 812 46\n289 840 4\n289 842 8\n289 909 15\n289 915 50\n289 950 1\n289 961 -1\n289 992 4\n290 3 -1\n290 42 7\n290 54 4\n290 72 32\n290 73 49\n290 84 14\n290 98 36\n290 105 5\n290 135 5\n290 198 4\n290 201 10\n290 220 12\n290 239 38\n290 265 21\n290 297 41\n290 302 14\n290 394 4\n290 396 0\n290 424 20\n290 459 24\n290 461 3\n290 468 37\n290 470 44\n290 506 -1\n290 522 41\n290 527 49\n290 536 27\n290 550 46\n290 570 9\n290 592 4\n290 596 -1\n290 631 31\n290 633 -2\n290 658 16\n290 687 18\n290 704 40\n290 712 1\n290 721 40\n290 747 13\n290 778 28\n290 795 48\n290 800 34\n290 825 34\n290 840 4\n290 841 14\n290 857 50\n290 923 5\n291 6 25\n291 23 49\n291 27 35\n291 42 15\n291 55 48\n291 69 28\n291 145 34\n291 175 37\n291 193 14\n291 195 37\n291 200 49\n291 214 40\n291 232 46\n291 244 48\n291 269 49\n291 279 0\n291 316 12\n291 338 45\n291 340 12\n291 352 17\n291 356 27\n291 421 11\n291 439 44\n291 451 50\n291 454 7\n291 485 -2\n291 503 2\n291 514 9\n291 532 6\n291 533 36\n291 588 43\n291 603 15\n291 604 1\n291 606 8\n291 616 42\n291 635 0\n291 648 1\n291 664 48\n291 677 38\n291 685 9\n291 690 23\n291 698 2\n291 712 5\n291 729 6\n291 740 49\n291 743 23\n291 751 12\n291 764 39\n291 766 36\n291 768 47\n291 770 30\n291 807 18\n291 809 49\n291 811 6\n291 815 5\n291 817 27\n291 831 24\n291 868 10\n291 900 50\n291 997 17\n292 37 38\n292 38 14\n292 119 10\n292 121 49\n292 129 47\n292 137 29\n292 143 33\n292 157 28\n292 163 47\n292 167 19\n292 203 8\n292 214 22\n292 217 31\n292 220 15\n292 236 5\n292 274 35\n292 285 50\n292 303 5\n292 333 44\n292 358 25\n292 384 31\n292 385 48\n292 454 -2\n292 468 36\n292 487 11\n292 547 41\n292 549 32\n292 555 15\n292 559 10\n292 572 48\n292 575 14\n292 606 17\n292 637 41\n292 655 39\n292 659 2\n292 685 24\n292 688 -2\n292 747 8\n292 748 35\n292 794 19\n292 827 3\n292 833 36\n292 874 20\n292 942 20\n292 948 1\n292 953 25\n292 963 26\n292 996 30\n293 2 42\n293 74 35\n293 93 31\n293 101 23\n293 161 45\n293 185 13\n293 200 22\n293 214 19\n293 249 -2\n293 260 5\n293 276 34\n293 297 4\n293 323 31\n293 343 34\n293 352 15\n293 366 14\n293 370 33\n293 371 43\n293 372 28\n293 376 37\n293 386 26\n293 407 40\n293 412 49\n293 418 13\n293 434 5\n293 460 13\n293 469 16\n293 482 39\n293 503 15\n293 519 47\n293 520 31\n293 541 22\n293 548 34\n293 562 27\n293 620 12\n293 625 27\n293 638 38\n293 639 2\n293 661 43\n293 685 13\n293 709 39\n293 733 11\n293 738 8\n293 754 38\n293 759 39\n293 761 43\n293 815 -2\n293 862 48\n293 879 4\n293 884 3\n293 898 42\n293 903 2\n293 907 23\n293 908 0\n293 931 46\n293 947 8\n293 955 39\n293 965 5\n293 970 30\n293 989 42\n294 7 42\n294 41 42\n294 55 -2\n294 78 48\n294 105 36\n294 133 0\n294 136 3\n294 209 33\n294 210 8\n294 230 39\n294 263 44\n294 265 12\n294 289 1\n294 305 33\n294 311 4\n294 312 22\n294 315 14\n294 321 50\n294 330 43\n294 350 36\n294 367 2\n294 392 10\n294 430 9\n294 431 23\n294 438 2\n294 465 43\n294 468 23\n294 470 17\n294 472 48\n294 485 19\n294 489 19\n294 502 47\n294 541 14\n294 564 35\n294 573 5\n294 596 50\n294 599 4\n294 615 19\n294 625 41\n294 629 20\n294 649 16\n294 683 4\n294 685 42\n294 704 28\n294 730 3\n294 732 11\n294 769 43\n294 797 47\n294 827 31\n294 886 30\n294 894 2\n294 932 32\n294 942 33\n294 962 46\n294 968 29\n294 990 30\n295 43 7\n295 69 23\n295 72 26\n295 204 24\n295 219 35\n295 224 28\n295 340 34\n295 356 32\n295 363 33\n295 369 48\n295 387 49\n295 406 25\n295 427 16\n295 459 15\n295 510 22\n295 528 15\n295 563 38\n295 575 22\n295 578 33\n295 579 19\n295 616 30\n295 622 6\n295 626 5\n295 667 30\n295 686 37\n295 703 5\n295 714 49\n295 718 29\n295 724 36\n295 737 29\n295 768 18\n295 770 26\n295 780 18\n295 783 32\n295 819 14\n295 852 22\n295 875 39\n295 881 26\n295 892 23\n295 899 25\n295 916 48\n295 939 -2\n295 956 1\n295 963 41\n295 968 23\n295 984 7\n295 989 46\n295 992 17\n296 10 25\n296 16 4\n296 26 35\n296 29 29\n296 34 31\n296 47 9\n296 50 17\n296 108 2\n296 109 43\n296 171 1\n296 218 48\n296 223 22\n296 224 22\n296 226 24\n296 253 9\n296 254 33\n296 258 33\n296 272 32\n296 273 24\n296 274 10\n296 303 19\n296 312 24\n296 315 4\n296 360 24\n296 409 -1\n296 414 37\n296 419 31\n296 479 17\n296 493 9\n296 497 43\n296 524 7\n296 533 13\n296 558 49\n296 559 4\n296 572 23\n296 597 10\n296 707 36\n296 715 18\n296 716 44\n296 719 26\n296 773 41\n296 784 24\n296 794 26\n296 810 1\n296 815 4\n296 840 47\n296 849 24\n296 850 36\n296 854 49\n296 865 21\n296 869 36\n296 924 25\n296 928 13\n296 942 4\n296 970 17\n296 975 22\n297 10 47\n297 24 35\n297 29 48\n297 33 12\n297 50 26\n297 72 18\n297 93 46\n297 97 49\n297 101 21\n297 120 39\n297 123 21\n297 135 18\n297 150 44\n297 210 16\n297 215 33\n297 216 15\n297 220 48\n297 222 41\n297 253 31\n297 258 38\n297 281 5\n297 284 7\n297 292 40\n297 336 9\n297 341 11\n297 360 42\n297 367 30\n297 392 6\n297 397 44\n297 409 1\n297 420 38\n297 434 38\n297 450 34\n297 461 46\n297 487 28\n297 496 19\n297 531 47\n297 534 25\n297 536 21\n297 624 5\n297 639 47\n297 673 42\n297 685 28\n297 712 40\n297 715 13\n297 754 4\n297 759 17\n297 781 46\n297 796 2\n297 812 9\n297 815 4\n297 820 -2\n297 866 19\n297 875 16\n297 898 12\n297 914 45\n297 928 -2\n297 930 14\n297 947 11\n297 971 0\n298 8 22\n298 20 -1\n298 22 47\n298 27 3\n298 42 28\n298 50 18\n298 90 45\n298 118 37\n298 121 12\n298 163 21\n298 179 45\n298 180 44\n298 181 43\n298 258 35\n298 268 18\n298 276 23\n298 309 35\n298 316 40\n298 324 49\n298 331 17\n298 336 27\n298 408 46\n298 418 19\n298 420 29\n298 422 39\n298 447 32\n298 467 29\n298 526 2\n298 529 44\n298 579 7\n298 587 9\n298 592 11\n298 598 6\n298 629 35\n298 647 -1\n298 667 14\n298 699 20\n298 700 16\n298 706 0\n298 720 16\n298 724 23\n298 725 17\n298 733 30\n298 741 11\n298 755 22\n298 788 43\n298 809 22\n298 810 5\n298 818 18\n298 837 26\n298 874 12\n298 880 39\n298 885 15\n298 965 50\n298 976 48\n298 984 39\n299 8 20\n299 15 26\n299 57 45\n299 67 13\n299 93 32\n299 118 33\n299 132 17\n299 177 24\n299 179 28\n299 233 33\n299 234 13\n299 247 20\n299 266 19\n299 288 8\n299 302 27\n299 326 21\n299 327 45\n299 337 31\n299 350 27\n299 352 2\n299 384 31\n299 454 3\n299 482 5\n299 505 37\n299 549 34\n299 559 8\n299 603 -2\n299 607 4\n299 615 14\n299 616 43\n299 620 1\n299 634 0\n299 691 1\n299 718 49\n299 733 -2\n299 742 43\n299 760 11\n299 777 -2\n299 830 22\n299 893 45\n299 917 35\n299 922 18\n299 935 34\n299 947 35\n299 963 49\n299 985 38\n299 986 15\n299 989 8\n299 992 33\n300 5 26\n300 65 19\n300 87 46\n300 109 24\n300 115 32\n300 133 47\n300 177 11\n300 193 40\n300 214 27\n300 227 7\n300 256 44\n300 352 43\n300 355 6\n300 373 -2\n300 385 26\n300 438 33\n300 444 8\n300 486 -2\n300 502 9\n300 567 25\n300 599 43\n300 613 10\n300 699 6\n300 735 32\n300 748 9\n300 788 36\n300 793 13\n300 797 15\n300 860 -1\n300 873 46\n300 911 35\n300 933 -1\n300 937 48\n300 941 8\n300 942 42\n300 944 40\n300 962 -2\n300 965 -1\n300 971 47\n300 972 49\n300 977 34\n301 41 18\n301 54 -2\n301 106 29\n301 110 6\n301 125 12\n301 131 -1\n301 146 25\n301 149 18\n301 150 46\n301 171 16\n301 198 40\n301 246 17\n301 260 33\n301 270 5\n301 306 16\n301 323 5\n301 325 -2\n301 381 49\n301 387 29\n301 402 41\n301 406 14\n301 444 -2\n301 448 50\n301 470 -2\n301 509 3\n301 551 4\n301 616 24\n301 621 0\n301 663 12\n301 670 8\n301 679 8\n301 683 39\n301 686 7\n301 699 49\n301 708 34\n301 734 7\n301 736 5\n301 749 50\n301 757 44\n301 794 25\n301 872 39\n301 880 6\n301 896 13\n301 901 25\n301 935 11\n301 944 13\n301 968 -1\n301 978 -1\n302 1 2\n302 32 34\n302 79 0\n302 98 40\n302 184 45\n302 228 -2\n302 277 3\n302 283 5\n302 309 40\n302 330 7\n302 348 12\n302 374 30\n302 379 34\n302 424 2\n302 432 29\n302 439 33\n302 447 33\n302 449 43\n302 452 48\n302 475 9\n302 506 41\n302 547 17\n302 574 33\n302 593 22\n302 611 16\n302 614 9\n302 627 41\n302 638 -2\n302 670 2\n302 677 27\n302 710 47\n302 713 18\n302 731 45\n302 757 37\n302 807 13\n302 831 45\n302 865 31\n302 885 7\n302 905 47\n302 934 24\n302 970 29\n303 17 30\n303 18 14\n303 37 5\n303 60 12\n303 93 28\n303 97 42\n303 126 24\n303 182 6\n303 183 6\n303 190 37\n303 203 49\n303 210 23\n303 216 13\n303 225 32\n303 236 24\n303 237 9\n303 323 50\n303 326 21\n303 328 46\n303 439 31\n303 472 -2\n303 540 30\n303 563 32\n303 588 20\n303 602 26\n303 706 -1\n303 725 26\n303 734 14\n303 735 12\n303 736 14\n303 749 25\n303 752 20\n303 753 -1\n303 767 46\n303 778 15\n303 795 39\n303 796 2\n303 818 28\n303 849 47\n303 866 38\n303 885 2\n303 943 45\n303 967 29\n303 974 50\n303 996 24\n304 15 33\n304 38 30\n304 86 44\n304 93 39\n304 124 48\n304 136 13\n304 149 33\n304 168 45\n304 172 46\n304 185 13\n304 210 5\n304 228 20\n304 301 49\n304 341 25\n304 342 41\n304 351 11\n304 387 27\n304 390 39\n304 406 15\n304 519 25\n304 525 -1\n304 535 39\n304 557 48\n304 578 48\n304 621 3\n304 663 0\n304 670 48\n304 682 14\n304 688 -1\n304 699 13\n304 705 48\n304 715 37\n304 794 4\n304 813 43\n304 834 10\n304 841 3\n304 860 36\n304 913 7\n304 914 34\n304 936 45\n304 959 1\n304 988 41\n305 69 5\n305 81 28\n305 124 14\n305 146 12\n305 147 36\n305 159 42\n305 176 18\n305 194 49\n305 202 14\n305 230 43\n305 232 20\n305 241 36\n305 242 35\n305 249 31\n305 270 19\n305 294 21\n305 318 49\n305 372 32\n305 394 15\n305 395 14\n305 404 7\n305 442 24\n305 465 13\n305 469 43\n305 484 1\n305 507 22\n305 525 24\n305 540 32\n305 549 46\n305 552 18\n305 565 49\n305 676 14\n305 688 8\n305 751 50\n305 769 1\n305 785 26\n305 786 35\n305 805 50\n305 815 7\n305 840 1\n305 880 26\n305 959 12\n305 983 7\n305 986 33\n305 987 3\n305 995 20\n306 7 43\n306 23 6\n306 25 4\n306 52 32\n306 66 1\n306 70 21\n306 84 -1\n306 96 24\n306 112 1\n306 130 46\n306 134 41\n306 136 24\n306 137 43\n306 139 13\n306 174 33\n306 195 41\n306 199 20\n306 223 19\n306 231 21\n306 246 49\n306 262 24\n306 312 18\n306 338 9\n306 342 18\n306 345 2\n306 384 19\n306 394 29\n306 409 24\n306 424 9\n306 538 24\n306 546 27\n306 562 19\n306 613 42\n306 614 24\n306 661 17\n306 671 19\n306 688 47\n306 698 0\n306 752 34\n306 769 8\n306 823 40\n306 848 31\n306 854 21\n306 866 45\n306 871 3\n306 873 32\n306 894 12\n306 904 38\n306 938 12\n306 941 0\n306 951 49\n306 961 13\n306 966 6\n306 968 31\n306 980 41\n306 988 28\n306 995 19\n307 11 40\n307 12 31\n307 49 40\n307 106 26\n307 112 13\n307 114 47\n307 180 45\n307 182 27\n307 189 17\n307 193 -1\n307 208 45\n307 225 12\n307 232 18\n307 245 40\n307 246 31\n307 249 36\n307 250 24\n307 253 9\n307 341 41\n307 348 35\n307 387 37\n307 405 31\n307 406 30\n307 428 22\n307 444 14\n307 446 24\n307 485 34\n307 490 31\n307 503 37\n307 507 29\n307 594 41\n307 609 43\n307 624 48\n307 657 22\n307 738 26\n307 740 39\n307 746 47\n307 758 16\n307 780 2\n307 781 22\n307 824 8\n307 878 12\n307 935 9\n307 940 45\n307 960 45\n307 990 50\n308 11 41\n308 69 4\n308 116 15\n308 163 29\n308 204 -2\n308 213 25\n308 219 6\n308 225 26\n308 233 22\n308 277 15\n308 296 31\n308 325 9\n308 337 50\n308 340 16\n308 343 45\n308 361 49\n308 453 26\n308 456 -1\n308 462 19\n308 477 4\n308 490 5\n308 507 19\n308 521 3\n308 541 15\n308 559 49\n308 561 9\n308 562 26\n308 573 45\n308 592 43\n308 604 40\n308 620 36\n308 652 44\n308 662 50\n308 694 26\n308 699 27\n308 708 27\n308 722 15\n308 726 37\n308 738 3\n308 745 7\n308 750 8\n308 754 3\n308 775 42\n308 783 31\n308 812 5\n308 825 5\n308 862 33\n308 871 27\n308 880 37\n308 897 28\n308 902 13\n308 917 33\n308 922 16\n308 930 3\n308 963 38\n308 964 14\n309 11 38\n309 13 26\n309 75 14\n309 137 2\n309 142 7\n309 155 42\n309 179 10\n309 191 44\n309 205 24\n309 216 12\n309 279 32\n309 328 49\n309 343 13\n309 349 0\n309 360 15\n309 365 28\n309 380 12\n309 409 42\n309 418 12\n309 427 34\n309 428 15\n309 439 28\n309 441 -1\n309 468 19\n309 483 33\n309 496 4\n309 517 22\n309 601 46\n309 607 4\n309 614 18\n309 691 38\n309 713 10\n309 715 24\n309 752 36\n309 788 22\n309 817 9\n309 850 27\n309 851 10\n309 871 41\n309 878 33\n309 903 44\n309 910 2\n309 936 27\n309 949 -2\n309 951 31\n309 998 45\n310 14 30\n310 67 37\n310 99 49\n310 108 10\n310 113 18\n310 117 2\n310 139 32\n310 154 33\n310 181 14\n310 201 4\n310 225 49\n310 241 49\n310 243 50\n310 267 23\n310 307 29\n310 315 39\n310 337 7\n310 351 28\n310 437 47\n310 451 5\n310 483 49\n310 484 10\n310 498 -2\n310 500 48\n310 541 45\n310 563 37\n310 569 7\n310 606 2\n310 618 16\n310 630 40\n310 635 21\n310 652 28\n310 654 19\n310 657 35\n310 666 3\n310 671 1\n310 706 45\n310 733 22\n310 757 35\n310 812 2\n310 871 40\n310 912 23\n310 960 38\n311 5 48\n311 18 50\n311 44 27\n311 80 9\n311 91 23\n311 114 41\n311 129 18\n311 158 24\n311 162 29\n311 167 6\n311 210 24\n311 301 27\n311 329 16\n311 364 31\n311 383 -1\n311 384 0\n311 416 17\n311 431 40\n311 449 40\n311 452 7\n311 462 35\n311 471 42\n311 476 43\n311 481 47\n311 540 18\n311 551 15\n311 574 22\n311 580 14\n311 581 48\n311 597 36\n311 599 16\n311 612 15\n311 633 32\n311 643 -2\n311 681 18\n311 706 41\n311 723 15\n311 739 19\n311 781 22\n311 841 11\n311 847 18\n311 851 16\n311 867 12\n311 869 34\n311 873 12\n311 913 12\n311 957 3\n311 959 5\n311 989 5\n311 991 43\n312 1 40\n312 7 12\n312 10 48\n312 29 10\n312 58 22\n312 60 2\n312 65 8\n312 70 22\n312 92 -1\n312 104 19\n312 131 33\n312 145 22\n312 147 23\n312 172 18\n312 207 37\n312 210 36\n312 215 13\n312 218 39\n312 230 7\n312 248 38\n312 255 27\n312 267 10\n312 278 27\n312 286 27\n312 299 17\n312 327 19\n312 334 27\n312 430 18\n312 452 31\n312 489 39\n312 503 42\n312 521 22\n312 539 35\n312 558 16\n312 560 17\n312 582 48\n312 594 16\n312 599 30\n312 620 37\n312 628 23\n312 657 22\n312 661 12\n312 705 29\n312 713 17\n312 714 14\n312 718 49\n312 736 15\n312 765 37\n312 768 15\n312 811 40\n312 812 43\n312 815 10\n312 818 4\n312 825 28\n312 883 7\n312 900 18\n312 925 46\n312 932 1\n312 955 40\n312 977 27\n312 997 32\n313 5 22\n313 14 50\n313 30 8\n313 67 21\n313 94 14\n313 120 2\n313 161 44\n313 180 9\n313 197 20\n313 221 40\n313 238 20\n313 239 45\n313 241 23\n313 245 32\n313 251 33\n313 285 25\n313 294 50\n313 310 11\n313 336 11\n313 353 49\n313 375 14\n313 381 35\n313 403 42\n313 414 18\n313 444 -1\n313 474 29\n313 495 10\n313 500 7\n313 515 6\n313 533 25\n313 534 37\n313 547 15\n313 548 15\n313 549 16\n313 558 43\n313 559 26\n313 602 40\n313 622 -2\n313 628 21\n313 672 47\n313 728 6\n313 743 2\n313 765 7\n313 779 24\n313 799 5\n313 814 28\n313 821 27\n313 826 11\n313 850 36\n313 876 29\n313 901 37\n313 917 1\n313 944 22\n313 959 34\n314 1 22\n314 5 39\n314 7 9\n314 28 14\n314 34 10\n314 43 49\n314 44 15\n314 157 28\n314 159 41\n314 187 46\n314 188 25\n314 195 11\n314 241 28\n314 263 4\n314 284 39\n314 295 8\n314 317 20\n314 323 5\n314 328 19\n314 348 43\n314 362 -2\n314 401 -1\n314 424 24\n314 425 10\n314 471 20\n314 478 16\n314 493 16\n314 523 18\n314 526 5\n314 563 42\n314 670 27\n314 689 21\n314 706 15\n314 733 10\n314 758 34\n314 760 45\n314 774 9\n314 790 33\n314 812 16\n314 820 14\n314 832 3\n314 863 22\n314 869 7\n314 881 10\n314 889 11\n314 897 24\n314 898 47\n314 944 0\n314 951 49\n314 986 23\n315 23 32\n315 55 -1\n315 81 24\n315 94 50\n315 128 9\n315 167 21\n315 187 46\n315 188 4\n315 189 44\n315 191 31\n315 202 9\n315 222 34\n315 247 6\n315 261 15\n315 297 -1\n315 303 0\n315 331 37\n315 350 30\n315 364 40\n315 406 37\n315 412 45\n315 430 27\n315 438 37\n315 448 36\n315 489 35\n315 504 28\n315 539 22\n315 557 41\n315 564 9\n315 585 43\n315 588 6\n315 609 10\n315 633 34\n315 637 29\n315 653 1\n315 719 33\n315 726 18\n315 730 44\n315 766 6\n315 804 39\n315 814 25\n315 833 31\n315 848 45\n315 857 46\n315 864 21\n315 865 25\n315 891 46\n315 944 22\n315 999 49\n316 53 40\n316 88 33\n316 98 34\n316 104 20\n316 111 5\n316 190 3\n316 202 33\n316 237 6\n316 240 0\n316 241 24\n316 246 -2\n316 262 19\n316 288 33\n316 322 17\n316 327 27\n316 332 23\n316 348 4\n316 374 40\n316 376 25\n316 383 2\n316 465 44\n316 492 0\n316 498 22\n316 508 16\n316 521 32\n316 541 3\n316 560 26\n316 574 18\n316 583 25\n316 641 39\n316 642 15\n316 651 30\n316 669 43\n316 673 32\n316 688 43\n316 713 33\n316 715 32\n316 717 6\n316 740 2\n316 745 1\n316 753 5\n316 773 27\n316 778 17\n316 782 25\n316 786 41\n316 813 9\n316 834 49\n316 853 30\n316 870 46\n316 902 0\n316 906 2\n316 931 32\n316 953 37\n316 979 17\n316 988 17\n317 2 26\n317 34 27\n317 47 30\n317 61 11\n317 99 6\n317 194 42\n317 195 4\n317 231 1\n317 243 24\n317 271 28\n317 276 24\n317 277 23\n317 305 1\n317 325 46\n317 358 38\n317 372 36\n317 434 29\n317 437 26\n317 446 27\n317 451 24\n317 454 4\n317 492 19\n317 568 50\n317 578 29\n317 604 48\n317 618 22\n317 637 37\n317 668 30\n317 672 22\n317 676 5\n317 678 32\n317 688 43\n317 707 47\n317 735 1\n317 737 15\n317 747 9\n317 756 37\n317 768 37\n317 783 50\n317 792 44\n317 819 18\n317 836 50\n317 843 34\n317 874 45\n317 878 10\n317 881 25\n317 899 3\n317 931 46\n317 933 50\n317 937 40\n317 977 14\n318 1 17\n318 4 27\n318 12 28\n318 107 19\n318 108 42\n318 119 33\n318 131 37\n318 156 46\n318 160 6\n318 203 40\n318 241 18\n318 242 15\n318 267 32\n318 268 3\n318 279 -2\n318 287 11\n318 333 50\n318 346 15\n318 372 0\n318 412 45\n318 414 27\n318 467 37\n318 524 14\n318 552 36\n318 570 31\n318 586 5\n318 611 13\n318 643 23\n318 658 46\n318 667 29\n318 668 23\n318 673 12\n318 679 41\n318 702 37\n318 733 17\n318 750 17\n318 799 37\n318 800 3\n318 883 1\n318 900 28\n318 926 18\n318 928 44\n318 936 14\n318 949 17\n318 984 23\n318 997 1\n319 11 -2\n319 18 28\n319 31 28\n319 52 11\n319 61 24\n319 111 29\n319 136 40\n319 140 28\n319 162 32\n319 179 47\n319 229 30\n319 232 18\n319 295 40\n319 306 44\n319 313 34\n319 336 25\n319 351 12\n319 374 29\n319 387 28\n319 426 32\n319 443 1\n319 449 36\n319 472 6\n319 503 48\n319 506 35\n319 509 9\n319 529 10\n319 533 2\n319 558 29\n319 583 30\n319 590 15\n319 596 23\n319 597 22\n319 616 12\n319 665 39\n319 669 30\n319 682 39\n319 760 2\n319 842 35\n319 849 5\n319 877 16\n319 893 1\n319 912 39\n319 915 6\n319 925 27\n319 926 4\n319 933 3\n319 934 28\n319 944 50\n320 38 31\n320 56 25\n320 66 8\n320 86 8\n320 92 4\n320 102 -1\n320 110 19\n320 130 25\n320 147 45\n320 161 50\n320 225 2\n320 226 49\n320 249 22\n320 279 6\n320 305 47\n320 306 29\n320 313 31\n320 351 36\n320 376 32\n320 397 35\n320 401 8\n320 406 45\n320 416 37\n320 422 38\n320 424 39\n320 470 20\n320 511 25\n320 514 47\n320 523 44\n320 590 23\n320 591 29\n320 612 36\n320 759 32\n320 763 30\n320 805 49\n320 816 20\n320 839 13\n320 857 43\n320 912 6\n320 923 29\n320 931 38\n320 955 7\n320 965 0\n320 971 47\n320 990 36\n320 992 25\n321 4 37\n321 46 2\n321 55 38\n321 82 45\n321 89 27\n321 141 22\n321 159 33\n321 177 39\n321 185 21\n321 204 25\n321 232 44\n321 239 44\n321 249 7\n321 250 24\n321 257 25\n321 271 16\n321 276 40\n321 301 0\n321 302 30\n321 318 11\n321 381 17\n321 386 21\n321 405 18\n321 422 16\n321 449 33\n321 455 20\n321 547 27\n321 598 8\n321 600 6\n321 604 33\n321 654 1\n321 687 11\n321 714 11\n321 728 31\n321 749 43\n321 751 37\n321 784 9\n321 792 32\n321 812 1\n321 815 0\n321 817 10\n321 824 16\n321 840 47\n321 876 31\n322 3 0\n322 19 31\n322 24 45\n322 25 3\n322 43 23\n322 73 40\n322 88 32\n322 94 42\n322 114 48\n322 139 18\n322 154 26\n322 172 19\n322 183 22\n322 207 -2\n322 270 46\n322 291 42\n322 323 31\n322 352 37\n322 389 22\n322 397 4\n322 430 15\n322 445 37\n322 467 7\n322 507 1\n322 558 17\n322 561 -2\n322 566 18\n322 572 12\n322 601 39\n322 612 44\n322 660 14\n322 662 10\n322 675 19\n322 686 39\n322 692 14\n322 709 22\n322 713 5\n322 729 18\n322 757 6\n322 780 46\n322 793 16\n322 813 35\n322 822 47\n322 842 40\n322 852 4\n322 937 31\n322 946 31\n322 989 1\n323 3 50\n323 4 38\n323 10 20\n323 21 30\n323 33 45\n323 36 43\n323 82 4\n323 126 31\n323 130 44\n323 134 46\n323 179 40\n323 213 24\n323 225 5\n323 255 34\n323 281 41\n323 299 35\n323 302 40\n323 322 24\n323 324 42\n323 337 43\n323 350 26\n323 369 10\n323 397 38\n323 398 48\n323 412 2\n323 447 49\n323 448 20\n323 452 39\n323 468 49\n323 501 3\n323 529 46\n323 534 10\n323 547 6\n323 550 49\n323 564 48\n323 596 9\n323 597 6\n323 621 45\n323 634 21\n323 648 35\n323 658 40\n323 662 11\n323 674 49\n323 676 23\n323 684 42\n323 699 30\n323 720 45\n323 763 29\n323 783 30\n323 839 50\n323 842 15\n323 843 24\n323 857 23\n323 859 6\n323 881 32\n323 887 40\n323 925 -2\n323 929 9\n323 964 5\n323 987 32\n324 2 40\n324 9 24\n324 37 5\n324 42 4\n324 47 7\n324 56 12\n324 58 9\n324 80 18\n324 84 35\n324 85 45\n324 141 29\n324 144 45\n324 167 45\n324 242 -1\n324 285 25\n324 337 20\n324 341 14\n324 366 19\n324 368 15\n324 403 48\n324 427 11\n324 434 40\n324 477 39\n324 483 15\n324 510 21\n324 511 -1\n324 521 3\n324 529 -1\n324 545 50\n324 560 36\n324 572 12\n324 587 46\n324 611 23\n324 617 23\n324 680 0\n324 728 3\n324 733 7\n324 765 25\n324 766 46\n324 768 12\n324 788 35\n324 798 23\n324 821 17\n324 823 38\n324 884 46\n324 925 25\n324 926 46\n324 932 41\n324 960 -2\n324 992 -1\n325 9 10\n325 32 50\n325 46 8\n325 69 6\n325 93 14\n325 118 50\n325 153 17\n325 166 31\n325 189 34\n325 261 13\n325 263 28\n325 297 42\n325 309 22\n325 333 1\n325 361 38\n325 370 5\n325 387 29\n325 404 3\n325 434 30\n325 441 16\n325 447 -1\n325 459 18\n325 462 49\n325 488 19\n325 522 7\n325 566 37\n325 569 27\n325 615 11\n325 621 48\n325 669 19\n325 691 17\n325 701 5\n325 729 23\n325 757 44\n325 771 4\n325 815 32\n325 817 10\n325 858 14\n325 864 23\n325 905 11\n325 910 20\n325 959 9\n326 1 43\n326 3 29\n326 5 12\n326 21 34\n326 84 1\n326 119 19\n326 137 47\n326 139 14\n326 148 39\n326 201 19\n326 245 44\n326 246 40\n326 287 20\n326 339 5\n326 349 13\n326 374 11\n326 411 9\n326 413 38\n326 414 35\n326 422 33\n326 464 19\n326 466 24\n326 493 36\n326 503 11\n326 510 39\n326 522 5\n326 526 8\n326 548 7\n326 558 5\n326 567 -2\n326 593 9\n326 594 26\n326 598 6\n326 600 11\n326 631 1\n326 675 34\n326 732 7\n326 761 12\n326 781 27\n326 798 36\n326 805 30\n326 816 29\n326 840 14\n326 904 13\n326 913 31\n326 930 1\n326 933 2\n326 934 10\n326 955 12\n326 989 14\n327 25 47\n327 30 20\n327 64 18\n327 81 14\n327 86 31\n327 90 19\n327 116 7\n327 125 13\n327 143 21\n327 197 44\n327 206 29\n327 248 49\n327 262 38\n327 265 1\n327 270 35\n327 271 15\n327 304 30\n327 309 16\n327 351 -2\n327 369 33\n327 405 48\n327 410 16\n327 413 1\n327 417 3\n327 451 21\n327 484 -1\n327 490 32\n327 507 32\n327 510 49\n327 514 17\n327 515 39\n327 601 12\n327 602 18\n327 670 45\n327 740 -1\n327 748 50\n327 761 25\n327 765 18\n327 794 3\n327 806 20\n327 818 5\n327 870 16\n327 893 2\n327 909 34\n327 920 43\n327 922 13\n327 930 4\n327 943 43\n327 949 0\n327 960 7\n327 980 12\n327 1000 36\n328 10 0\n328 17 50\n328 41 13\n328 44 26\n328 47 -2\n328 52 1\n328 60 46\n328 68 38\n328 94 33\n328 97 22\n328 147 4\n328 247 38\n328 253 21\n328 325 26\n328 360 21\n328 362 33\n328 389 11\n328 405 50\n328 412 21\n328 416 4\n328 417 0\n328 421 31\n328 471 14\n328 479 17\n328 520 33\n328 540 20\n328 545 18\n328 556 9\n328 587 7\n328 606 24\n328 611 12\n328 650 8\n328 686 16\n328 728 8\n328 738 10\n328 762 -2\n328 774 11\n328 783 15\n328 819 9\n328 846 39\n328 851 0\n328 857 9\n328 893 11\n328 905 27\n328 910 5\n328 915 27\n328 934 48\n328 958 37\n328 966 6\n329 7 21\n329 15 47\n329 50 33\n329 62 15\n329 83 31\n329 85 4\n329 99 8\n329 101 33\n329 117 46\n329 133 32\n329 155 34\n329 166 35\n329 168 36\n329 201 39\n329 253 10\n329 264 42\n329 277 45\n329 309 18\n329 312 20\n329 320 17\n329 404 23\n329 422 31\n329 444 39\n329 451 38\n329 464 17\n329 474 3\n329 507 42\n329 508 46\n329 537 3\n329 562 15\n329 580 22\n329 593 46\n329 602 19\n329 603 22\n329 606 -1\n329 609 5\n329 620 23\n329 643 23\n329 658 22\n329 670 38\n329 679 47\n329 684 31\n329 697 48\n329 706 33\n329 764 49\n329 785 24\n329 864 23\n329 898 20\n329 915 3\n329 956 10\n329 978 15\n330 43 19\n330 44 3\n330 65 18\n330 112 32\n330 121 10\n330 128 20\n330 167 30\n330 188 17\n330 192 8\n330 271 4\n330 299 41\n330 307 5\n330 314 39\n330 331 1\n330 356 46\n330 362 37\n330 367 5\n330 383 43\n330 399 47\n330 408 39\n330 433 36\n330 469 34\n330 485 29\n330 524 -2\n330 528 43\n330 532 17\n330 546 31\n330 560 4\n330 571 11\n330 578 9\n330 621 42\n330 627 20\n330 629 17\n330 644 20\n330 668 46\n330 681 25\n330 702 41\n330 733 15\n330 746 43\n330 756 38\n330 772 36\n330 806 48\n330 811 45\n330 837 14\n330 864 32\n330 879 39\n330 883 31\n330 897 21\n330 951 12\n330 957 17\n330 988 29\n331 32 41\n331 67 43\n331 71 20\n331 89 15\n331 105 27\n331 125 12\n331 245 16\n331 274 11\n331 296 35\n331 325 2\n331 359 34\n331 371 20\n331 373 47\n331 401 42\n331 406 35\n331 411 30\n331 424 16\n331 428 29\n331 449 44\n331 465 -2\n331 499 40\n331 519 33\n331 540 32\n331 558 9\n331 566 12\n331 602 50\n331 609 40\n331 612 29\n331 632 27\n331 667 15\n331 689 0\n331 726 2\n331 754 44\n331 762 46\n331 785 29\n331 807 13\n331 851 41\n331 878 13\n331 884 33\n331 893 6\n331 894 14\n331 930 13\n331 940 14\n331 977 9\n331 993 27\n331 996 16\n332 26 30\n332 43 34\n332 50 45\n332 59 35\n332 62 23\n332 66 32\n332 67 18\n332 90 44\n332 133 23\n332 134 28\n332 146 37\n332 150 7\n332 162 48\n332 202 44\n332 212 29\n332 231 41\n332 232 36\n332 233 17\n332 281 35\n332 331 38\n332 375 8\n332 417 23\n332 438 14\n332 445 13\n332 449 38\n332 458 28\n332 463 28\n332 481 15\n332 503 29\n332 514 37\n332 520 33\n332 573 49\n332 574 15\n332 581 2\n332 595 1\n332 659 6\n332 708 0\n332 723 46\n332 736 22\n332 739 21\n332 747 1\n332 763 0\n332 764 27\n332 770 39\n332 803 11\n332 861 27\n332 891 32\n332 930 16\n332 951 50\n332 980 48\n333 15 42\n333 67 2\n333 70 5\n333 117 2\n333 122 46\n333 136 48\n333 138 15\n333 140 9\n333 144 16\n333 165 38\n333 167 7\n333 177 31\n333 182 27\n333 193 2\n333 221 15\n333 262 35\n333 266 4\n333 273 1\n333 280 40\n333 309 37\n333 348 39\n333 356 -1\n333 436 33\n333 449 31\n333 457 29\n333 496 28\n333 503 39\n333 542 -1\n333 551 36\n333 555 4\n333 569 47\n333 590 2\n333 602 19\n333 603 10\n333 616 18\n333 620 -2\n333 655 29\n333 679 25\n333 687 40\n333 736 24\n333 743 19\n333 765 48\n333 775 44\n333 815 41\n333 820 39\n333 856 6\n333 896 21\n333 927 14\n333 930 39\n333 944 11\n334 34 21\n334 40 43\n334 43 10\n334 116 16\n334 152 40\n334 157 3\n334 198 21\n334 204 18\n334 222 18\n334 239 13\n334 259 14\n334 265 11\n334 278 42\n334 294 33\n334 308 31\n334 338 0\n334 374 9\n334 376 36\n334 387 24\n334 403 28\n334 426 46\n334 435 40\n334 443 -1\n334 501 50\n334 543 11\n334 545 40\n334 559 -2\n334 582 43\n334 682 14\n334 704 1\n334 706 49\n334 710 12\n334 726 26\n334 729 11\n334 736 18\n334 791 1\n334 804 48\n334 841 41\n334 852 17\n334 881 49\n334 914 11\n334 932 40\n334 940 50\n334 994 46\n335 84 43\n335 103 21\n335 139 46\n335 160 0\n335 162 34\n335 196 46\n335 202 25\n335 216 13\n335 235 5\n335 313 18\n335 352 34\n335 384 45\n335 392 44\n335 401 49\n335 409 29\n335 421 37\n335 435 7\n335 487 46\n335 505 21\n335 506 48\n335 558 22\n335 570 45\n335 586 28\n335 592 46\n335 601 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22\n416 456 39\n416 493 16\n416 502 3\n416 521 48\n416 557 22\n416 600 43\n416 723 8\n416 726 26\n416 746 19\n416 751 48\n416 773 39\n416 830 22\n416 847 24\n416 849 0\n416 857 28\n416 865 6\n416 887 17\n416 890 23\n416 933 13\n416 937 7\n416 952 26\n416 958 13\n417 22 11\n417 44 2\n417 120 43\n417 163 6\n417 165 12\n417 206 10\n417 245 45\n417 255 48\n417 277 49\n417 281 20\n417 283 23\n417 336 1\n417 348 30\n417 352 14\n417 388 28\n417 458 33\n417 475 48\n417 502 13\n417 562 48\n417 574 19\n417 582 29\n417 590 37\n417 596 13\n417 617 38\n417 619 11\n417 631 -2\n417 650 45\n417 672 36\n417 704 43\n417 721 42\n417 723 9\n417 757 13\n417 758 33\n417 778 39\n417 785 3\n417 803 18\n417 817 28\n417 818 6\n417 866 36\n417 874 5\n417 885 15\n417 892 34\n417 901 40\n417 927 28\n417 994 13\n418 25 47\n418 84 15\n418 115 3\n418 139 15\n418 150 39\n418 154 13\n418 163 -2\n418 168 32\n418 228 30\n418 237 43\n418 271 10\n418 276 45\n418 287 32\n418 291 10\n418 309 20\n418 317 18\n418 338 48\n418 343 46\n418 353 1\n418 358 25\n418 367 19\n418 373 41\n418 387 42\n418 474 7\n418 475 37\n418 621 49\n418 675 17\n418 724 1\n418 769 49\n418 819 27\n418 837 6\n418 839 13\n418 844 43\n418 857 33\n418 869 43\n418 978 42\n418 992 2\n419 4 10\n419 84 7\n419 90 44\n419 103 42\n419 137 46\n419 157 14\n419 164 10\n419 219 32\n419 220 45\n419 238 43\n419 318 27\n419 335 49\n419 398 7\n419 402 6\n419 467 11\n419 475 11\n419 487 2\n419 502 44\n419 534 31\n419 540 0\n419 546 9\n419 555 47\n419 586 44\n419 626 13\n419 630 10\n419 650 5\n419 693 27\n419 701 4\n419 713 8\n419 716 26\n419 728 31\n419 729 47\n419 740 4\n419 755 7\n419 779 19\n419 810 2\n419 832 36\n419 857 36\n419 870 24\n419 873 47\n419 880 38\n419 893 8\n419 895 3\n419 904 18\n419 905 0\n419 920 0\n419 964 30\n419 969 38\n420 2 36\n420 12 33\n420 15 35\n420 16 5\n420 60 50\n420 76 33\n420 78 31\n420 80 13\n420 82 42\n420 88 33\n420 133 26\n420 149 23\n420 151 33\n420 221 -2\n420 236 23\n420 257 14\n420 261 47\n420 278 -2\n420 312 31\n420 322 7\n420 396 32\n420 401 47\n420 424 24\n420 435 26\n420 439 44\n420 450 28\n420 462 13\n420 472 36\n420 485 37\n420 487 19\n420 507 26\n420 527 26\n420 544 3\n420 559 11\n420 583 49\n420 607 -2\n420 612 41\n420 629 26\n420 716 10\n420 719 14\n420 724 3\n420 727 45\n420 745 4\n420 758 1\n420 780 46\n420 782 37\n420 792 15\n420 843 10\n420 844 6\n420 848 5\n420 861 23\n420 999 6\n421 21 42\n421 65 6\n421 109 12\n421 134 2\n421 148 31\n421 191 48\n421 192 40\n421 193 24\n421 208 6\n421 223 48\n421 231 27\n421 233 19\n421 273 20\n421 278 33\n421 292 41\n421 300 15\n421 336 14\n421 344 18\n421 349 15\n421 372 26\n421 404 4\n421 417 16\n421 464 29\n421 466 19\n421 486 49\n421 542 45\n421 553 0\n421 563 5\n421 597 37\n421 606 18\n421 617 32\n421 635 15\n421 647 0\n421 688 5\n421 721 32\n421 722 12\n421 730 1\n421 734 31\n421 839 44\n421 840 -1\n421 842 1\n421 855 0\n421 875 29\n421 883 28\n421 886 12\n421 889 1\n421 961 7\n421 973 34\n421 975 8\n421 992 23\n421 1000 15\n422 7 24\n422 51 35\n422 118 14\n422 128 49\n422 181 9\n422 193 8\n422 215 27\n422 223 22\n422 237 14\n422 240 8\n422 248 17\n422 256 22\n422 272 35\n422 288 17\n422 290 13\n422 303 41\n422 326 27\n422 327 12\n422 338 0\n422 364 27\n422 372 36\n422 394 27\n422 409 13\n422 421 28\n422 428 9\n422 437 17\n422 467 36\n422 487 19\n422 494 20\n422 537 9\n422 559 15\n422 560 42\n422 578 0\n422 589 14\n422 600 27\n422 602 27\n422 604 25\n422 608 48\n422 653 27\n422 732 10\n422 768 35\n422 814 37\n422 826 25\n422 843 7\n422 860 8\n422 861 34\n422 878 44\n422 884 27\n422 902 37\n422 911 47\n422 936 12\n422 976 12\n422 985 13\n422 988 0\n423 5 41\n423 22 25\n423 73 11\n423 148 17\n423 158 7\n423 230 21\n423 271 14\n423 302 14\n423 325 28\n423 329 21\n423 356 2\n423 358 48\n423 395 25\n423 396 26\n423 410 34\n423 411 48\n423 468 34\n423 500 47\n423 504 32\n423 505 12\n423 515 0\n423 519 30\n423 523 8\n423 573 1\n423 596 29\n423 599 31\n423 602 50\n423 607 39\n423 635 0\n423 639 40\n423 652 7\n423 660 22\n423 680 13\n423 723 27\n423 785 22\n423 800 9\n423 815 13\n423 818 26\n423 839 29\n423 847 8\n423 855 34\n423 912 4\n423 922 40\n423 948 49\n423 974 12\n424 17 29\n424 88 18\n424 116 13\n424 124 38\n424 194 25\n424 207 15\n424 216 49\n424 221 15\n424 254 33\n424 288 18\n424 308 13\n424 378 36\n424 407 44\n424 449 10\n424 465 0\n424 482 42\n424 497 40\n424 499 2\n424 500 -2\n424 525 2\n424 546 10\n424 560 10\n424 593 10\n424 598 2\n424 600 48\n424 607 1\n424 635 0\n424 709 24\n424 723 44\n424 737 40\n424 755 16\n424 780 10\n424 786 6\n424 792 8\n424 805 14\n424 815 12\n424 817 22\n424 820 34\n424 829 43\n424 836 15\n424 844 -1\n424 848 26\n424 849 28\n424 861 5\n424 867 -2\n424 873 12\n424 887 33\n424 915 -2\n424 978 1\n425 72 26\n425 95 16\n425 153 38\n425 156 22\n425 166 10\n425 181 8\n425 214 7\n425 231 23\n425 243 26\n425 251 5\n425 279 8\n425 286 45\n425 297 50\n425 299 19\n425 331 7\n425 332 35\n425 338 18\n425 348 25\n425 388 18\n425 398 25\n425 403 28\n425 414 19\n425 424 41\n425 437 27\n425 469 4\n425 478 33\n425 493 34\n425 495 9\n425 501 42\n425 575 37\n425 577 48\n425 614 38\n425 618 25\n425 689 38\n425 741 2\n425 743 14\n425 764 40\n425 780 45\n425 792 6\n425 804 14\n425 859 45\n425 874 6\n425 912 32\n425 940 35\n426 5 46\n426 69 40\n426 75 5\n426 101 22\n426 111 2\n426 122 39\n426 231 17\n426 254 43\n426 257 39\n426 262 30\n426 274 50\n426 281 48\n426 289 11\n426 299 24\n426 339 14\n426 369 11\n426 397 33\n426 410 23\n426 458 5\n426 462 26\n426 499 20\n426 517 -1\n426 531 47\n426 533 45\n426 539 1\n426 541 14\n426 545 21\n426 546 32\n426 558 48\n426 565 47\n426 616 29\n426 634 37\n426 713 11\n426 724 41\n426 726 27\n426 740 10\n426 777 37\n426 778 48\n426 807 17\n426 820 37\n426 874 27\n426 881 5\n426 897 28\n426 899 23\n426 900 39\n426 923 20\n426 924 21\n426 930 16\n426 979 15\n426 983 38\n427 24 23\n427 75 18\n427 107 35\n427 151 -2\n427 161 28\n427 184 16\n427 236 29\n427 240 30\n427 271 23\n427 299 46\n427 301 29\n427 353 44\n427 369 37\n427 392 1\n427 404 14\n427 409 -2\n427 432 29\n427 440 22\n427 459 17\n427 476 43\n427 479 29\n427 492 34\n427 512 39\n427 514 27\n427 526 27\n427 532 17\n427 540 25\n427 545 33\n427 600 33\n427 620 42\n427 630 3\n427 659 44\n427 663 50\n427 664 30\n427 671 49\n427 679 49\n427 759 37\n427 807 20\n427 826 5\n427 849 17\n427 865 42\n427 936 24\n427 959 34\n428 11 8\n428 32 6\n428 40 4\n428 48 25\n428 53 12\n428 64 50\n428 83 4\n428 89 9\n428 112 2\n428 177 42\n428 209 48\n428 210 5\n428 216 1\n428 253 46\n428 258 39\n428 299 34\n428 310 43\n428 317 10\n428 319 40\n428 337 35\n428 351 30\n428 388 45\n428 450 13\n428 455 36\n428 483 23\n428 526 38\n428 543 20\n428 573 41\n428 585 13\n428 592 25\n428 613 47\n428 616 -2\n428 650 19\n428 655 49\n428 684 -1\n428 735 13\n428 741 35\n428 744 17\n428 746 16\n428 757 41\n428 774 12\n428 802 38\n428 803 32\n428 808 1\n428 816 26\n428 848 48\n428 867 50\n428 923 9\n428 925 35\n428 930 31\n428 933 29\n428 950 12\n428 956 13\n428 990 35\n429 45 37\n429 67 1\n429 70 9\n429 71 44\n429 86 39\n429 131 35\n429 136 2\n429 160 48\n429 195 34\n429 200 12\n429 220 25\n429 223 21\n429 302 28\n429 343 34\n429 360 13\n429 402 27\n429 414 17\n429 436 34\n429 502 47\n429 526 20\n429 528 7\n429 540 38\n429 545 6\n429 548 33\n429 569 13\n429 583 40\n429 627 35\n429 634 17\n429 653 45\n429 673 47\n429 676 21\n429 678 8\n429 686 29\n429 696 40\n429 737 18\n429 739 9\n429 751 0\n429 769 19\n429 779 34\n429 807 29\n429 818 34\n429 828 47\n429 835 5\n429 836 31\n429 837 38\n429 842 37\n429 909 42\n429 916 35\n429 979 29\n429 987 38\n429 992 15\n430 9 3\n430 19 0\n430 24 19\n430 57 39\n430 73 3\n430 77 17\n430 78 31\n430 130 13\n430 137 34\n430 231 1\n430 284 17\n430 307 35\n430 336 10\n430 345 20\n430 348 42\n430 363 43\n430 365 42\n430 404 11\n430 409 6\n430 420 37\n430 459 42\n430 469 34\n430 489 11\n430 503 25\n430 522 27\n430 561 27\n430 599 5\n430 605 33\n430 622 17\n430 637 15\n430 684 26\n430 690 -1\n430 691 41\n430 712 27\n430 741 48\n430 752 21\n430 770 17\n430 816 13\n430 817 9\n430 831 21\n430 838 8\n430 852 12\n430 874 50\n430 889 34\n430 927 25\n430 935 -2\n430 952 41\n430 975 22\n431 16 41\n431 45 47\n431 46 18\n431 73 19\n431 74 6\n431 89 47\n431 107 16\n431 142 9\n431 152 8\n431 164 37\n431 190 38\n431 223 23\n431 239 18\n431 246 -2\n431 267 44\n431 295 32\n431 303 25\n431 331 38\n431 367 39\n431 372 14\n431 385 -1\n431 401 37\n431 422 24\n431 447 40\n431 449 34\n431 453 19\n431 459 16\n431 477 14\n431 502 44\n431 505 45\n431 515 -1\n431 541 45\n431 546 21\n431 547 46\n431 582 9\n431 595 31\n431 598 50\n431 656 17\n431 658 20\n431 681 9\n431 702 35\n431 725 44\n431 737 17\n431 771 21\n431 795 12\n431 809 41\n431 814 29\n431 826 4\n431 848 6\n431 851 49\n431 861 16\n431 884 17\n431 893 -1\n431 900 13\n431 950 16\n431 951 47\n431 952 23\n431 964 41\n431 988 20\n432 5 47\n432 37 10\n432 48 10\n432 55 30\n432 61 29\n432 113 31\n432 156 25\n432 166 21\n432 234 23\n432 279 38\n432 297 23\n432 332 41\n432 348 11\n432 410 41\n432 426 5\n432 427 26\n432 433 22\n432 440 41\n432 445 3\n432 458 38\n432 503 14\n432 518 26\n432 537 50\n432 547 12\n432 562 9\n432 585 24\n432 592 27\n432 594 33\n432 605 37\n432 621 27\n432 633 27\n432 647 18\n432 671 46\n432 673 43\n432 686 30\n432 702 28\n432 704 26\n432 721 38\n432 804 11\n432 809 33\n432 843 7\n432 846 49\n432 900 -1\n432 907 22\n432 908 8\n432 911 18\n432 913 20\n432 917 44\n432 942 30\n433 49 38\n433 50 9\n433 54 36\n433 58 48\n433 92 21\n433 96 39\n433 118 24\n433 139 16\n433 164 20\n433 209 24\n433 214 23\n433 247 25\n433 248 32\n433 270 2\n433 272 32\n433 291 34\n433 295 8\n433 302 31\n433 333 43\n433 337 10\n433 367 38\n433 374 49\n433 376 49\n433 408 27\n433 410 50\n433 432 45\n433 459 15\n433 471 40\n433 473 16\n433 501 38\n433 510 12\n433 525 49\n433 533 5\n433 576 1\n433 580 4\n433 608 20\n433 618 1\n433 633 50\n433 659 48\n433 670 6\n433 692 41\n433 706 19\n433 742 47\n433 794 6\n433 803 35\n433 855 26\n433 878 30\n433 886 4\n433 903 20\n433 915 13\n433 932 32\n433 937 47\n433 953 19\n433 970 9\n433 980 33\n433 990 48\n434 19 35\n434 33 7\n434 39 6\n434 41 2\n434 47 4\n434 53 11\n434 62 21\n434 70 5\n434 86 8\n434 90 38\n434 131 0\n434 178 48\n434 213 3\n434 234 22\n434 268 43\n434 278 0\n434 283 18\n434 314 20\n434 319 19\n434 321 5\n434 333 45\n434 339 48\n434 350 41\n434 357 46\n434 379 40\n434 386 34\n434 489 6\n434 491 11\n434 501 34\n434 570 18\n434 586 24\n434 595 16\n434 604 24\n434 633 35\n434 649 32\n434 651 19\n434 655 38\n434 682 44\n434 708 -2\n434 735 30\n434 741 20\n434 743 44\n434 758 44\n434 794 10\n434 865 18\n434 876 27\n434 892 5\n434 893 32\n434 952 43\n434 968 45\n434 980 31\n435 29 6\n435 74 47\n435 92 16\n435 119 33\n435 140 37\n435 176 38\n435 197 20\n435 201 41\n435 227 13\n435 270 46\n435 279 47\n435 280 29\n435 297 47\n435 337 34\n435 338 22\n435 351 33\n435 381 45\n435 419 18\n435 427 5\n435 434 36\n435 465 45\n435 489 7\n435 503 15\n435 507 14\n435 577 31\n435 625 28\n435 626 11\n435 636 1\n435 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39 8\n439 66 42\n439 91 29\n439 97 9\n439 100 25\n439 105 4\n439 108 35\n439 120 9\n439 160 22\n439 203 13\n439 206 30\n439 211 47\n439 221 30\n439 274 43\n439 331 6\n439 335 17\n439 342 35\n439 387 18\n439 394 20\n439 396 29\n439 417 31\n439 421 48\n439 431 24\n439 436 17\n439 461 22\n439 462 40\n439 475 46\n439 480 3\n439 505 33\n439 508 8\n439 516 48\n439 532 17\n439 538 47\n439 552 19\n439 579 25\n439 613 29\n439 702 15\n439 712 33\n439 754 30\n439 769 3\n439 777 12\n439 786 5\n439 787 8\n439 812 28\n439 846 5\n439 868 28\n439 870 28\n439 873 46\n439 877 34\n439 961 34\n439 985 22\n439 992 39\n439 997 49\n440 33 36\n440 36 17\n440 40 24\n440 48 10\n440 86 47\n440 92 18\n440 133 8\n440 140 42\n440 154 38\n440 187 16\n440 193 40\n440 215 31\n440 236 33\n440 292 7\n440 314 48\n440 321 50\n440 329 30\n440 331 34\n440 337 20\n440 365 38\n440 366 1\n440 367 34\n440 397 21\n440 405 24\n440 414 9\n440 486 6\n440 493 35\n440 507 25\n440 508 33\n440 517 30\n440 523 30\n440 529 45\n440 542 24\n440 546 44\n440 550 48\n440 551 43\n440 553 42\n440 566 11\n440 582 8\n440 606 18\n440 611 44\n440 612 48\n440 651 35\n440 683 40\n440 703 32\n440 744 17\n440 776 9\n440 813 24\n440 881 7\n440 890 40\n440 930 10\n440 951 50\n440 967 3\n441 7 44\n441 168 37\n441 179 13\n441 261 21\n441 352 48\n441 365 41\n441 377 23\n441 384 4\n441 407 5\n441 427 10\n441 450 46\n441 470 1\n441 475 49\n441 477 6\n441 496 5\n441 500 36\n441 557 20\n441 599 25\n441 607 10\n441 623 37\n441 692 38\n441 698 0\n441 707 46\n441 714 37\n441 722 7\n441 744 7\n441 765 23\n441 766 40\n441 770 18\n441 796 26\n441 801 20\n441 830 9\n441 846 41\n441 929 28\n441 951 10\n441 964 37\n442 2 26\n442 29 11\n442 42 6\n442 48 11\n442 138 19\n442 221 31\n442 231 3\n442 291 31\n442 328 25\n442 334 30\n442 369 8\n442 407 4\n442 465 30\n442 508 20\n442 518 26\n442 527 5\n442 545 44\n442 551 48\n442 570 28\n442 579 47\n442 583 16\n442 603 1\n442 610 39\n442 652 45\n442 713 42\n442 724 43\n442 767 37\n442 768 17\n442 778 29\n442 782 31\n442 788 19\n442 790 47\n442 793 33\n442 813 27\n442 828 44\n442 852 9\n442 869 24\n442 877 9\n442 898 13\n442 985 9\n442 998 48\n443 21 43\n443 56 30\n443 75 1\n443 78 44\n443 90 40\n443 113 30\n443 120 15\n443 127 22\n443 234 34\n443 279 19\n443 290 29\n443 300 34\n443 302 43\n443 303 7\n443 320 44\n443 329 37\n443 361 21\n443 366 22\n443 373 37\n443 374 6\n443 414 32\n443 433 17\n443 436 10\n443 464 5\n443 468 22\n443 472 10\n443 483 20\n443 495 40\n443 531 18\n443 535 43\n443 548 37\n443 595 24\n443 597 3\n443 614 21\n443 673 13\n443 698 50\n443 729 31\n443 744 31\n443 774 9\n443 779 23\n443 794 22\n443 797 17\n443 850 31\n443 887 9\n443 899 9\n443 900 46\n443 920 45\n443 955 48\n444 8 47\n444 19 37\n444 23 32\n444 63 8\n444 129 11\n444 131 3\n444 157 34\n444 202 2\n444 246 20\n444 269 18\n444 285 16\n444 288 0\n444 297 50\n444 327 23\n444 334 49\n444 371 37\n444 393 26\n444 396 18\n444 402 4\n444 433 50\n444 434 32\n444 446 37\n444 453 17\n444 466 40\n444 512 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28\n447 798 28\n447 802 -1\n447 841 9\n447 878 23\n447 914 24\n447 932 23\n447 989 47\n447 993 32\n447 996 37\n447 999 33\n448 7 23\n448 10 29\n448 34 47\n448 43 25\n448 57 23\n448 58 4\n448 60 9\n448 65 3\n448 70 25\n448 87 12\n448 116 17\n448 138 3\n448 157 14\n448 168 38\n448 184 5\n448 216 34\n448 218 9\n448 223 29\n448 249 24\n448 281 28\n448 322 9\n448 347 28\n448 427 34\n448 432 21\n448 479 44\n448 486 50\n448 493 11\n448 496 30\n448 505 13\n448 527 6\n448 532 5\n448 533 19\n448 546 12\n448 602 23\n448 642 33\n448 690 9\n448 700 33\n448 747 32\n448 761 10\n448 769 2\n448 776 29\n448 807 21\n448 817 29\n448 837 1\n448 855 23\n448 913 -1\n448 945 40\n448 954 42\n449 10 40\n449 26 33\n449 48 6\n449 52 4\n449 53 -2\n449 75 35\n449 95 34\n449 170 28\n449 177 36\n449 223 35\n449 229 42\n449 232 7\n449 241 17\n449 279 30\n449 305 24\n449 316 37\n449 336 40\n449 340 10\n449 344 20\n449 352 7\n449 392 9\n449 410 9\n449 416 7\n449 489 29\n449 490 34\n449 517 16\n449 530 23\n449 602 37\n449 606 10\n449 631 45\n449 643 28\n449 663 41\n449 706 11\n449 709 15\n449 736 25\n449 744 38\n449 746 25\n449 747 31\n449 751 7\n449 754 45\n449 759 40\n449 774 33\n449 781 0\n449 788 1\n449 797 35\n449 828 -2\n449 859 14\n449 893 18\n449 902 46\n449 926 24\n449 947 7\n449 950 -2\n449 978 4\n449 993 26\n450 39 43\n450 44 11\n450 55 46\n450 72 49\n450 91 12\n450 95 10\n450 112 34\n450 172 16\n450 210 17\n450 217 -2\n450 224 34\n450 254 33\n450 281 6\n450 293 47\n450 301 35\n450 307 38\n450 315 39\n450 335 34\n450 361 1\n450 363 10\n450 371 40\n450 378 30\n450 381 8\n450 414 43\n450 475 18\n450 494 18\n450 521 5\n450 551 0\n450 580 16\n450 641 2\n450 664 45\n450 665 31\n450 699 5\n450 712 31\n450 749 7\n450 759 7\n450 760 48\n450 810 15\n450 844 11\n450 873 6\n450 922 -2\n450 923 11\n450 926 5\n450 932 24\n450 952 13\n450 971 0\n450 980 17\n450 990 34\n450 997 29\n451 4 36\n451 8 16\n451 27 24\n451 55 13\n451 78 23\n451 122 23\n451 174 2\n451 215 23\n451 233 42\n451 279 42\n451 307 37\n451 310 34\n451 345 15\n451 375 1\n451 377 38\n451 391 28\n451 418 49\n451 489 12\n451 495 38\n451 528 25\n451 535 4\n451 542 33\n451 569 4\n451 590 10\n451 627 42\n451 644 21\n451 646 24\n451 647 4\n451 675 6\n451 685 36\n451 713 11\n451 724 13\n451 733 22\n451 744 23\n451 759 41\n451 791 5\n451 805 34\n451 809 17\n451 839 1\n451 855 15\n451 865 1\n451 891 23\n451 896 46\n451 954 10\n451 959 34\n451 963 24\n452 4 49\n452 7 7\n452 47 36\n452 105 33\n452 115 30\n452 119 19\n452 134 28\n452 148 17\n452 157 43\n452 167 1\n452 292 45\n452 309 41\n452 342 39\n452 369 16\n452 398 28\n452 420 48\n452 460 14\n452 514 32\n452 523 33\n452 576 28\n452 590 43\n452 592 42\n452 602 13\n452 606 18\n452 608 28\n452 631 39\n452 652 12\n452 658 36\n452 659 4\n452 664 32\n452 684 9\n452 687 30\n452 693 31\n452 737 38\n452 742 20\n452 770 -1\n452 783 11\n452 804 28\n452 829 27\n452 835 3\n452 840 50\n452 841 42\n452 906 43\n452 911 0\n452 938 23\n452 943 42\n452 952 44\n452 955 36\n452 959 42\n452 987 20\n452 995 21\n452 999 27\n452 1000 1\n453 7 39\n453 14 31\n453 49 33\n453 86 30\n453 93 31\n453 110 28\n453 116 11\n453 119 37\n453 129 25\n453 149 49\n453 177 33\n453 180 41\n453 191 1\n453 210 8\n453 227 28\n453 231 39\n453 243 11\n453 258 8\n453 259 39\n453 269 26\n453 278 -1\n453 300 18\n453 302 42\n453 304 40\n453 317 26\n453 331 1\n453 366 29\n453 375 35\n453 380 36\n453 384 0\n453 423 5\n453 434 50\n453 437 27\n453 494 8\n453 497 20\n453 517 40\n453 521 39\n453 529 14\n453 594 47\n453 604 28\n453 639 3\n453 655 39\n453 756 43\n453 770 14\n453 786 6\n453 809 49\n453 826 0\n453 844 48\n453 876 47\n453 909 19\n453 924 27\n453 936 38\n453 938 13\n453 943 34\n453 987 32\n454 7 17\n454 23 32\n454 49 17\n454 97 42\n454 103 32\n454 186 18\n454 193 50\n454 195 42\n454 233 41\n454 239 26\n454 243 13\n454 260 19\n454 280 12\n454 288 43\n454 316 25\n454 319 27\n454 347 41\n454 375 33\n454 384 17\n454 400 46\n454 445 49\n454 476 32\n454 508 36\n454 529 6\n454 548 24\n454 553 22\n454 562 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15\n456 490 34\n456 498 4\n456 535 40\n456 560 8\n456 567 48\n456 608 35\n456 615 31\n456 619 15\n456 624 33\n456 661 40\n456 687 17\n456 751 10\n456 785 -2\n456 791 14\n456 799 45\n456 804 25\n456 823 8\n456 843 37\n456 926 31\n456 935 28\n456 944 39\n456 954 37\n456 965 37\n456 974 33\n456 979 46\n456 995 -1\n457 13 40\n457 30 16\n457 48 34\n457 64 45\n457 68 44\n457 70 16\n457 91 17\n457 98 48\n457 111 4\n457 132 46\n457 134 -2\n457 180 -2\n457 206 46\n457 216 28\n457 221 27\n457 245 28\n457 279 19\n457 331 1\n457 338 13\n457 339 26\n457 354 12\n457 365 9\n457 377 42\n457 382 28\n457 399 36\n457 417 40\n457 433 7\n457 460 49\n457 502 -1\n457 514 17\n457 534 13\n457 562 8\n457 609 13\n457 631 46\n457 640 41\n457 669 18\n457 671 8\n457 674 39\n457 683 24\n457 718 26\n457 738 21\n457 749 21\n457 767 34\n457 826 32\n457 837 48\n457 860 16\n457 868 42\n457 915 8\n457 938 6\n457 944 28\n457 965 31\n457 969 20\n457 981 46\n458 45 7\n458 76 38\n458 145 25\n458 153 42\n458 253 41\n458 258 20\n458 276 25\n458 307 50\n458 351 18\n458 358 50\n458 368 38\n458 414 15\n458 428 36\n458 433 13\n458 450 39\n458 452 43\n458 466 13\n458 489 46\n458 517 7\n458 525 47\n458 566 27\n458 577 3\n458 581 -2\n458 600 17\n458 607 27\n458 616 24\n458 649 5\n458 654 9\n458 665 -2\n458 681 26\n458 683 11\n458 710 35\n458 722 32\n458 731 40\n458 740 19\n458 753 26\n458 782 16\n458 836 27\n458 887 26\n458 901 50\n458 912 32\n458 924 37\n458 939 23\n458 946 9\n458 951 1\n458 972 32\n459 26 44\n459 27 5\n459 41 24\n459 75 10\n459 79 14\n459 97 50\n459 114 32\n459 127 42\n459 153 7\n459 164 8\n459 188 45\n459 217 49\n459 267 25\n459 273 21\n459 299 24\n459 309 16\n459 344 7\n459 388 43\n459 394 23\n459 398 19\n459 399 13\n459 420 29\n459 463 43\n459 469 33\n459 516 3\n459 525 25\n459 527 0\n459 532 43\n459 536 47\n459 544 10\n459 557 43\n459 570 20\n459 573 38\n459 596 23\n459 599 31\n459 600 43\n459 616 3\n459 625 15\n459 641 32\n459 695 49\n459 725 15\n459 727 30\n459 748 46\n459 760 15\n459 799 35\n459 831 16\n459 861 43\n459 868 12\n459 871 21\n459 902 0\n459 953 28\n460 13 17\n460 17 35\n460 42 0\n460 88 16\n460 131 36\n460 162 47\n460 178 44\n460 179 30\n460 208 29\n460 210 34\n460 217 19\n460 233 4\n460 234 38\n460 244 7\n460 292 5\n460 300 18\n460 307 45\n460 365 16\n460 407 30\n460 451 2\n460 462 -2\n460 533 43\n460 546 26\n460 552 28\n460 555 19\n460 583 37\n460 599 16\n460 603 15\n460 674 15\n460 720 3\n460 738 25\n460 767 28\n460 778 18\n460 816 23\n460 825 6\n460 850 39\n460 873 14\n460 874 38\n460 910 25\n460 963 -1\n460 971 22\n461 30 25\n461 82 0\n461 98 28\n461 104 35\n461 117 28\n461 216 -2\n461 237 25\n461 244 -1\n461 256 2\n461 258 6\n461 298 24\n461 345 -2\n461 360 26\n461 406 24\n461 410 26\n461 436 44\n461 485 42\n461 496 5\n461 525 41\n461 538 11\n461 573 35\n461 575 6\n461 577 6\n461 641 39\n461 648 0\n461 650 26\n461 668 33\n461 695 7\n461 721 33\n461 743 45\n461 755 8\n461 764 6\n461 806 42\n461 809 26\n461 855 50\n461 874 43\n461 897 2\n461 912 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9\n513 140 50\n513 143 13\n513 147 27\n513 244 21\n513 246 28\n513 250 11\n513 258 25\n513 259 13\n513 293 7\n513 317 2\n513 342 39\n513 374 22\n513 375 28\n513 380 48\n513 393 50\n513 400 36\n513 402 17\n513 406 10\n513 421 1\n513 434 23\n513 437 11\n513 458 18\n513 480 15\n513 544 -2\n513 553 42\n513 555 3\n513 568 35\n513 582 36\n513 590 40\n513 620 16\n513 646 18\n513 655 40\n513 658 21\n513 731 14\n513 754 41\n513 762 24\n513 799 43\n513 807 -2\n513 832 24\n513 838 42\n513 845 43\n513 854 46\n513 874 3\n513 883 4\n513 888 40\n513 908 36\n513 965 40\n513 982 33\n513 999 43\n514 9 46\n514 13 33\n514 58 37\n514 71 45\n514 79 17\n514 95 28\n514 96 47\n514 116 27\n514 162 50\n514 185 17\n514 196 14\n514 200 17\n514 202 6\n514 207 22\n514 260 14\n514 275 38\n514 305 13\n514 326 36\n514 330 31\n514 358 38\n514 387 37\n514 447 34\n514 476 13\n514 522 41\n514 526 27\n514 535 50\n514 536 38\n514 539 34\n514 542 11\n514 543 20\n514 555 26\n514 578 4\n514 592 50\n514 609 35\n514 625 18\n514 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341 12\n518 353 42\n518 364 46\n518 377 27\n518 394 1\n518 471 41\n518 528 45\n518 561 40\n518 601 20\n518 614 16\n518 615 12\n518 638 28\n518 670 29\n518 701 43\n518 719 10\n518 745 15\n518 753 9\n518 806 9\n518 810 39\n518 831 10\n518 898 28\n518 932 43\n518 951 26\n519 6 0\n519 16 48\n519 21 16\n519 40 35\n519 59 12\n519 68 44\n519 97 45\n519 103 4\n519 119 -2\n519 122 37\n519 175 13\n519 180 15\n519 186 22\n519 191 49\n519 230 41\n519 235 24\n519 241 35\n519 272 12\n519 363 35\n519 367 45\n519 373 49\n519 374 1\n519 383 0\n519 405 50\n519 411 11\n519 413 0\n519 436 10\n519 442 39\n519 448 10\n519 449 26\n519 518 11\n519 564 28\n519 569 43\n519 570 36\n519 596 47\n519 598 44\n519 609 16\n519 624 28\n519 658 25\n519 668 -2\n519 670 4\n519 679 18\n519 686 41\n519 708 10\n519 729 45\n519 731 42\n519 747 -1\n519 750 2\n519 756 49\n519 763 49\n519 773 3\n519 784 3\n519 799 38\n519 812 47\n519 816 -1\n519 819 5\n519 878 49\n519 887 30\n519 930 37\n519 983 42\n519 1000 6\n520 20 22\n520 23 41\n520 72 11\n520 82 30\n520 97 32\n520 101 6\n520 125 44\n520 154 16\n520 172 4\n520 181 17\n520 244 40\n520 292 15\n520 304 33\n520 331 1\n520 365 4\n520 369 18\n520 375 18\n520 381 34\n520 423 33\n520 435 18\n520 458 12\n520 463 35\n520 472 42\n520 481 44\n520 489 27\n520 513 21\n520 543 7\n520 563 4\n520 582 49\n520 597 1\n520 613 5\n520 617 41\n520 626 8\n520 634 48\n520 635 39\n520 656 24\n520 678 19\n520 695 25\n520 708 -2\n520 712 -1\n520 732 44\n520 756 49\n520 759 24\n520 815 25\n520 819 41\n520 837 4\n520 865 42\n520 887 25\n520 927 16\n520 976 47\n521 7 16\n521 11 50\n521 33 42\n521 40 11\n521 68 6\n521 101 21\n521 118 44\n521 151 50\n521 169 14\n521 220 25\n521 227 21\n521 272 31\n521 277 23\n521 314 38\n521 327 13\n521 340 18\n521 365 22\n521 368 8\n521 371 22\n521 373 49\n521 409 26\n521 412 34\n521 434 9\n521 461 45\n521 462 41\n521 502 12\n521 514 44\n521 555 1\n521 561 16\n521 566 30\n521 587 13\n521 588 30\n521 600 34\n521 604 38\n521 606 15\n521 608 46\n521 621 23\n521 631 19\n521 677 48\n521 686 -1\n521 687 36\n521 701 29\n521 707 24\n521 711 18\n521 715 17\n521 738 7\n521 752 34\n521 771 41\n521 818 49\n521 838 36\n521 848 12\n521 876 27\n521 896 15\n521 977 0\n521 979 12\n521 993 28\n521 998 41\n521 999 42\n522 16 9\n522 22 8\n522 23 47\n522 24 18\n522 34 23\n522 65 16\n522 92 35\n522 111 41\n522 135 40\n522 180 26\n522 205 45\n522 223 5\n522 239 41\n522 243 17\n522 255 16\n522 265 20\n522 326 17\n522 333 9\n522 339 13\n522 361 34\n522 365 47\n522 384 23\n522 397 1\n522 415 17\n522 425 15\n522 494 44\n522 536 35\n522 538 20\n522 550 -2\n522 564 42\n522 566 45\n522 595 46\n522 617 42\n522 619 17\n522 624 45\n522 663 10\n522 689 10\n522 696 10\n522 732 46\n522 778 42\n522 801 25\n522 887 25\n522 905 34\n522 913 46\n522 923 10\n522 928 26\n522 939 40\n522 999 35\n523 29 26\n523 39 35\n523 74 18\n523 90 7\n523 102 -2\n523 110 40\n523 152 35\n523 155 32\n523 189 19\n523 239 20\n523 258 27\n523 265 1\n523 278 47\n523 285 24\n523 290 17\n523 291 37\n523 292 13\n523 301 18\n523 308 3\n523 325 25\n523 328 31\n523 331 44\n523 341 6\n523 346 6\n523 364 44\n523 400 32\n523 402 -1\n523 407 37\n523 431 4\n523 456 46\n523 461 42\n523 466 37\n523 475 9\n523 478 13\n523 485 49\n523 526 47\n523 551 19\n523 564 40\n523 601 1\n523 609 25\n523 634 3\n523 674 44\n523 677 32\n523 701 36\n523 707 6\n523 710 42\n523 718 19\n523 763 21\n523 776 36\n523 781 34\n523 808 33\n523 814 8\n523 832 21\n523 851 14\n523 865 12\n523 866 21\n523 914 -1\n523 942 33\n523 959 23\n523 966 27\n523 969 48\n523 987 43\n523 990 32\n523 992 37\n523 993 0\n524 9 48\n524 17 42\n524 54 4\n524 61 47\n524 74 19\n524 107 39\n524 148 39\n524 167 41\n524 175 38\n524 195 11\n524 209 47\n524 254 11\n524 288 7\n524 301 20\n524 303 8\n524 311 27\n524 325 48\n524 332 35\n524 334 23\n524 336 21\n524 391 48\n524 418 19\n524 423 13\n524 435 42\n524 459 30\n524 461 23\n524 485 38\n524 512 18\n524 513 7\n524 514 50\n524 521 36\n524 551 18\n524 559 3\n524 561 42\n524 565 1\n524 578 -1\n524 612 44\n524 620 15\n524 631 26\n524 659 9\n524 684 23\n524 685 38\n524 690 43\n524 709 27\n524 712 41\n524 731 46\n524 733 27\n524 746 45\n524 766 13\n524 818 32\n524 854 46\n524 891 40\n524 928 15\n524 930 16\n524 943 20\n524 958 39\n524 960 27\n524 973 6\n524 974 12\n525 8 37\n525 17 25\n525 29 43\n525 63 23\n525 107 40\n525 122 34\n525 217 50\n525 322 24\n525 337 41\n525 343 8\n525 347 43\n525 357 26\n525 431 13\n525 433 19\n525 434 43\n525 458 -1\n525 467 41\n525 469 43\n525 475 1\n525 504 6\n525 527 10\n525 557 46\n525 637 45\n525 686 40\n525 695 34\n525 773 3\n525 790 37\n525 801 18\n525 873 2\n525 885 2\n525 927 31\n525 944 32\n525 949 23\n525 988 9\n526 7 38\n526 36 17\n526 38 8\n526 41 21\n526 55 42\n526 94 39\n526 121 16\n526 204 6\n526 208 12\n526 230 28\n526 256 23\n526 271 16\n526 279 24\n526 288 49\n526 306 8\n526 308 3\n526 355 37\n526 356 4\n526 357 27\n526 420 23\n526 437 15\n526 499 48\n526 503 14\n526 517 11\n526 553 -1\n526 589 -1\n526 610 6\n526 615 40\n526 680 6\n526 690 7\n526 699 7\n526 701 31\n526 704 32\n526 755 44\n526 789 -1\n526 840 -1\n526 856 40\n526 857 42\n526 862 17\n526 873 9\n526 874 0\n526 885 43\n526 890 2\n526 913 36\n526 934 0\n526 941 23\n526 947 44\n527 15 47\n527 50 9\n527 55 28\n527 63 40\n527 96 10\n527 116 14\n527 132 41\n527 140 11\n527 143 2\n527 174 38\n527 176 49\n527 196 23\n527 218 24\n527 266 10\n527 349 32\n527 367 36\n527 393 39\n527 395 23\n527 420 47\n527 431 19\n527 451 23\n527 471 13\n527 517 2\n527 522 20\n527 538 7\n527 543 -1\n527 548 0\n527 552 7\n527 581 27\n527 585 31\n527 594 10\n527 613 0\n527 619 4\n527 638 16\n527 653 49\n527 659 9\n527 691 27\n527 692 25\n527 697 26\n527 728 26\n527 732 47\n527 761 0\n527 775 24\n527 808 16\n527 820 29\n527 828 26\n527 832 -2\n527 843 21\n527 864 22\n527 866 49\n527 893 -2\n527 895 0\n527 902 28\n527 980 17\n527 981 33\n527 987 30\n528 16 8\n528 63 27\n528 90 42\n528 92 21\n528 110 5\n528 121 1\n528 176 -1\n528 199 45\n528 301 12\n528 304 2\n528 329 10\n528 338 48\n528 341 3\n528 347 7\n528 357 27\n528 384 39\n528 433 27\n528 486 47\n528 519 34\n528 549 6\n528 568 17\n528 574 17\n528 619 17\n528 624 3\n528 649 41\n528 661 28\n528 662 27\n528 727 47\n528 757 1\n528 787 41\n528 820 7\n528 828 25\n528 835 13\n528 839 26\n528 840 28\n528 863 -1\n528 864 3\n528 893 44\n528 955 2\n528 973 32\n528 974 49\n528 986 18\n529 16 47\n529 33 46\n529 54 14\n529 59 15\n529 84 24\n529 96 9\n529 153 7\n529 158 30\n529 208 48\n529 237 38\n529 273 35\n529 278 35\n529 307 38\n529 315 19\n529 318 10\n529 380 44\n529 385 22\n529 454 49\n529 477 9\n529 491 6\n529 522 8\n529 526 49\n529 531 47\n529 550 21\n529 555 50\n529 562 7\n529 574 29\n529 666 7\n529 683 27\n529 686 39\n529 710 41\n529 742 11\n529 774 33\n529 818 38\n529 827 39\n529 851 33\n529 865 48\n529 903 11\n529 907 13\n529 935 21\n529 941 27\n529 954 42\n529 955 44\n529 960 3\n529 997 27\n530 61 6\n530 100 26\n530 159 25\n530 161 38\n530 183 41\n530 213 42\n530 226 21\n530 232 2\n530 236 37\n530 244 27\n530 265 43\n530 283 36\n530 299 3\n530 326 2\n530 344 32\n530 347 4\n530 391 47\n530 409 5\n530 416 38\n530 417 40\n530 436 43\n530 443 39\n530 451 8\n530 458 8\n530 468 5\n530 500 30\n530 508 33\n530 561 47\n530 580 42\n530 597 34\n530 602 45\n530 617 14\n530 652 31\n530 665 5\n530 670 0\n530 686 -1\n530 692 41\n530 726 34\n530 730 9\n530 775 4\n530 784 45\n530 788 13\n530 818 48\n530 832 12\n530 846 48\n530 857 45\n530 858 10\n530 861 32\n530 869 47\n530 890 22\n530 891 -1\n530 895 13\n530 910 22\n530 927 50\n530 964 50\n530 978 8\n531 23 24\n531 24 24\n531 99 31\n531 101 40\n531 106 3\n531 171 7\n531 172 36\n531 204 40\n531 228 42\n531 300 39\n531 329 1\n531 338 12\n531 342 2\n531 353 19\n531 385 34\n531 408 20\n531 433 -1\n531 434 4\n531 450 30\n531 480 36\n531 503 19\n531 510 19\n531 539 45\n531 602 46\n531 609 9\n531 630 34\n531 662 15\n531 704 28\n531 718 7\n531 745 9\n531 781 17\n531 835 33\n531 849 17\n531 856 4\n531 917 3\n531 936 31\n531 945 41\n531 947 30\n531 963 26\n531 989 39\n531 999 28\n532 3 19\n532 50 40\n532 51 5\n532 52 21\n532 53 11\n532 66 50\n532 99 48\n532 123 7\n532 137 13\n532 151 27\n532 174 0\n532 233 37\n532 255 11\n532 258 45\n532 262 27\n532 266 40\n532 291 9\n532 292 50\n532 295 0\n532 307 8\n532 312 0\n532 354 48\n532 371 50\n532 411 24\n532 441 49\n532 457 42\n532 481 14\n532 485 38\n532 502 0\n532 503 13\n532 558 38\n532 568 18\n532 572 36\n532 612 22\n532 613 24\n532 619 15\n532 621 26\n532 624 14\n532 641 45\n532 643 16\n532 655 33\n532 665 49\n532 671 29\n532 694 22\n532 702 4\n532 710 17\n532 722 37\n532 730 22\n532 778 36\n532 784 9\n532 863 46\n532 864 2\n532 876 38\n532 886 35\n532 931 15\n532 935 1\n532 939 12\n532 983 25\n533 46 32\n533 58 1\n533 70 39\n533 84 49\n533 104 31\n533 138 16\n533 141 36\n533 152 50\n533 159 15\n533 173 34\n533 178 3\n533 185 40\n533 227 25\n533 236 23\n533 254 43\n533 267 25\n533 390 49\n533 421 11\n533 426 -1\n533 468 42\n533 483 20\n533 496 28\n533 542 29\n533 564 18\n533 619 40\n533 621 14\n533 639 7\n533 652 31\n533 669 4\n533 687 40\n533 696 1\n533 724 26\n533 726 24\n533 732 15\n533 750 22\n533 766 17\n533 802 47\n533 814 27\n533 823 18\n533 826 3\n533 828 12\n533 837 18\n533 845 3\n533 880 11\n533 904 38\n533 926 44\n533 932 34\n533 967 47\n533 995 50\n534 66 31\n534 74 42\n534 99 14\n534 118 33\n534 122 36\n534 172 27\n534 193 32\n534 216 24\n534 272 44\n534 318 11\n534 324 30\n534 459 15\n534 461 17\n534 491 16\n534 505 13\n534 513 9\n534 514 19\n534 516 21\n534 525 27\n534 529 4\n534 563 23\n534 593 38\n534 609 28\n534 613 19\n534 682 48\n534 695 11\n534 701 12\n534 703 21\n534 705 1\n534 739 -2\n534 777 34\n534 794 1\n534 803 26\n534 804 26\n534 836 29\n534 860 39\n534 890 2\n534 917 43\n534 929 10\n534 949 33\n534 954 49\n534 960 33\n534 961 1\n535 5 27\n535 23 30\n535 33 20\n535 37 46\n535 80 17\n535 82 47\n535 85 25\n535 118 39\n535 135 7\n535 138 8\n535 142 10\n535 198 38\n535 240 26\n535 265 50\n535 268 36\n535 282 9\n535 297 49\n535 311 20\n535 322 27\n535 329 23\n535 351 27\n535 393 17\n535 405 13\n535 516 43\n535 568 9\n535 572 36\n535 587 30\n535 610 21\n535 617 10\n535 669 17\n535 690 35\n535 707 12\n535 724 41\n535 727 35\n535 754 45\n535 764 42\n535 792 10\n535 795 8\n535 800 8\n535 856 31\n535 868 39\n535 899 6\n535 914 30\n535 925 20\n535 939 36\n535 960 39\n535 963 15\n536 1 25\n536 9 21\n536 14 19\n536 38 8\n536 59 36\n536 63 36\n536 82 40\n536 161 14\n536 223 45\n536 225 43\n536 237 49\n536 239 34\n536 244 50\n536 255 18\n536 292 4\n536 309 8\n536 329 27\n536 363 33\n536 382 19\n536 393 27\n536 460 4\n536 463 10\n536 471 11\n536 474 7\n536 496 24\n536 513 35\n536 546 13\n536 567 26\n536 600 21\n536 606 45\n536 614 26\n536 627 8\n536 646 8\n536 668 40\n536 669 44\n536 683 0\n536 684 5\n536 703 50\n536 733 49\n536 734 37\n536 778 39\n536 786 37\n536 800 40\n536 829 5\n536 845 44\n536 850 48\n536 876 22\n536 881 34\n536 891 36\n536 894 42\n536 897 41\n536 905 25\n536 948 20\n537 10 25\n537 24 13\n537 32 46\n537 38 18\n537 42 8\n537 76 37\n537 127 3\n537 135 48\n537 146 15\n537 174 3\n537 181 31\n537 217 19\n537 227 8\n537 254 48\n537 293 25\n537 322 49\n537 327 42\n537 341 11\n537 389 39\n537 393 14\n537 398 6\n537 419 14\n537 422 15\n537 424 6\n537 441 47\n537 454 12\n537 465 9\n537 471 44\n537 486 -1\n537 488 44\n537 495 6\n537 499 23\n537 507 5\n537 526 27\n537 561 30\n537 568 2\n537 571 25\n537 624 28\n537 628 10\n537 642 22\n537 644 18\n537 731 43\n537 749 48\n537 782 3\n537 825 19\n537 864 48\n537 932 39\n537 943 0\n537 997 34\n538 11 22\n538 41 39\n538 57 21\n538 58 35\n538 63 28\n538 106 46\n538 127 4\n538 128 12\n538 131 28\n538 143 3\n538 154 43\n538 181 19\n538 198 13\n538 205 28\n538 314 13\n538 334 40\n538 351 10\n538 353 6\n538 355 43\n538 362 17\n538 371 39\n538 378 6\n538 407 47\n538 428 9\n538 429 39\n538 468 21\n538 518 41\n538 540 37\n538 553 28\n538 557 35\n538 594 42\n538 611 39\n538 616 9\n538 679 10\n538 726 50\n538 749 3\n538 763 44\n538 770 46\n538 775 15\n538 811 12\n538 877 44\n538 917 16\n538 926 32\n538 928 29\n538 945 34\n539 9 13\n539 22 39\n539 32 49\n539 64 30\n539 69 45\n539 150 42\n539 177 29\n539 188 40\n539 195 47\n539 196 29\n539 236 37\n539 247 14\n539 260 39\n539 329 42\n539 396 23\n539 405 2\n539 423 41\n539 433 23\n539 449 9\n539 454 32\n539 528 45\n539 546 0\n539 550 4\n539 563 38\n539 580 0\n539 600 29\n539 618 16\n539 633 43\n539 670 24\n539 745 44\n539 749 36\n539 757 21\n539 793 40\n539 819 6\n539 842 -1\n539 858 19\n539 907 31\n539 910 42\n539 915 18\n539 942 32\n539 991 33\n540 1 44\n540 14 39\n540 17 48\n540 96 40\n540 145 4\n540 148 5\n540 165 25\n540 183 12\n540 208 47\n540 216 4\n540 235 17\n540 239 7\n540 315 36\n540 320 36\n540 355 28\n540 378 46\n540 412 4\n540 417 20\n540 436 10\n540 483 16\n540 499 4\n540 504 43\n540 532 2\n540 572 36\n540 580 6\n540 622 36\n540 625 18\n540 648 46\n540 668 23\n540 681 4\n540 683 34\n540 688 16\n540 702 33\n540 718 16\n540 741 6\n540 797 26\n540 802 4\n540 803 6\n540 816 -1\n540 820 27\n540 854 0\n540 856 15\n540 861 27\n540 869 17\n540 872 1\n540 884 45\n540 896 0\n540 932 4\n540 998 18\n541 23 42\n541 72 10\n541 89 45\n541 157 27\n541 162 27\n541 169 33\n541 199 30\n541 220 33\n541 241 35\n541 303 34\n541 342 24\n541 358 8\n541 362 6\n541 417 29\n541 448 31\n541 471 44\n541 496 39\n541 529 17\n541 532 46\n541 533 44\n541 559 13\n541 611 42\n541 613 42\n541 644 2\n541 656 45\n541 661 7\n541 672 0\n541 705 5\n541 755 19\n541 760 40\n541 767 1\n541 775 3\n541 780 18\n541 814 33\n541 818 45\n541 862 33\n541 864 42\n541 875 44\n541 908 29\n541 911 28\n541 925 4\n541 940 2\n541 949 13\n541 956 44\n541 966 4\n541 976 41\n542 8 32\n542 11 23\n542 12 8\n542 27 12\n542 44 40\n542 50 43\n542 77 12\n542 78 32\n542 101 30\n542 122 3\n542 130 44\n542 161 20\n542 163 45\n542 176 46\n542 188 15\n542 207 7\n542 216 43\n542 227 15\n542 241 38\n542 244 16\n542 255 34\n542 311 8\n542 319 43\n542 330 17\n542 364 23\n542 365 45\n542 366 41\n542 399 33\n542 415 33\n542 424 38\n542 434 21\n542 447 26\n542 448 9\n542 476 50\n542 517 6\n542 553 19\n542 575 13\n542 685 40\n542 691 50\n542 706 31\n542 722 2\n542 734 8\n542 769 42\n542 773 46\n542 788 33\n542 806 8\n542 816 34\n542 851 34\n542 890 38\n542 913 45\n542 925 26\n542 962 3\n543 24 50\n543 27 3\n543 46 44\n543 53 10\n543 79 18\n543 87 17\n543 92 34\n543 170 20\n543 187 20\n543 195 2\n543 199 25\n543 282 13\n543 290 44\n543 316 19\n543 330 47\n543 353 19\n543 371 35\n543 374 45\n543 380 22\n543 383 39\n543 385 43\n543 396 36\n543 413 20\n543 448 16\n543 454 33\n543 476 19\n543 547 39\n543 555 37\n543 563 -1\n543 579 24\n543 643 46\n543 663 30\n543 693 -2\n543 704 48\n543 738 35\n543 752 37\n543 772 19\n543 773 1\n543 794 24\n543 833 29\n543 853 3\n543 858 49\n543 862 4\n543 890 40\n543 896 34\n543 969 3\n543 979 30\n543 1000 12\n544 80 50\n544 93 27\n544 101 39\n544 166 30\n544 193 42\n544 200 14\n544 209 48\n544 210 43\n544 216 31\n544 259 42\n544 261 0\n544 296 -1\n544 300 35\n544 362 4\n544 404 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7\n654 526 45\n654 537 16\n654 545 30\n654 555 14\n654 556 22\n654 587 5\n654 592 26\n654 601 31\n654 621 35\n654 630 36\n654 652 26\n654 682 20\n654 689 21\n654 690 9\n654 708 3\n654 715 6\n654 743 4\n654 759 9\n654 761 1\n654 772 37\n654 775 17\n654 801 9\n654 843 3\n654 859 8\n654 864 41\n654 878 22\n654 881 25\n654 886 7\n654 888 34\n654 920 31\n654 921 12\n654 925 15\n654 936 -2\n654 951 17\n654 961 16\n655 10 44\n655 35 11\n655 37 23\n655 48 47\n655 71 2\n655 103 7\n655 124 9\n655 146 24\n655 167 42\n655 208 5\n655 210 18\n655 224 45\n655 232 22\n655 236 13\n655 257 15\n655 266 5\n655 271 42\n655 284 18\n655 287 16\n655 314 23\n655 394 35\n655 396 41\n655 414 49\n655 418 39\n655 439 47\n655 455 5\n655 485 -1\n655 520 12\n655 530 43\n655 539 8\n655 542 32\n655 551 16\n655 567 12\n655 590 10\n655 613 31\n655 634 33\n655 639 31\n655 673 24\n655 691 3\n655 701 0\n655 715 28\n655 774 22\n655 792 25\n655 809 40\n655 813 3\n655 818 27\n655 823 8\n655 824 22\n655 830 40\n655 863 6\n655 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213 37\n705 215 39\n705 218 24\n705 219 44\n705 255 28\n705 296 29\n705 323 37\n705 357 28\n705 412 31\n705 429 5\n705 477 10\n705 490 23\n705 493 14\n705 593 8\n705 607 -1\n705 661 42\n705 665 31\n705 670 20\n705 683 19\n705 689 31\n705 708 24\n705 726 32\n705 738 40\n705 775 31\n705 788 7\n705 808 0\n705 818 3\n705 849 13\n705 858 7\n705 860 34\n705 878 38\n705 902 4\n705 910 14\n705 933 1\n705 950 12\n705 952 43\n705 986 13\n706 9 18\n706 21 26\n706 37 29\n706 98 34\n706 151 6\n706 157 36\n706 163 8\n706 179 21\n706 181 15\n706 189 5\n706 239 26\n706 251 24\n706 260 47\n706 284 21\n706 301 40\n706 305 28\n706 340 31\n706 347 4\n706 390 3\n706 405 40\n706 473 31\n706 521 50\n706 526 37\n706 531 2\n706 585 5\n706 590 1\n706 634 15\n706 650 47\n706 653 24\n706 666 21\n706 679 -1\n706 707 6\n706 724 30\n706 749 3\n706 811 11\n706 844 46\n706 958 40\n707 27 30\n707 44 35\n707 80 21\n707 91 42\n707 102 26\n707 120 33\n707 124 19\n707 145 13\n707 152 32\n707 208 10\n707 226 16\n707 239 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35\n709 178 8\n709 209 18\n709 232 25\n709 262 6\n709 266 22\n709 333 11\n709 382 6\n709 393 16\n709 445 18\n709 448 31\n709 512 46\n709 522 38\n709 590 38\n709 638 49\n709 680 12\n709 740 7\n709 744 33\n709 766 -2\n709 788 19\n709 789 7\n709 800 31\n709 842 42\n709 892 4\n710 46 12\n710 71 3\n710 77 42\n710 109 39\n710 168 18\n710 181 23\n710 183 14\n710 205 39\n710 214 38\n710 243 13\n710 278 9\n710 286 47\n710 304 36\n710 312 32\n710 431 13\n710 449 26\n710 454 17\n710 466 6\n710 544 40\n710 593 1\n710 619 25\n710 696 36\n710 725 30\n710 733 15\n710 739 46\n710 752 47\n710 763 25\n710 776 41\n710 791 35\n710 794 33\n710 796 8\n710 799 46\n710 821 9\n710 826 28\n710 829 -2\n710 835 26\n710 850 22\n710 871 38\n710 892 22\n710 918 -1\n710 945 18\n710 954 44\n710 963 46\n710 980 13\n710 1000 21\n711 15 31\n711 24 14\n711 57 49\n711 67 45\n711 70 35\n711 71 16\n711 82 11\n711 97 15\n711 105 28\n711 135 6\n711 147 26\n711 156 45\n711 168 37\n711 173 19\n711 191 4\n711 197 17\n711 205 39\n711 212 47\n711 218 39\n711 232 47\n711 266 3\n711 281 45\n711 288 45\n711 289 37\n711 310 39\n711 319 46\n711 320 30\n711 339 7\n711 342 17\n711 349 36\n711 355 3\n711 428 16\n711 454 22\n711 455 40\n711 478 9\n711 486 0\n711 506 35\n711 524 40\n711 568 10\n711 599 21\n711 604 44\n711 667 5\n711 690 5\n711 691 42\n711 703 47\n711 720 31\n711 722 26\n711 739 7\n711 787 50\n711 789 1\n711 796 29\n711 811 4\n711 845 35\n711 857 28\n711 879 5\n711 947 4\n711 951 32\n711 990 26\n712 31 35\n712 44 26\n712 48 48\n712 52 36\n712 112 25\n712 122 33\n712 171 14\n712 190 10\n712 221 21\n712 226 3\n712 272 39\n712 275 4\n712 286 35\n712 300 -1\n712 367 37\n712 400 26\n712 438 38\n712 442 5\n712 449 30\n712 487 10\n712 507 28\n712 517 40\n712 565 36\n712 589 -1\n712 590 30\n712 594 38\n712 603 46\n712 611 -2\n712 645 30\n712 649 29\n712 650 14\n712 708 21\n712 713 29\n712 717 32\n712 738 34\n712 745 41\n712 748 34\n712 786 -2\n712 826 13\n712 842 46\n712 874 12\n712 911 30\n712 929 12\n712 935 43\n712 994 28\n712 998 24\n713 37 37\n713 63 21\n713 82 29\n713 89 46\n713 105 46\n713 147 40\n713 276 46\n713 281 13\n713 318 35\n713 331 32\n713 340 38\n713 346 48\n713 360 29\n713 367 12\n713 385 8\n713 431 36\n713 439 41\n713 464 23\n713 493 29\n713 503 14\n713 513 33\n713 533 48\n713 534 36\n713 546 32\n713 563 42\n713 580 6\n713 607 32\n713 614 39\n713 624 32\n713 655 14\n713 670 32\n713 703 48\n713 705 41\n713 731 22\n713 762 43\n713 793 -2\n713 822 20\n713 904 49\n713 905 28\n713 929 48\n713 942 29\n713 953 4\n713 963 20\n713 971 23\n713 991 16\n714 32 43\n714 54 32\n714 64 27\n714 80 31\n714 142 9\n714 161 43\n714 162 10\n714 192 48\n714 218 22\n714 235 44\n714 290 21\n714 316 18\n714 330 18\n714 366 4\n714 536 1\n714 544 44\n714 546 14\n714 568 32\n714 598 27\n714 600 31\n714 616 45\n714 637 21\n714 640 33\n714 709 28\n714 717 47\n714 730 8\n714 756 26\n714 767 -1\n714 776 19\n714 780 16\n714 795 41\n714 802 21\n714 811 9\n714 856 -1\n714 865 40\n714 868 39\n714 872 17\n714 877 -2\n714 891 10\n714 906 26\n714 910 23\n714 920 36\n714 948 4\n714 977 36\n714 982 22\n714 984 19\n714 985 10\n714 994 39\n715 5 14\n715 39 26\n715 96 36\n715 97 20\n715 143 37\n715 167 29\n715 206 10\n715 209 28\n715 213 37\n715 225 46\n715 345 47\n715 378 26\n715 393 27\n715 408 17\n715 424 21\n715 461 46\n715 484 25\n715 515 4\n715 540 42\n715 547 38\n715 566 4\n715 587 34\n715 673 41\n715 677 46\n715 722 27\n715 780 31\n715 784 33\n715 798 -2\n715 823 5\n715 826 22\n715 848 32\n715 854 0\n715 887 3\n715 900 25\n715 915 -1\n715 993 29\n715 996 41\n716 31 12\n716 40 34\n716 48 48\n716 78 9\n716 87 31\n716 97 16\n716 129 42\n716 148 9\n716 154 18\n716 161 17\n716 209 22\n716 227 33\n716 277 10\n716 353 13\n716 360 27\n716 361 41\n716 365 34\n716 437 36\n716 457 17\n716 471 18\n716 516 45\n716 518 15\n716 528 33\n716 530 49\n716 537 29\n716 542 18\n716 547 23\n716 591 7\n716 606 25\n716 627 46\n716 630 23\n716 632 27\n716 645 46\n716 664 47\n716 668 50\n716 697 46\n716 701 5\n716 714 50\n716 744 30\n716 752 47\n716 756 49\n716 768 30\n716 795 26\n716 808 14\n716 816 32\n716 844 21\n716 893 39\n716 897 29\n716 939 -1\n716 943 5\n716 976 43\n716 990 36\n717 9 11\n717 24 27\n717 32 22\n717 96 43\n717 99 21\n717 114 38\n717 115 26\n717 128 49\n717 181 38\n717 195 48\n717 213 9\n717 290 32\n717 309 19\n717 337 34\n717 372 16\n717 379 22\n717 384 38\n717 388 48\n717 448 19\n717 479 14\n717 491 44\n717 509 47\n717 517 45\n717 549 9\n717 594 44\n717 617 11\n717 623 26\n717 628 44\n717 644 28\n717 663 19\n717 728 41\n717 757 35\n717 759 13\n717 771 45\n717 800 15\n717 818 12\n717 853 9\n717 857 31\n717 920 44\n717 939 13\n717 963 10\n717 991 18\n718 51 9\n718 75 12\n718 79 10\n718 86 18\n718 127 34\n718 141 45\n718 151 41\n718 209 32\n718 213 20\n718 260 16\n718 263 20\n718 321 12\n718 340 26\n718 346 31\n718 384 13\n718 398 -1\n718 412 41\n718 414 47\n718 422 14\n718 430 8\n718 435 32\n718 466 45\n718 472 38\n718 496 9\n718 506 47\n718 532 25\n718 580 19\n718 584 -1\n718 594 49\n718 602 16\n718 626 21\n718 655 5\n718 678 49\n718 689 34\n718 699 39\n718 702 12\n718 752 44\n718 759 15\n718 785 16\n718 787 8\n718 807 50\n718 813 2\n718 869 28\n718 877 17\n718 883 40\n718 899 3\n718 918 30\n718 926 34\n718 938 43\n718 985 6\n719 97 47\n719 136 35\n719 145 43\n719 168 38\n719 192 45\n719 198 11\n719 221 32\n719 234 35\n719 235 3\n719 238 17\n719 256 49\n719 303 41\n719 304 7\n719 357 6\n719 358 11\n719 365 47\n719 383 19\n719 389 3\n719 399 18\n719 420 14\n719 470 43\n719 552 50\n719 556 30\n719 574 14\n719 577 25\n719 607 38\n719 624 5\n719 659 45\n719 703 48\n719 716 49\n719 718 32\n719 754 2\n719 803 44\n719 824 22\n719 828 29\n719 837 8\n719 862 -2\n719 875 31\n719 881 16\n719 901 45\n719 903 30\n719 921 45\n719 947 6\n719 962 7\n719 967 34\n719 972 12\n719 973 25\n719 974 13\n719 990 35\n720 6 19\n720 38 33\n720 65 23\n720 67 19\n720 111 38\n720 112 13\n720 120 49\n720 131 27\n720 162 34\n720 171 21\n720 206 33\n720 224 15\n720 234 32\n720 238 34\n720 274 35\n720 281 50\n720 330 50\n720 343 4\n720 364 6\n720 395 16\n720 444 22\n720 449 33\n720 464 44\n720 465 37\n720 495 24\n720 535 4\n720 540 50\n720 607 26\n720 626 16\n720 640 47\n720 654 47\n720 672 24\n720 709 8\n720 710 48\n720 741 21\n720 750 30\n720 773 39\n720 777 -2\n720 799 24\n720 819 35\n720 828 16\n720 834 11\n720 930 14\n720 940 48\n720 957 23\n720 962 21\n720 986 26\n720 991 -1\n721 9 41\n721 10 32\n721 92 21\n721 99 45\n721 111 50\n721 147 4\n721 159 28\n721 164 49\n721 207 0\n721 269 18\n721 291 47\n721 307 45\n721 309 8\n721 334 9\n721 341 3\n721 354 11\n721 357 46\n721 374 26\n721 380 6\n721 416 44\n721 438 -2\n721 461 48\n721 490 23\n721 506 4\n721 519 39\n721 643 41\n721 651 39\n721 661 25\n721 710 48\n721 724 30\n721 736 45\n721 744 47\n721 756 32\n721 757 8\n721 773 29\n721 777 24\n721 793 16\n721 824 7\n721 832 42\n721 864 40\n721 874 3\n721 898 19\n721 926 35\n721 939 5\n721 941 20\n721 947 24\n722 25 9\n722 33 32\n722 37 10\n722 57 12\n722 75 33\n722 82 38\n722 113 50\n722 114 45\n722 193 33\n722 239 9\n722 252 13\n722 285 15\n722 287 44\n722 386 38\n722 387 35\n722 435 12\n722 462 12\n722 470 7\n722 477 41\n722 485 30\n722 562 43\n722 589 6\n722 621 43\n722 666 45\n722 683 2\n722 724 36\n722 741 48\n722 749 23\n722 753 35\n722 760 20\n722 767 5\n722 778 22\n722 784 13\n722 824 20\n722 828 1\n722 835 40\n722 854 43\n722 868 16\n722 899 33\n722 931 41\n722 940 30\n722 952 10\n722 998 41\n722 999 15\n723 30 48\n723 41 26\n723 51 11\n723 54 12\n723 57 25\n723 76 44\n723 102 49\n723 105 8\n723 111 44\n723 133 46\n723 141 29\n723 163 3\n723 185 24\n723 190 37\n723 224 42\n723 238 28\n723 270 43\n723 343 34\n723 345 6\n723 348 5\n723 399 46\n723 402 33\n723 410 32\n723 456 13\n723 472 9\n723 478 10\n723 487 21\n723 489 33\n723 504 39\n723 525 32\n723 532 26\n723 559 48\n723 563 50\n723 571 27\n723 573 43\n723 578 33\n723 580 20\n723 592 33\n723 601 44\n723 612 41\n723 618 38\n723 632 4\n723 670 18\n723 676 10\n723 683 50\n723 698 45\n723 729 17\n723 735 44\n723 784 -1\n723 795 25\n723 807 39\n723 814 23\n723 820 5\n723 825 2\n723 839 50\n723 851 27\n723 863 38\n723 865 45\n723 919 27\n723 936 1\n724 8 20\n724 13 8\n724 43 4\n724 47 44\n724 60 39\n724 65 23\n724 97 7\n724 126 5\n724 139 7\n724 144 8\n724 148 36\n724 153 31\n724 175 11\n724 204 0\n724 209 28\n724 217 6\n724 219 6\n724 247 36\n724 252 13\n724 263 12\n724 303 39\n724 316 29\n724 363 17\n724 390 42\n724 394 32\n724 434 36\n724 483 20\n724 502 34\n724 507 47\n724 557 47\n724 592 7\n724 604 5\n724 616 5\n724 634 23\n724 638 42\n724 644 33\n724 650 39\n724 654 8\n724 656 33\n724 699 3\n724 701 21\n724 713 29\n724 749 18\n724 750 20\n724 762 46\n724 791 12\n724 817 30\n724 828 12\n724 869 7\n724 874 -1\n724 878 17\n724 894 32\n724 910 26\n724 914 17\n724 949 -1\n724 959 49\n724 971 13\n724 976 3\n724 985 3\n724 991 -1\n725 4 18\n725 40 11\n725 42 24\n725 46 25\n725 48 48\n725 54 17\n725 57 4\n725 61 6\n725 89 44\n725 100 28\n725 123 18\n725 155 43\n725 212 7\n725 288 6\n725 305 19\n725 325 39\n725 339 27\n725 366 48\n725 377 20\n725 397 29\n725 407 42\n725 412 9\n725 416 30\n725 428 27\n725 463 14\n725 514 44\n725 543 32\n725 583 9\n725 599 1\n725 616 41\n725 645 45\n725 691 29\n725 715 47\n725 720 47\n725 739 44\n725 747 7\n725 804 3\n725 842 40\n725 850 33\n725 851 41\n725 876 27\n725 882 33\n725 883 5\n725 900 41\n725 902 27\n725 903 29\n725 933 45\n725 962 13\n725 970 6\n726 66 33\n726 87 22\n726 91 38\n726 100 23\n726 112 28\n726 136 36\n726 149 34\n726 155 30\n726 207 2\n726 285 33\n726 314 38\n726 317 43\n726 338 37\n726 372 45\n726 386 30\n726 390 40\n726 392 23\n726 400 17\n726 404 28\n726 412 9\n726 428 43\n726 449 32\n726 460 3\n726 472 48\n726 511 33\n726 516 25\n726 545 18\n726 552 41\n726 555 14\n726 606 32\n726 671 7\n726 732 23\n726 749 50\n726 787 26\n726 803 46\n726 817 25\n726 818 50\n726 867 13\n726 908 29\n726 910 22\n726 951 37\n726 961 49\n726 974 21\n726 979 38\n726 991 37\n727 22 38\n727 31 20\n727 38 25\n727 41 12\n727 75 3\n727 85 20\n727 111 38\n727 126 5\n727 204 36\n727 207 15\n727 214 49\n727 225 16\n727 228 39\n727 234 13\n727 246 35\n727 273 42\n727 283 38\n727 289 16\n727 320 13\n727 331 23\n727 334 25\n727 365 46\n727 399 42\n727 407 46\n727 463 27\n727 483 34\n727 516 45\n727 524 29\n727 542 24\n727 547 48\n727 568 44\n727 591 3\n727 592 7\n727 605 34\n727 635 1\n727 722 -1\n727 726 22\n727 728 21\n727 738 4\n727 764 8\n727 784 16\n727 793 2\n727 797 18\n727 819 39\n727 826 16\n727 890 19\n727 945 49\n727 980 6\n728 49 45\n728 120 33\n728 198 13\n728 219 20\n728 232 35\n728 241 33\n728 246 -1\n728 257 48\n728 288 40\n728 319 12\n728 332 38\n728 337 4\n728 341 50\n728 343 41\n728 347 38\n728 353 10\n728 355 35\n728 363 35\n728 417 31\n728 421 24\n728 422 13\n728 425 26\n728 441 17\n728 447 16\n728 495 19\n728 498 49\n728 510 6\n728 537 16\n728 539 36\n728 545 -1\n728 582 41\n728 601 12\n728 633 24\n728 647 49\n728 681 10\n728 699 27\n728 709 1\n728 716 29\n728 806 20\n728 823 33\n728 832 7\n728 880 46\n728 883 3\n728 925 32\n728 926 6\n728 937 30\n728 995 49\n728 1000 -2\n729 24 15\n729 52 11\n729 80 23\n729 101 10\n729 111 16\n729 112 49\n729 122 43\n729 156 20\n729 170 42\n729 193 23\n729 217 49\n729 251 25\n729 256 15\n729 270 49\n729 271 35\n729 338 6\n729 404 40\n729 422 26\n729 451 15\n729 453 31\n729 459 18\n729 474 29\n729 480 9\n729 483 48\n729 521 48\n729 548 30\n729 565 34\n729 612 9\n729 649 40\n729 663 32\n729 664 47\n729 674 -1\n729 687 32\n729 716 4\n729 720 7\n729 762 47\n729 765 19\n729 776 30\n729 782 14\n729 797 40\n729 828 41\n729 872 49\n729 887 34\n729 903 24\n729 908 -2\n729 921 36\n729 938 10\n729 971 44\n730 47 41\n730 96 13\n730 145 35\n730 159 26\n730 183 26\n730 221 7\n730 228 46\n730 278 42\n730 374 6\n730 395 6\n730 414 43\n730 489 49\n730 535 29\n730 590 40\n730 594 32\n730 613 23\n730 715 0\n730 723 44\n730 747 0\n730 837 11\n730 846 3\n730 865 20\n730 866 0\n730 875 27\n730 914 30\n730 931 -1\n730 932 22\n730 939 29\n730 949 50\n730 971 15\n730 981 42\n731 22 49\n731 55 34\n731 58 11\n731 84 37\n731 86 24\n731 100 14\n731 134 26\n731 138 47\n731 140 23\n731 170 20\n731 205 13\n731 226 26\n731 250 9\n731 272 17\n731 277 19\n731 287 22\n731 336 19\n731 340 41\n731 382 46\n731 409 36\n731 463 20\n731 490 39\n731 556 43\n731 568 37\n731 591 15\n731 610 35\n731 652 45\n731 659 2\n731 680 32\n731 701 24\n731 702 16\n731 729 48\n731 740 50\n731 801 36\n731 805 10\n731 817 36\n731 846 10\n731 882 31\n731 893 -1\n731 940 50\n731 951 1\n731 955 21\n731 962 47\n731 983 14\n732 1 21\n732 70 34\n732 76 29\n732 87 22\n732 99 45\n732 103 42\n732 108 19\n732 114 32\n732 125 26\n732 153 21\n732 182 25\n732 192 10\n732 209 39\n732 246 45\n732 276 18\n732 291 26\n732 343 14\n732 407 26\n732 421 16\n732 490 45\n732 497 33\n732 518 50\n732 528 35\n732 582 29\n732 583 20\n732 625 11\n732 665 44\n732 680 47\n732 693 44\n732 713 36\n732 720 36\n732 741 25\n732 742 -2\n732 762 11\n732 789 19\n732 799 11\n732 812 24\n732 828 33\n732 937 45\n732 941 -1\n732 946 46\n732 962 32\n732 993 48\n733 23 23\n733 41 25\n733 49 10\n733 73 13\n733 107 8\n733 110 6\n733 121 37\n733 123 9\n733 129 22\n733 151 18\n733 157 46\n733 182 30\n733 199 38\n733 221 24\n733 245 34\n733 263 12\n733 269 10\n733 362 45\n733 365 16\n733 382 7\n733 394 35\n733 408 19\n733 422 15\n733 446 16\n733 492 15\n733 528 33\n733 554 41\n733 556 12\n733 558 24\n733 564 37\n733 569 9\n733 598 37\n733 624 29\n733 650 32\n733 717 34\n733 721 19\n733 734 19\n733 748 37\n733 768 9\n733 858 35\n733 867 32\n733 877 41\n733 891 7\n733 931 5\n733 947 31\n733 989 46\n734 13 39\n734 17 46\n734 27 6\n734 34 29\n734 55 39\n734 106 5\n734 145 28\n734 184 -1\n734 225 46\n734 281 41\n734 297 42\n734 335 44\n734 387 23\n734 411 3\n734 449 47\n734 493 22\n734 510 20\n734 525 45\n734 532 17\n734 533 1\n734 579 22\n734 586 33\n734 617 27\n734 629 30\n734 667 38\n734 689 21\n734 722 40\n734 740 40\n734 750 31\n734 764 47\n734 785 0\n734 796 31\n734 800 19\n734 802 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423 -2\n738 441 24\n738 468 15\n738 472 28\n738 506 49\n738 508 17\n738 524 0\n738 558 48\n738 624 48\n738 651 35\n738 653 12\n738 665 41\n738 670 19\n738 672 32\n738 686 41\n738 696 24\n738 704 50\n738 727 45\n738 807 5\n738 811 42\n738 819 41\n738 823 50\n738 854 15\n738 903 16\n738 938 47\n738 975 20\n738 983 48\n738 994 15\n739 9 31\n739 15 18\n739 20 47\n739 42 28\n739 52 8\n739 104 24\n739 143 38\n739 161 18\n739 217 44\n739 275 21\n739 276 50\n739 298 39\n739 354 20\n739 392 31\n739 417 31\n739 421 42\n739 454 4\n739 482 36\n739 502 7\n739 505 28\n739 579 27\n739 609 11\n739 640 14\n739 712 32\n739 794 45\n739 813 23\n739 825 10\n739 829 -2\n739 845 20\n739 862 43\n739 877 38\n739 880 20\n739 897 37\n739 908 35\n739 924 33\n739 927 31\n739 930 0\n739 948 42\n739 968 41\n739 976 31\n739 980 13\n739 983 37\n740 4 11\n740 48 36\n740 55 8\n740 70 4\n740 99 33\n740 151 50\n740 154 29\n740 161 48\n740 204 15\n740 212 24\n740 222 11\n740 228 49\n740 273 26\n740 281 49\n740 301 27\n740 341 38\n740 343 0\n740 381 25\n740 430 35\n740 433 5\n740 476 35\n740 498 7\n740 528 27\n740 539 20\n740 548 3\n740 564 15\n740 575 19\n740 594 31\n740 624 21\n740 632 24\n740 658 23\n740 669 42\n740 688 20\n740 708 31\n740 765 9\n740 807 28\n740 844 44\n740 911 29\n740 914 23\n740 917 46\n740 974 40\n740 986 15\n741 4 29\n741 13 24\n741 15 44\n741 58 26\n741 62 40\n741 80 13\n741 111 50\n741 113 39\n741 115 48\n741 140 38\n741 144 3\n741 185 26\n741 192 14\n741 210 35\n741 267 18\n741 313 6\n741 334 6\n741 409 2\n741 436 32\n741 486 33\n741 510 44\n741 533 42\n741 537 39\n741 568 47\n741 578 36\n741 586 20\n741 604 36\n741 620 25\n741 636 49\n741 644 22\n741 665 44\n741 687 3\n741 726 49\n741 770 2\n741 774 27\n741 803 49\n741 814 42\n741 822 28\n741 832 27\n741 843 8\n741 846 40\n741 862 31\n741 889 45\n741 916 47\n741 952 48\n741 959 50\n741 995 0\n742 1 43\n742 17 38\n742 58 38\n742 114 16\n742 145 26\n742 184 15\n742 206 25\n742 224 25\n742 225 26\n742 227 40\n742 267 22\n742 275 33\n742 279 14\n742 287 22\n742 302 22\n742 331 48\n742 341 32\n742 386 27\n742 389 17\n742 422 41\n742 429 40\n742 443 22\n742 458 38\n742 466 19\n742 501 24\n742 546 21\n742 558 16\n742 564 17\n742 579 42\n742 586 46\n742 608 24\n742 621 23\n742 646 46\n742 660 36\n742 680 18\n742 683 30\n742 734 45\n742 753 22\n742 819 2\n742 860 8\n742 878 16\n742 893 13\n742 928 13\n742 967 19\n742 997 36\n743 20 31\n743 21 40\n743 45 38\n743 105 19\n743 137 40\n743 193 32\n743 215 25\n743 217 35\n743 289 49\n743 295 24\n743 328 23\n743 409 17\n743 473 34\n743 475 3\n743 487 11\n743 502 2\n743 511 41\n743 525 5\n743 549 15\n743 651 36\n743 705 32\n743 773 8\n743 812 36\n743 824 25\n743 829 -2\n743 830 17\n743 896 12\n743 897 50\n743 978 12\n743 992 16\n744 28 48\n744 51 11\n744 65 49\n744 111 17\n744 133 13\n744 156 9\n744 176 48\n744 203 24\n744 232 18\n744 264 40\n744 265 43\n744 297 24\n744 323 18\n744 329 7\n744 362 25\n744 383 41\n744 465 48\n744 494 44\n744 499 39\n744 523 9\n744 529 40\n744 542 22\n744 548 9\n744 560 41\n744 584 22\n744 594 16\n744 615 39\n744 621 26\n744 679 38\n744 711 24\n744 740 43\n744 741 39\n744 749 9\n744 759 4\n744 768 50\n744 769 50\n744 775 27\n744 795 45\n744 828 5\n744 862 36\n744 886 35\n744 903 3\n744 936 16\n744 946 22\n744 968 20\n745 34 34\n745 36 30\n745 61 20\n745 89 43\n745 124 22\n745 176 12\n745 198 29\n745 217 15\n745 218 16\n745 234 33\n745 237 32\n745 300 2\n745 332 25\n745 357 43\n745 359 40\n745 369 22\n745 403 18\n745 412 9\n745 428 36\n745 473 34\n745 514 23\n745 531 19\n745 562 33\n745 589 24\n745 600 13\n745 618 41\n745 619 5\n745 637 29\n745 639 30\n745 669 40\n745 742 4\n745 746 34\n745 790 23\n745 827 41\n745 838 4\n745 843 39\n745 850 28\n745 887 37\n745 893 41\n745 914 15\n745 915 31\n745 929 33\n745 961 41\n745 965 41\n745 987 7\n745 995 13\n745 996 38\n746 4 40\n746 15 42\n746 53 44\n746 57 37\n746 77 41\n746 82 47\n746 98 36\n746 102 8\n746 107 34\n746 114 39\n746 151 19\n746 187 35\n746 217 40\n746 221 13\n746 259 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20\n748 532 16\n748 559 44\n748 567 42\n748 568 -1\n748 569 37\n748 575 11\n748 601 8\n748 609 3\n748 630 3\n748 642 2\n748 701 6\n748 702 18\n748 724 11\n748 799 2\n748 802 5\n748 818 -2\n748 840 31\n748 851 33\n748 890 26\n748 910 26\n748 920 16\n748 921 16\n748 922 42\n748 937 29\n748 939 23\n748 940 49\n748 955 29\n748 959 8\n748 967 26\n748 975 49\n748 988 19\n749 37 7\n749 47 15\n749 49 25\n749 54 -1\n749 62 37\n749 65 38\n749 70 44\n749 76 11\n749 83 43\n749 117 23\n749 121 22\n749 124 25\n749 125 14\n749 161 23\n749 173 32\n749 223 34\n749 232 49\n749 251 13\n749 274 26\n749 301 45\n749 325 8\n749 361 28\n749 365 1\n749 368 17\n749 370 0\n749 405 33\n749 418 19\n749 444 50\n749 452 26\n749 513 19\n749 537 22\n749 554 37\n749 596 40\n749 622 50\n749 631 39\n749 644 27\n749 689 47\n749 702 16\n749 706 21\n749 784 13\n749 796 37\n749 822 19\n749 826 23\n749 855 33\n749 857 19\n749 872 15\n749 884 44\n749 898 26\n749 911 30\n749 939 14\n749 950 40\n749 968 18\n749 974 17\n749 978 25\n749 996 41\n750 28 17\n750 35 37\n750 48 12\n750 70 44\n750 76 17\n750 162 26\n750 164 40\n750 178 17\n750 188 22\n750 205 27\n750 214 21\n750 241 42\n750 248 15\n750 305 36\n750 338 12\n750 355 21\n750 371 23\n750 397 48\n750 399 38\n750 401 35\n750 427 33\n750 428 41\n750 448 14\n750 479 9\n750 552 13\n750 559 37\n750 560 33\n750 573 38\n750 606 19\n750 629 19\n750 641 23\n750 678 48\n750 689 8\n750 723 37\n750 786 16\n750 788 1\n750 791 50\n750 793 31\n750 821 22\n750 841 29\n750 860 7\n750 880 49\n750 908 19\n750 943 27\n750 963 43\n750 996 28\n750 1000 30\n751 31 19\n751 47 37\n751 61 39\n751 127 28\n751 136 41\n751 219 29\n751 231 17\n751 254 26\n751 258 36\n751 264 4\n751 315 19\n751 316 5\n751 333 28\n751 386 13\n751 425 16\n751 446 29\n751 453 33\n751 498 30\n751 534 20\n751 594 40\n751 661 47\n751 689 28\n751 692 10\n751 705 25\n751 706 13\n751 750 5\n751 769 23\n751 775 48\n751 786 17\n751 797 20\n751 815 29\n751 816 22\n751 851 19\n751 894 11\n751 901 21\n751 981 30\n751 984 35\n751 998 32\n752 47 33\n752 53 39\n752 57 11\n752 65 50\n752 67 4\n752 88 42\n752 109 26\n752 114 19\n752 119 31\n752 144 17\n752 208 5\n752 223 28\n752 283 8\n752 294 14\n752 296 13\n752 301 17\n752 305 48\n752 317 21\n752 334 1\n752 385 28\n752 398 9\n752 405 12\n752 417 13\n752 447 29\n752 464 2\n752 504 25\n752 516 42\n752 524 28\n752 525 39\n752 540 9\n752 565 38\n752 567 39\n752 568 14\n752 606 21\n752 622 33\n752 623 31\n752 668 37\n752 701 46\n752 705 47\n752 747 50\n752 756 15\n752 790 0\n752 815 2\n752 923 28\n752 936 6\n752 944 10\n752 950 5\n752 973 40\n753 84 32\n753 97 46\n753 117 38\n753 149 40\n753 169 10\n753 178 27\n753 206 19\n753 234 34\n753 239 23\n753 259 14\n753 280 7\n753 285 25\n753 287 44\n753 324 37\n753 347 34\n753 362 24\n753 371 11\n753 384 50\n753 457 44\n753 459 38\n753 536 43\n753 537 48\n753 598 13\n753 607 13\n753 616 24\n753 619 45\n753 627 23\n753 634 11\n753 693 45\n753 698 18\n753 707 30\n753 718 26\n753 757 42\n753 816 20\n753 840 8\n753 853 1\n753 860 21\n753 884 -2\n753 920 16\n753 936 11\n753 944 26\n753 994 36\n754 11 31\n754 21 34\n754 27 29\n754 58 20\n754 101 24\n754 193 5\n754 196 13\n754 237 27\n754 265 26\n754 281 30\n754 292 50\n754 329 19\n754 351 22\n754 373 6\n754 381 42\n754 428 40\n754 502 35\n754 505 46\n754 532 27\n754 558 5\n754 583 3\n754 600 10\n754 605 27\n754 612 34\n754 626 25\n754 650 38\n754 683 18\n754 750 19\n754 755 31\n754 756 16\n754 768 13\n754 789 14\n754 804 26\n754 812 16\n754 817 44\n754 830 22\n754 838 32\n754 860 -2\n754 887 1\n754 945 33\n754 963 1\n755 36 25\n755 51 16\n755 72 24\n755 76 20\n755 78 37\n755 89 13\n755 91 29\n755 92 13\n755 94 31\n755 101 31\n755 115 20\n755 117 42\n755 126 25\n755 127 30\n755 131 43\n755 142 10\n755 152 6\n755 182 40\n755 226 25\n755 250 9\n755 254 22\n755 291 25\n755 307 22\n755 323 20\n755 404 22\n755 447 31\n755 486 38\n755 542 25\n755 553 10\n755 586 29\n755 589 41\n755 624 46\n755 626 37\n755 648 25\n755 690 2\n755 694 34\n755 695 50\n755 729 27\n755 731 15\n755 778 0\n755 780 2\n755 791 10\n755 818 12\n755 891 50\n755 895 8\n755 938 37\n755 964 18\n755 973 32\n755 984 27\n755 997 31\n756 22 50\n756 23 17\n756 50 47\n756 63 35\n756 76 47\n756 87 33\n756 89 45\n756 102 37\n756 141 32\n756 175 41\n756 188 44\n756 199 42\n756 215 6\n756 216 40\n756 288 31\n756 314 50\n756 351 30\n756 362 33\n756 381 19\n756 407 21\n756 434 34\n756 459 29\n756 465 40\n756 480 32\n756 540 5\n756 545 29\n756 576 16\n756 603 43\n756 622 18\n756 668 14\n756 670 16\n756 678 32\n756 687 41\n756 693 22\n756 734 46\n756 775 3\n756 780 32\n756 855 23\n756 890 49\n756 907 7\n757 27 35\n757 28 25\n757 31 15\n757 89 6\n757 91 41\n757 137 39\n757 141 21\n757 180 21\n757 181 21\n757 230 17\n757 238 16\n757 246 18\n757 250 21\n757 256 18\n757 276 35\n757 312 18\n757 353 12\n757 387 9\n757 422 8\n757 435 34\n757 472 22\n757 483 28\n757 499 40\n757 501 38\n757 509 33\n757 517 0\n757 538 46\n757 541 44\n757 575 15\n757 623 39\n757 624 1\n757 642 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45\n801 659 38\n801 662 44\n801 690 49\n801 700 50\n801 706 8\n801 733 35\n801 737 47\n801 763 -2\n801 781 34\n801 815 35\n801 840 27\n801 918 31\n801 922 14\n801 933 20\n801 934 33\n801 999 24\n802 30 16\n802 104 41\n802 124 34\n802 171 25\n802 219 32\n802 234 17\n802 306 48\n802 322 27\n802 325 48\n802 340 42\n802 411 45\n802 415 11\n802 482 25\n802 502 34\n802 513 23\n802 519 17\n802 532 37\n802 557 48\n802 596 25\n802 603 30\n802 611 48\n802 644 36\n802 649 1\n802 719 2\n802 731 46\n802 751 17\n802 755 48\n802 772 45\n802 794 2\n802 799 32\n802 810 31\n802 837 43\n802 844 47\n802 856 8\n802 908 16\n802 918 36\n802 920 21\n802 939 24\n802 954 31\n802 981 15\n802 988 4\n802 998 5\n803 18 12\n803 52 24\n803 59 14\n803 65 34\n803 106 13\n803 126 17\n803 168 32\n803 169 20\n803 240 27\n803 302 27\n803 318 24\n803 324 35\n803 394 40\n803 418 26\n803 464 15\n803 523 38\n803 532 14\n803 618 26\n803 638 27\n803 664 20\n803 695 33\n803 713 18\n803 716 42\n803 722 32\n803 747 10\n803 749 50\n803 773 15\n803 791 44\n803 812 18\n803 828 9\n803 848 31\n803 862 28\n803 885 8\n803 898 43\n803 921 17\n803 924 20\n803 934 48\n803 948 -2\n803 975 5\n803 996 -1\n804 1 24\n804 3 37\n804 5 38\n804 26 39\n804 55 19\n804 108 8\n804 140 42\n804 144 49\n804 195 45\n804 221 9\n804 262 29\n804 295 18\n804 298 22\n804 313 24\n804 321 25\n804 352 22\n804 364 35\n804 379 17\n804 388 14\n804 421 5\n804 457 39\n804 501 26\n804 533 44\n804 545 38\n804 555 38\n804 569 27\n804 578 18\n804 579 44\n804 585 44\n804 589 22\n804 598 22\n804 600 18\n804 620 16\n804 634 25\n804 636 13\n804 667 19\n804 672 32\n804 715 39\n804 762 25\n804 777 28\n804 808 45\n804 840 37\n804 884 20\n804 914 10\n804 919 50\n804 920 16\n804 935 7\n805 12 18\n805 26 44\n805 43 50\n805 73 26\n805 86 27\n805 106 28\n805 119 19\n805 125 18\n805 208 27\n805 247 17\n805 279 29\n805 282 45\n805 295 28\n805 318 35\n805 336 20\n805 345 17\n805 383 11\n805 390 5\n805 457 40\n805 545 49\n805 548 12\n805 581 49\n805 585 25\n805 649 20\n805 667 33\n805 672 28\n805 707 14\n805 757 38\n805 759 16\n805 806 49\n805 829 50\n805 841 50\n805 848 7\n805 858 13\n805 888 25\n805 930 35\n805 940 44\n805 941 21\n805 962 25\n805 991 -2\n805 993 50\n806 22 20\n806 28 30\n806 33 43\n806 40 34\n806 112 9\n806 122 33\n806 159 35\n806 171 33\n806 224 44\n806 291 41\n806 312 19\n806 317 29\n806 355 17\n806 362 29\n806 377 21\n806 395 34\n806 419 48\n806 455 43\n806 461 24\n806 513 47\n806 541 8\n806 597 37\n806 609 8\n806 633 27\n806 684 13\n806 707 39\n806 730 17\n806 735 9\n806 740 40\n806 744 43\n806 764 37\n806 767 44\n806 839 23\n806 841 -2\n806 886 38\n806 891 50\n806 899 9\n806 901 42\n806 903 32\n806 932 16\n806 947 44\n806 954 2\n806 957 37\n806 991 18\n807 14 36\n807 24 33\n807 42 12\n807 43 9\n807 50 32\n807 103 12\n807 109 27\n807 123 43\n807 132 0\n807 141 9\n807 146 30\n807 148 5\n807 220 29\n807 278 43\n807 280 48\n807 282 3\n807 290 32\n807 297 45\n807 333 38\n807 344 45\n807 347 25\n807 375 -1\n807 396 49\n807 397 22\n807 403 40\n807 411 18\n807 416 10\n807 419 6\n807 484 4\n807 495 9\n807 535 4\n807 538 49\n807 558 46\n807 573 46\n807 598 20\n807 602 2\n807 604 40\n807 609 28\n807 613 -2\n807 627 9\n807 631 18\n807 655 31\n807 748 26\n807 755 26\n807 869 8\n807 872 5\n807 888 36\n807 895 8\n807 905 36\n807 906 33\n807 929 25\n807 936 16\n807 972 18\n807 998 14\n808 28 39\n808 43 6\n808 59 32\n808 65 13\n808 95 31\n808 133 37\n808 228 9\n808 244 6\n808 289 22\n808 338 17\n808 342 19\n808 383 16\n808 420 38\n808 449 42\n808 473 43\n808 480 48\n808 522 24\n808 538 23\n808 541 5\n808 555 30\n808 561 47\n808 582 37\n808 625 44\n808 640 18\n808 697 40\n808 703 23\n808 735 32\n808 759 9\n808 791 7\n808 794 48\n808 804 10\n808 828 38\n808 838 26\n808 842 49\n808 853 39\n808 862 15\n808 863 50\n808 893 18\n808 935 22\n808 949 21\n808 959 40\n808 971 20\n808 974 24\n808 986 38\n808 994 47\n809 9 21\n809 19 32\n809 37 4\n809 39 23\n809 57 48\n809 58 8\n809 60 48\n809 85 3\n809 119 33\n809 161 14\n809 173 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49\n810 819 43\n810 828 7\n810 849 35\n810 879 34\n810 880 23\n810 885 25\n810 895 -2\n810 920 24\n810 956 30\n810 991 26\n810 1000 44\n811 1 18\n811 21 35\n811 33 42\n811 80 14\n811 180 13\n811 183 18\n811 200 15\n811 209 16\n811 219 38\n811 265 40\n811 304 7\n811 309 28\n811 318 37\n811 319 33\n811 341 30\n811 359 25\n811 370 17\n811 390 26\n811 432 32\n811 448 8\n811 467 8\n811 468 7\n811 497 28\n811 525 49\n811 530 30\n811 533 25\n811 676 29\n811 682 32\n811 692 14\n811 701 40\n811 705 26\n811 708 46\n811 731 10\n811 747 41\n811 778 10\n811 789 34\n811 812 19\n811 815 41\n811 823 42\n811 824 24\n811 869 45\n811 872 8\n811 873 39\n811 917 37\n811 927 1\n811 954 24\n811 955 11\n811 963 20\n811 974 22\n811 977 41\n811 983 48\n812 4 10\n812 35 20\n812 113 6\n812 116 20\n812 144 1\n812 216 14\n812 222 49\n812 285 9\n812 295 47\n812 299 10\n812 310 37\n812 329 0\n812 333 8\n812 412 27\n812 417 6\n812 419 14\n812 420 23\n812 427 38\n812 459 20\n812 516 -1\n812 567 21\n812 608 -2\n812 617 39\n812 632 16\n812 658 9\n812 667 29\n812 715 33\n812 722 11\n812 740 38\n812 741 38\n812 745 6\n812 787 45\n812 802 20\n812 808 39\n812 816 48\n812 836 14\n812 858 27\n812 869 29\n812 870 41\n812 878 33\n812 885 42\n812 920 34\n812 929 18\n812 930 29\n812 972 17\n812 989 32\n813 5 35\n813 30 22\n813 73 38\n813 88 18\n813 90 32\n813 107 20\n813 179 19\n813 188 24\n813 189 30\n813 191 45\n813 192 29\n813 193 41\n813 204 32\n813 234 50\n813 316 43\n813 330 11\n813 410 15\n813 427 46\n813 434 12\n813 446 49\n813 490 14\n813 494 24\n813 518 30\n813 581 47\n813 604 29\n813 609 23\n813 617 19\n813 637 13\n813 667 22\n813 692 50\n813 697 26\n813 745 30\n813 757 41\n813 781 49\n813 785 12\n813 790 48\n813 791 30\n813 807 3\n813 823 24\n813 965 28\n814 18 35\n814 32 10\n814 37 38\n814 78 5\n814 80 46\n814 82 5\n814 87 50\n814 92 39\n814 116 13\n814 131 3\n814 146 28\n814 175 36\n814 181 7\n814 220 15\n814 235 47\n814 236 11\n814 245 36\n814 276 44\n814 287 5\n814 310 25\n814 325 26\n814 348 48\n814 349 30\n814 377 2\n814 401 8\n814 412 40\n814 413 32\n814 417 28\n814 428 2\n814 458 20\n814 472 17\n814 479 30\n814 498 5\n814 512 22\n814 524 31\n814 546 36\n814 594 39\n814 597 -2\n814 609 16\n814 620 43\n814 621 36\n814 631 22\n814 647 18\n814 656 42\n814 657 36\n814 684 22\n814 770 31\n814 785 45\n814 888 34\n814 891 9\n814 894 46\n814 912 40\n814 952 -1\n814 970 24\n814 975 36\n814 993 36\n815 5 35\n815 57 11\n815 59 26\n815 97 40\n815 100 10\n815 115 8\n815 131 27\n815 166 50\n815 168 10\n815 181 33\n815 288 48\n815 327 26\n815 333 47\n815 344 33\n815 383 12\n815 388 2\n815 391 20\n815 444 12\n815 495 15\n815 499 43\n815 500 26\n815 528 47\n815 542 24\n815 549 4\n815 567 7\n815 600 36\n815 630 44\n815 649 45\n815 671 5\n815 676 33\n815 677 45\n815 693 27\n815 706 48\n815 771 26\n815 824 34\n815 867 37\n815 895 36\n815 904 41\n815 925 10\n815 951 29\n815 962 12\n816 21 11\n816 31 34\n816 129 39\n816 185 20\n816 202 15\n816 228 45\n816 240 47\n816 255 15\n816 273 47\n816 279 45\n816 302 47\n816 344 7\n816 374 38\n816 378 29\n816 392 43\n816 397 31\n816 500 20\n816 516 25\n816 524 49\n816 585 14\n816 623 48\n816 670 22\n816 692 26\n816 695 49\n816 705 9\n816 706 46\n816 716 50\n816 746 5\n816 749 15\n816 751 25\n816 754 24\n816 761 26\n816 778 48\n816 853 26\n816 857 32\n816 882 26\n816 887 35\n816 891 50\n816 908 42\n816 932 44\n816 950 2\n816 951 24\n816 952 43\n816 958 14\n816 984 22\n816 998 44\n817 19 47\n817 35 28\n817 88 37\n817 134 34\n817 180 15\n817 183 30\n817 184 41\n817 222 11\n817 260 25\n817 267 21\n817 277 14\n817 359 34\n817 370 29\n817 392 38\n817 398 9\n817 404 26\n817 415 48\n817 418 29\n817 464 12\n817 530 32\n817 558 16\n817 596 37\n817 614 5\n817 623 22\n817 640 47\n817 644 27\n817 658 27\n817 690 11\n817 709 29\n817 717 10\n817 729 25\n817 765 35\n817 767 45\n817 787 36\n817 788 11\n817 816 26\n817 822 22\n817 851 41\n817 860 47\n817 872 25\n817 876 0\n817 877 35\n817 883 48\n817 890 45\n817 914 40\n817 923 6\n817 950 3\n817 972 49\n817 991 35\n818 1 10\n818 4 16\n818 7 18\n818 15 31\n818 21 22\n818 33 30\n818 55 1\n818 68 28\n818 89 28\n818 119 18\n818 131 41\n818 157 12\n818 160 24\n818 175 16\n818 214 28\n818 251 34\n818 258 18\n818 259 13\n818 272 18\n818 295 21\n818 334 18\n818 388 32\n818 452 40\n818 503 13\n818 505 33\n818 512 -1\n818 528 19\n818 541 26\n818 579 12\n818 595 3\n818 601 50\n818 618 24\n818 619 37\n818 628 5\n818 660 42\n818 661 12\n818 662 3\n818 702 3\n818 722 35\n818 723 6\n818 732 36\n818 773 31\n818 781 4\n818 790 12\n818 886 27\n818 893 13\n818 917 41\n818 919 1\n818 924 41\n818 967 21\n818 979 16\n818 989 0\n818 997 45\n819 27 6\n819 32 39\n819 67 27\n819 68 20\n819 79 9\n819 84 35\n819 106 31\n819 114 35\n819 131 42\n819 153 44\n819 179 15\n819 186 47\n819 205 33\n819 257 46\n819 259 47\n819 260 33\n819 285 8\n819 325 8\n819 352 31\n819 373 5\n819 400 31\n819 409 27\n819 438 5\n819 450 42\n819 459 40\n819 491 26\n819 514 30\n819 515 3\n819 519 14\n819 554 39\n819 559 49\n819 565 21\n819 600 11\n819 619 43\n819 635 27\n819 646 26\n819 667 24\n819 708 18\n819 718 37\n819 719 7\n819 745 7\n819 766 45\n819 777 35\n819 793 41\n819 812 19\n819 824 36\n819 830 34\n819 840 32\n819 877 42\n819 907 33\n819 935 39\n819 979 33\n820 5 19\n820 13 44\n820 40 41\n820 48 8\n820 70 36\n820 94 14\n820 102 26\n820 126 30\n820 133 40\n820 165 32\n820 177 48\n820 205 0\n820 221 20\n820 228 11\n820 241 13\n820 275 5\n820 282 45\n820 294 13\n820 321 41\n820 326 34\n820 328 10\n820 339 49\n820 344 29\n820 374 28\n820 432 10\n820 441 19\n820 446 1\n820 451 8\n820 457 34\n820 463 21\n820 507 6\n820 563 31\n820 568 32\n820 572 2\n820 660 25\n820 674 50\n820 680 9\n820 693 40\n820 756 27\n820 770 8\n820 779 33\n820 805 3\n820 812 8\n820 816 11\n820 831 11\n820 838 -2\n820 886 50\n820 905 5\n820 906 13\n820 917 45\n820 929 -2\n820 931 46\n820 942 33\n820 959 22\n820 979 48\n820 993 19\n820 997 15\n821 11 16\n821 22 17\n821 188 44\n821 213 30\n821 219 21\n821 342 16\n821 343 26\n821 345 44\n821 349 50\n821 411 47\n821 435 47\n821 448 35\n821 492 47\n821 501 20\n821 506 21\n821 535 46\n821 554 18\n821 653 25\n821 681 25\n821 708 40\n821 710 34\n821 720 25\n821 750 45\n821 789 32\n821 790 20\n821 800 49\n821 802 42\n821 809 13\n821 864 -2\n821 879 21\n821 894 -2\n821 912 3\n821 917 44\n821 961 34\n821 987 11\n821 995 21\n822 61 41\n822 86 16\n822 150 46\n822 168 25\n822 177 46\n822 229 35\n822 230 14\n822 267 10\n822 310 33\n822 323 33\n822 350 23\n822 371 9\n822 400 19\n822 411 18\n822 447 39\n822 455 47\n822 479 27\n822 487 30\n822 488 27\n822 491 14\n822 494 40\n822 505 49\n822 534 15\n822 604 17\n822 643 17\n822 669 41\n822 728 42\n822 731 16\n822 739 33\n822 797 43\n822 818 5\n822 857 5\n822 875 31\n822 898 44\n822 912 40\n822 916 25\n822 919 15\n822 922 8\n822 924 -2\n822 942 35\n822 969 -2\n822 984 37\n823 7 10\n823 41 23\n823 51 36\n823 54 16\n823 103 30\n823 113 37\n823 127 20\n823 128 22\n823 130 26\n823 180 6\n823 185 34\n823 193 27\n823 214 27\n823 229 21\n823 281 45\n823 308 25\n823 310 35\n823 345 39\n823 369 10\n823 395 23\n823 401 39\n823 419 20\n823 426 44\n823 432 47\n823 464 18\n823 508 4\n823 513 41\n823 520 39\n823 556 24\n823 576 8\n823 577 34\n823 595 38\n823 609 6\n823 619 28\n823 641 37\n823 657 9\n823 669 15\n823 672 9\n823 725 25\n823 775 30\n823 784 25\n823 793 13\n823 802 5\n823 839 31\n823 858 50\n823 868 20\n823 869 40\n823 874 12\n823 901 14\n823 934 32\n823 965 43\n823 968 8\n823 973 13\n823 980 33\n823 982 41\n824 28 16\n824 46 6\n824 51 20\n824 93 7\n824 101 37\n824 108 26\n824 129 41\n824 130 15\n824 167 42\n824 185 12\n824 198 21\n824 203 28\n824 223 17\n824 241 31\n824 243 34\n824 257 43\n824 266 48\n824 271 6\n824 305 27\n824 323 17\n824 337 46\n824 368 12\n824 379 42\n824 397 11\n824 399 26\n824 418 11\n824 455 24\n824 476 50\n824 479 19\n824 487 14\n824 498 21\n824 527 46\n824 529 22\n824 546 29\n824 559 -1\n824 561 3\n824 562 36\n824 595 25\n824 623 35\n824 655 39\n824 672 18\n824 673 7\n824 739 37\n824 775 2\n824 794 31\n824 835 33\n824 836 0\n824 843 28\n824 883 4\n824 895 41\n824 908 6\n824 939 20\n824 950 14\n824 957 43\n824 958 4\n825 49 18\n825 52 26\n825 62 33\n825 78 39\n825 97 7\n825 102 16\n825 118 50\n825 123 5\n825 128 9\n825 138 27\n825 141 20\n825 161 36\n825 180 49\n825 230 45\n825 273 19\n825 303 50\n825 345 25\n825 369 47\n825 373 3\n825 406 21\n825 417 15\n825 427 47\n825 539 35\n825 592 35\n825 630 23\n825 721 46\n825 756 50\n825 764 11\n825 793 26\n825 801 41\n825 813 41\n825 862 10\n825 874 16\n825 964 47\n825 965 10\n825 972 33\n826 4 29\n826 11 49\n826 13 29\n826 56 4\n826 57 36\n826 58 18\n826 85 34\n826 89 41\n826 109 24\n826 133 44\n826 149 35\n826 151 26\n826 166 47\n826 178 15\n826 193 32\n826 194 40\n826 210 10\n826 235 22\n826 243 45\n826 252 14\n826 264 19\n826 276 18\n826 318 5\n826 350 24\n826 364 37\n826 376 15\n826 434 29\n826 473 44\n826 479 18\n826 554 37\n826 565 48\n826 588 32\n826 598 22\n826 607 47\n826 630 42\n826 634 29\n826 638 24\n826 674 43\n826 682 13\n826 692 13\n826 693 42\n826 694 12\n826 722 38\n826 734 15\n826 772 49\n826 773 36\n826 808 35\n826 890 33\n826 924 29\n826 932 27\n826 938 24\n826 942 14\n826 972 41\n827 21 19\n827 83 12\n827 127 49\n827 130 37\n827 134 37\n827 141 11\n827 143 43\n827 149 34\n827 250 18\n827 297 22\n827 304 50\n827 349 45\n827 372 14\n827 400 2\n827 445 45\n827 446 40\n827 453 29\n827 459 49\n827 467 32\n827 472 12\n827 485 46\n827 490 42\n827 512 4\n827 536 33\n827 548 36\n827 549 22\n827 550 37\n827 573 38\n827 578 9\n827 580 23\n827 582 15\n827 615 1\n827 634 23\n827 662 37\n827 693 -2\n827 695 4\n827 701 40\n827 740 12\n827 749 22\n827 779 47\n827 807 50\n827 824 35\n827 849 25\n827 858 19\n827 902 49\n827 923 11\n827 952 18\n827 961 34\n827 987 14\n827 993 33\n827 998 10\n828 24 25\n828 28 16\n828 39 22\n828 55 8\n828 64 35\n828 109 39\n828 164 16\n828 166 7\n828 169 30\n828 195 25\n828 219 9\n828 235 45\n828 246 50\n828 247 44\n828 256 14\n828 298 12\n828 342 50\n828 351 32\n828 372 17\n828 436 28\n828 448 46\n828 455 16\n828 468 13\n828 485 15\n828 491 13\n828 514 42\n828 523 13\n828 550 8\n828 565 15\n828 583 23\n828 595 41\n828 600 8\n828 613 8\n828 615 16\n828 636 15\n828 707 30\n828 740 20\n828 749 42\n828 765 11\n828 770 33\n828 773 12\n828 778 35\n828 788 26\n828 804 45\n828 835 10\n828 870 -2\n828 882 2\n828 884 11\n828 905 29\n828 947 23\n828 950 34\n828 969 47\n828 994 18\n828 998 21\n829 44 45\n829 80 22\n829 91 45\n829 107 13\n829 166 43\n829 171 50\n829 189 10\n829 203 45\n829 232 34\n829 305 46\n829 363 20\n829 383 44\n829 386 49\n829 395 31\n829 437 16\n829 438 5\n829 444 35\n829 468 22\n829 488 43\n829 499 36\n829 513 26\n829 543 31\n829 544 22\n829 557 50\n829 576 49\n829 600 24\n829 615 16\n829 666 21\n829 674 23\n829 689 28\n829 697 35\n829 699 13\n829 705 5\n829 711 49\n829 741 48\n829 759 16\n829 767 40\n829 794 48\n829 832 -1\n829 850 28\n829 879 15\n829 884 25\n829 899 5\n829 902 8\n829 908 2\n829 918 7\n829 934 17\n829 994 33\n829 996 9\n829 999 12\n830 25 31\n830 40 18\n830 47 38\n830 86 36\n830 87 13\n830 101 35\n830 115 46\n830 129 0\n830 151 14\n830 153 43\n830 189 23\n830 228 13\n830 266 30\n830 267 48\n830 273 34\n830 310 10\n830 322 41\n830 402 6\n830 405 13\n830 420 50\n830 422 42\n830 488 17\n830 516 46\n830 521 18\n830 535 48\n830 544 28\n830 547 7\n830 593 13\n830 603 33\n830 608 50\n830 626 24\n830 643 12\n830 650 38\n830 724 6\n830 744 37\n830 745 31\n830 768 8\n830 803 12\n830 806 9\n830 814 43\n830 829 17\n830 855 21\n830 859 47\n830 902 35\n830 917 -2\n830 918 37\n830 945 38\n830 947 50\n830 955 14\n831 67 2\n831 120 48\n831 155 27\n831 184 46\n831 191 15\n831 213 47\n831 254 33\n831 304 45\n831 312 34\n831 320 48\n831 335 36\n831 344 23\n831 353 12\n831 383 41\n831 454 45\n831 515 24\n831 516 34\n831 519 9\n831 560 40\n831 688 26\n831 703 7\n831 716 3\n831 722 29\n831 735 42\n831 736 8\n831 737 30\n831 753 39\n831 762 16\n831 778 13\n831 780 17\n831 792 49\n831 827 43\n831 838 8\n831 871 8\n831 873 16\n831 876 42\n831 895 21\n831 916 49\n831 920 26\n831 929 4\n831 943 18\n831 946 30\n832 21 40\n832 28 35\n832 74 49\n832 87 26\n832 98 36\n832 110 15\n832 143 25\n832 173 43\n832 212 24\n832 245 32\n832 254 40\n832 269 31\n832 290 34\n832 336 21\n832 343 30\n832 356 27\n832 403 31\n832 415 36\n832 419 41\n832 484 43\n832 500 45\n832 572 40\n832 579 14\n832 600 23\n832 623 6\n832 655 44\n832 664 49\n832 677 11\n832 687 16\n832 715 12\n832 717 28\n832 725 22\n832 729 34\n832 730 36\n832 759 36\n832 768 9\n832 789 18\n832 806 43\n832 871 31\n832 910 9\n832 965 40\n833 25 26\n833 58 14\n833 94 19\n833 95 32\n833 101 34\n833 113 15\n833 152 22\n833 168 35\n833 233 8\n833 266 21\n833 271 13\n833 279 47\n833 301 27\n833 309 35\n833 317 32\n833 350 44\n833 392 16\n833 395 10\n833 413 39\n833 433 8\n833 450 26\n833 460 7\n833 469 37\n833 475 42\n833 493 15\n833 543 21\n833 560 14\n833 605 13\n833 648 18\n833 663 27\n833 675 19\n833 713 48\n833 718 21\n833 723 6\n833 744 40\n833 785 50\n833 803 24\n833 842 48\n833 918 49\n833 942 18\n833 963 4\n834 33 33\n834 49 36\n834 54 4\n834 68 3\n834 77 8\n834 117 50\n834 137 49\n834 154 32\n834 200 17\n834 205 30\n834 214 17\n834 215 6\n834 224 18\n834 286 24\n834 294 24\n834 321 6\n834 327 15\n834 331 3\n834 333 44\n834 367 41\n834 382 34\n834 392 5\n834 396 12\n834 427 49\n834 430 22\n834 457 46\n834 467 11\n834 468 41\n834 521 36\n834 540 39\n834 559 22\n834 596 25\n834 605 22\n834 606 16\n834 614 20\n834 623 -2\n834 679 43\n834 687 44\n834 717 25\n834 740 14\n834 755 17\n834 815 11\n834 830 26\n834 837 49\n834 858 29\n834 940 50\n834 987 35\n835 32 10\n835 45 27\n835 59 44\n835 78 11\n835 81 43\n835 96 39\n835 122 48\n835 123 19\n835 125 9\n835 130 2\n835 139 15\n835 170 44\n835 173 37\n835 217 42\n835 228 35\n835 239 50\n835 247 21\n835 261 48\n835 282 20\n835 330 30\n835 344 2\n835 351 50\n835 368 37\n835 441 38\n835 445 25\n835 453 6\n835 476 42\n835 498 19\n835 504 48\n835 507 48\n835 508 33\n835 510 13\n835 548 14\n835 591 22\n835 625 37\n835 636 14\n835 663 38\n835 665 21\n835 694 2\n835 710 20\n835 733 27\n835 752 17\n835 754 3\n835 765 2\n835 779 29\n835 789 44\n835 794 4\n835 797 37\n835 824 35\n835 826 22\n835 853 32\n835 874 8\n835 880 38\n835 881 36\n835 882 19\n835 893 37\n835 921 4\n835 926 20\n835 954 11\n835 962 22\n835 975 35\n835 984 -1\n836 19 23\n836 49 24\n836 87 11\n836 92 43\n836 142 29\n836 151 17\n836 158 30\n836 161 41\n836 175 47\n836 198 48\n836 256 39\n836 266 10\n836 286 24\n836 295 42\n836 305 22\n836 312 24\n836 315 21\n836 426 19\n836 453 31\n836 466 20\n836 468 14\n836 486 38\n836 515 38\n836 547 27\n836 581 48\n836 645 34\n836 687 47\n836 839 35\n836 890 -1\n836 968 19\n836 971 17\n837 11 37\n837 78 30\n837 89 6\n837 149 6\n837 228 34\n837 234 31\n837 240 39\n837 251 38\n837 288 3\n837 317 18\n837 384 26\n837 397 35\n837 466 20\n837 476 28\n837 484 8\n837 487 23\n837 549 32\n837 562 10\n837 579 18\n837 593 29\n837 631 26\n837 669 44\n837 681 10\n837 690 36\n837 693 45\n837 703 20\n837 727 38\n837 745 32\n837 746 13\n837 747 34\n837 798 30\n837 812 7\n837 937 45\n837 969 40\n838 14 25\n838 28 26\n838 49 28\n838 71 33\n838 94 11\n838 97 11\n838 111 -1\n838 124 38\n838 140 16\n838 171 31\n838 231 39\n838 253 16\n838 273 42\n838 311 23\n838 321 7\n838 365 21\n838 375 15\n838 382 29\n838 393 5\n838 424 24\n838 426 41\n838 428 29\n838 463 37\n838 466 21\n838 487 15\n838 493 26\n838 505 14\n838 536 25\n838 565 20\n838 610 10\n838 623 6\n838 625 6\n838 647 11\n838 655 4\n838 656 4\n838 714 33\n838 785 3\n838 834 2\n838 859 49\n838 876 4\n838 880 29\n838 961 28\n838 964 32\n838 968 37\n839 38 47\n839 78 35\n839 130 34\n839 172 50\n839 225 21\n839 233 12\n839 240 38\n839 258 49\n839 259 29\n839 273 48\n839 277 49\n839 284 19\n839 303 13\n839 320 14\n839 369 42\n839 398 39\n839 431 45\n839 459 20\n839 462 46\n839 468 30\n839 474 34\n839 478 9\n839 481 49\n839 498 23\n839 605 14\n839 690 30\n839 691 29\n839 696 47\n839 745 24\n839 746 18\n839 768 15\n839 809 22\n839 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24\n919 724 10\n919 730 16\n919 745 45\n919 766 28\n919 826 22\n919 853 36\n919 867 45\n919 912 32\n919 930 26\n919 939 20\n919 940 21\n919 968 6\n919 974 10\n919 983 23\n919 993 40\n920 1 44\n920 2 16\n920 12 48\n920 30 30\n920 43 5\n920 78 47\n920 85 21\n920 105 39\n920 131 19\n920 135 26\n920 165 24\n920 167 27\n920 188 11\n920 192 50\n920 241 35\n920 306 36\n920 372 27\n920 383 49\n920 388 43\n920 390 4\n920 403 1\n920 406 23\n920 410 7\n920 418 1\n920 425 10\n920 433 43\n920 438 43\n920 452 42\n920 491 20\n920 492 25\n920 493 25\n920 505 7\n920 508 22\n920 510 1\n920 530 34\n920 573 12\n920 590 9\n920 626 47\n920 627 21\n920 688 20\n920 717 -1\n920 766 37\n920 809 40\n920 831 41\n920 869 0\n920 879 3\n920 908 44\n920 914 17\n920 921 14\n920 946 5\n920 963 1\n920 993 22\n921 34 41\n921 56 17\n921 78 18\n921 94 37\n921 107 23\n921 121 21\n921 131 42\n921 175 33\n921 187 33\n921 195 22\n921 230 49\n921 235 36\n921 263 46\n921 269 34\n921 286 21\n921 309 32\n921 314 23\n921 317 18\n921 319 20\n921 334 34\n921 346 32\n921 379 8\n921 402 19\n921 407 13\n921 423 28\n921 452 14\n921 486 35\n921 538 41\n921 549 42\n921 569 26\n921 615 40\n921 690 31\n921 697 45\n921 747 10\n921 761 17\n921 785 27\n921 787 7\n921 792 15\n921 833 25\n921 836 26\n921 901 13\n921 954 21\n921 961 27\n921 983 42\n921 993 10\n922 20 43\n922 48 50\n922 65 43\n922 75 47\n922 79 31\n922 86 50\n922 106 21\n922 113 48\n922 119 34\n922 137 19\n922 148 48\n922 163 10\n922 182 48\n922 191 22\n922 204 17\n922 221 32\n922 253 49\n922 254 24\n922 264 22\n922 292 46\n922 307 20\n922 321 20\n922 347 36\n922 366 39\n922 385 39\n922 394 11\n922 465 15\n922 504 33\n922 554 11\n922 584 48\n922 601 30\n922 603 45\n922 620 48\n922 636 35\n922 643 26\n922 687 22\n922 690 10\n922 743 48\n922 807 6\n922 812 20\n922 819 24\n922 830 45\n922 858 26\n922 864 34\n922 870 27\n922 898 30\n922 908 33\n922 916 32\n922 967 16\n922 970 46\n922 987 42\n923 3 7\n923 9 12\n923 38 50\n923 54 41\n923 55 46\n923 131 47\n923 137 17\n923 185 11\n923 209 42\n923 218 42\n923 223 16\n923 230 24\n923 250 25\n923 252 37\n923 300 39\n923 318 37\n923 339 5\n923 365 17\n923 401 23\n923 405 12\n923 424 19\n923 443 43\n923 486 33\n923 487 23\n923 500 20\n923 516 24\n923 524 15\n923 529 29\n923 569 50\n923 614 17\n923 664 42\n923 666 6\n923 672 47\n923 680 15\n923 706 45\n923 713 28\n923 735 26\n923 769 6\n923 778 27\n923 792 3\n923 795 12\n923 817 28\n923 824 18\n923 865 14\n923 867 36\n923 887 19\n923 892 28\n923 909 48\n923 914 49\n923 933 1\n923 935 43\n923 955 38\n923 966 0\n923 985 3\n923 986 38\n923 993 8\n924 22 36\n924 51 7\n924 93 13\n924 127 20\n924 175 25\n924 201 27\n924 214 14\n924 226 34\n924 286 22\n924 291 13\n924 303 23\n924 307 33\n924 318 48\n924 327 47\n924 331 48\n924 333 13\n924 368 26\n924 395 12\n924 397 39\n924 409 50\n924 418 16\n924 427 50\n924 442 38\n924 447 14\n924 462 47\n924 466 31\n924 492 20\n924 498 42\n924 527 26\n924 581 11\n924 612 46\n924 615 33\n924 652 11\n924 667 47\n924 726 22\n924 732 29\n924 743 38\n924 772 11\n924 826 37\n924 829 44\n924 831 40\n924 905 37\n924 958 1\n924 992 41\n925 27 24\n925 49 38\n925 62 16\n925 74 24\n925 129 37\n925 194 39\n925 202 50\n925 210 32\n925 236 38\n925 272 35\n925 330 25\n925 353 6\n925 371 48\n925 410 19\n925 419 18\n925 476 31\n925 527 42\n925 534 30\n925 538 20\n925 549 4\n925 590 5\n925 610 10\n925 630 48\n925 633 46\n925 652 31\n925 739 30\n925 746 17\n925 761 32\n925 764 12\n925 765 37\n925 791 15\n925 793 1\n925 827 8\n925 831 47\n925 855 31\n925 858 12\n925 894 29\n925 895 39\n925 917 39\n925 929 -1\n925 930 16\n925 981 7\n926 26 7\n926 30 8\n926 37 29\n926 47 5\n926 94 9\n926 119 40\n926 127 20\n926 138 40\n926 146 15\n926 150 37\n926 163 10\n926 208 20\n926 256 7\n926 261 28\n926 294 0\n926 334 27\n926 337 3\n926 374 8\n926 386 32\n926 389 4\n926 392 20\n926 399 9\n926 431 44\n926 450 40\n926 457 41\n926 461 8\n926 474 5\n926 475 36\n926 512 42\n926 514 30\n926 531 9\n926 591 18\n926 605 40\n926 620 15\n926 637 47\n926 671 15\n926 674 11\n926 690 10\n926 740 1\n926 750 30\n926 760 34\n926 775 16\n926 796 29\n926 800 28\n926 807 30\n926 810 44\n926 822 37\n926 856 33\n926 893 8\n926 927 43\n926 930 48\n926 979 33\n926 980 24\n926 984 14\n926 992 16\n926 998 31\n927 7 17\n927 27 39\n927 34 7\n927 86 15\n927 133 23\n927 139 15\n927 259 40\n927 311 39\n927 334 48\n927 378 30\n927 435 42\n927 482 25\n927 524 8\n927 538 33\n927 549 15\n927 568 38\n927 588 34\n927 599 43\n927 605 23\n927 636 19\n927 641 43\n927 680 31\n927 694 19\n927 722 12\n927 732 30\n927 753 2\n927 789 32\n927 795 14\n927 802 6\n927 854 25\n927 869 25\n927 871 50\n927 872 42\n927 873 48\n927 884 45\n927 897 3\n927 934 19\n927 964 37\n927 969 8\n927 988 28\n927 996 8\n928 43 44\n928 51 29\n928 70 15\n928 73 15\n928 86 49\n928 90 24\n928 116 33\n928 126 10\n928 131 18\n928 152 46\n928 156 9\n928 214 23\n928 228 19\n928 230 30\n928 257 30\n928 288 36\n928 325 17\n928 329 50\n928 331 46\n928 395 17\n928 405 2\n928 445 11\n928 469 22\n928 534 47\n928 535 50\n928 597 14\n928 601 26\n928 603 42\n928 693 18\n928 696 17\n928 705 40\n928 717 23\n928 748 41\n928 789 34\n928 790 20\n928 794 21\n928 798 31\n928 807 11\n928 870 29\n928 875 37\n928 940 14\n928 945 2\n928 947 46\n928 956 -1\n929 37 47\n929 64 25\n929 128 26\n929 172 35\n929 205 16\n929 209 17\n929 238 24\n929 252 44\n929 255 21\n929 274 17\n929 299 43\n929 315 46\n929 432 48\n929 442 43\n929 454 3\n929 497 37\n929 519 25\n929 524 31\n929 532 30\n929 557 29\n929 568 35\n929 575 10\n929 577 26\n929 661 35\n929 708 19\n929 716 35\n929 721 45\n929 728 49\n929 730 48\n929 735 12\n929 757 38\n929 772 2\n929 774 4\n929 794 19\n929 795 20\n929 799 13\n929 845 29\n929 850 46\n929 856 4\n929 859 31\n929 901 10\n929 904 42\n929 914 28\n929 937 48\n929 943 13\n930 31 33\n930 37 25\n930 50 34\n930 72 41\n930 107 21\n930 153 30\n930 168 15\n930 183 50\n930 198 28\n930 211 12\n930 249 13\n930 272 17\n930 284 49\n930 361 15\n930 367 42\n930 378 20\n930 384 18\n930 400 16\n930 412 46\n930 455 42\n930 509 13\n930 512 26\n930 517 10\n930 527 12\n930 533 29\n930 551 25\n930 561 36\n930 567 35\n930 589 40\n930 622 12\n930 699 40\n930 703 46\n930 715 48\n930 717 24\n930 727 19\n930 751 19\n930 795 14\n930 800 49\n930 813 13\n930 829 33\n930 929 33\n930 946 37\n930 954 48\n930 972 47\n930 997 23\n930 999 1\n931 1 14\n931 57 46\n931 62 50\n931 64 20\n931 75 41\n931 82 27\n931 91 11\n931 159 29\n931 168 29\n931 179 10\n931 208 45\n931 218 38\n931 245 36\n931 278 15\n931 288 12\n931 341 45\n931 373 25\n931 379 39\n931 390 16\n931 394 22\n931 405 19\n931 411 35\n931 432 16\n931 433 7\n931 435 17\n931 437 27\n931 450 13\n931 454 39\n931 462 43\n931 468 27\n931 469 42\n931 486 29\n931 542 23\n931 584 24\n931 610 6\n931 638 20\n931 654 15\n931 658 25\n931 702 26\n931 730 16\n931 767 25\n931 771 37\n931 795 21\n931 803 42\n931 826 24\n931 870 20\n931 878 20\n931 880 7\n931 901 28\n931 906 9\n931 951 39\n931 973 48\n931 999 30\n931 1000 26\n932 3 22\n932 7 13\n932 22 39\n932 62 38\n932 64 41\n932 74 9\n932 92 36\n932 97 35\n932 113 17\n932 129 37\n932 207 18\n932 238 28\n932 265 41\n932 268 23\n932 319 21\n932 324 27\n932 327 32\n932 348 10\n932 385 36\n932 393 40\n932 407 24\n932 412 40\n932 422 22\n932 427 43\n932 482 13\n932 517 35\n932 571 37\n932 622 26\n932 631 2\n932 670 8\n932 683 25\n932 686 14\n932 701 26\n932 710 43\n932 722 20\n932 767 27\n932 802 22\n932 813 35\n932 827 11\n932 833 8\n932 834 35\n932 836 39\n932 843 0\n932 889 19\n932 923 31\n933 9 22\n933 28 25\n933 153 13\n933 171 24\n933 225 42\n933 267 34\n933 280 26\n933 282 33\n933 296 42\n933 301 21\n933 302 19\n933 315 50\n933 413 5\n933 423 49\n933 436 30\n933 460 41\n933 500 22\n933 501 40\n933 519 11\n933 522 33\n933 523 28\n933 540 47\n933 559 5\n933 589 9\n933 698 5\n933 708 41\n933 730 14\n933 775 40\n933 797 30\n933 800 46\n933 843 47\n933 846 29\n933 909 17\n933 927 4\n933 948 42\n933 983 25\n933 992 19\n934 5 14\n934 18 15\n934 21 20\n934 42 10\n934 45 38\n934 103 35\n934 154 30\n934 163 15\n934 213 37\n934 215 49\n934 276 34\n934 279 50\n934 280 8\n934 298 17\n934 346 16\n934 355 28\n934 360 24\n934 385 48\n934 417 50\n934 439 35\n934 441 21\n934 462 43\n934 471 31\n934 496 21\n934 500 20\n934 543 50\n934 553 30\n934 568 47\n934 571 37\n934 583 34\n934 616 49\n934 625 37\n934 652 14\n934 659 15\n934 671 19\n934 676 23\n934 683 10\n934 693 21\n934 694 7\n934 715 16\n934 743 43\n934 759 5\n934 800 28\n934 805 18\n934 806 12\n934 807 24\n934 814 40\n934 851 5\n934 928 8\n934 933 12\n934 955 1\n934 973 1\n934 981 48\n935 2 27\n935 55 33\n935 60 31\n935 115 18\n935 134 24\n935 148 30\n935 149 25\n935 151 31\n935 180 41\n935 228 39\n935 245 40\n935 247 13\n935 251 19\n935 269 26\n935 305 40\n935 330 50\n935 362 40\n935 365 28\n935 368 18\n935 393 33\n935 397 13\n935 414 25\n935 453 45\n935 456 26\n935 479 36\n935 527 22\n935 586 25\n935 603 43\n935 613 5\n935 619 17\n935 664 25\n935 679 43\n935 747 40\n935 762 9\n935 770 19\n935 776 44\n935 853 22\n935 896 34\n935 908 30\n935 930 8\n935 957 3\n935 986 13\n935 995 34\n936 30 42\n936 31 36\n936 58 44\n936 76 20\n936 105 28\n936 206 19\n936 233 8\n936 249 5\n936 250 23\n936 254 39\n936 309 47\n936 326 45\n936 339 48\n936 411 29\n936 436 39\n936 464 49\n936 482 29\n936 486 37\n936 490 16\n936 522 48\n936 558 14\n936 565 6\n936 610 50\n936 617 23\n936 631 16\n936 639 21\n936 655 6\n936 665 39\n936 737 20\n936 747 24\n936 830 8\n936 880 41\n936 884 42\n936 924 32\n936 941 47\n936 960 2\n936 964 41\n936 999 5\n937 6 35\n937 11 36\n937 50 39\n937 56 47\n937 121 33\n937 144 30\n937 148 19\n937 246 27\n937 292 42\n937 310 36\n937 316 39\n937 340 38\n937 360 34\n937 390 37\n937 415 28\n937 451 26\n937 454 -1\n937 476 34\n937 496 34\n937 519 18\n937 533 37\n937 563 48\n937 572 20\n937 582 25\n937 595 40\n937 603 34\n937 649 47\n937 658 47\n937 709 6\n937 711 18\n937 727 1\n937 753 30\n937 801 14\n937 806 40\n937 830 42\n937 836 1\n937 849 49\n937 851 18\n937 869 38\n937 875 12\n937 888 2\n937 913 31\n937 922 3\n937 924 10\n937 978 39\n937 991 17\n938 15 44\n938 37 37\n938 50 10\n938 59 49\n938 121 23\n938 143 12\n938 235 23\n938 273 39\n938 339 25\n938 351 19\n938 367 13\n938 396 27\n938 415 41\n938 463 26\n938 468 20\n938 475 10\n938 506 45\n938 513 36\n938 555 10\n938 597 37\n938 601 31\n938 644 18\n938 665 29\n938 668 42\n938 670 46\n938 674 16\n938 685 17\n938 709 42\n938 731 27\n938 768 45\n938 787 17\n938 833 40\n938 841 31\n938 856 29\n938 898 1\n938 947 43\n938 955 50\n938 963 34\n938 964 31\n938 978 31\n938 986 21\n939 5 33\n939 7 34\n939 17 27\n939 46 48\n939 58 18\n939 73 25\n939 93 38\n939 122 24\n939 126 43\n939 169 23\n939 171 39\n939 179 24\n939 197 41\n939 216 12\n939 260 19\n939 262 11\n939 338 25\n939 345 48\n939 391 29\n939 392 22\n939 411 10\n939 452 24\n939 486 25\n939 493 24\n939 550 45\n939 590 33\n939 625 9\n939 666 45\n939 693 27\n939 700 20\n939 719 32\n939 783 43\n939 809 31\n939 828 29\n939 850 45\n939 851 36\n939 858 25\n939 862 21\n939 865 30\n939 877 4\n939 889 17\n939 917 38\n939 919 41\n939 986 6\n939 1000 32\n940 4 16\n940 15 32\n940 23 46\n940 37 43\n940 104 17\n940 112 43\n940 153 27\n940 242 1\n940 245 48\n940 246 10\n940 252 20\n940 270 38\n940 323 15\n940 339 15\n940 342 5\n940 369 20\n940 394 40\n940 403 37\n940 410 45\n940 412 29\n940 413 35\n940 444 39\n940 450 25\n940 452 26\n940 454 29\n940 506 7\n940 534 15\n940 537 13\n940 539 22\n940 561 11\n940 634 20\n940 635 6\n940 644 11\n940 669 26\n940 680 50\n940 702 13\n940 712 9\n940 714 21\n940 721 8\n940 736 21\n940 741 23\n940 767 38\n940 823 37\n940 863 45\n940 867 3\n940 888 30\n940 891 22\n940 908 18\n940 919 36\n940 921 35\n940 945 33\n941 1 33\n941 17 50\n941 48 35\n941 137 49\n941 197 41\n941 268 27\n941 288 17\n941 300 13\n941 327 30\n941 383 37\n941 439 18\n941 478 25\n941 482 19\n941 525 30\n941 531 41\n941 590 50\n941 596 21\n941 620 16\n941 638 12\n941 647 17\n941 657 39\n941 699 9\n941 702 10\n941 727 30\n941 736 28\n941 750 15\n941 758 37\n941 762 29\n941 767 36\n941 798 18\n941 800 13\n941 832 50\n941 836 23\n941 847 47\n941 910 25\n941 935 48\n941 936 44\n941 993 14\n942 35 40\n942 52 24\n942 74 8\n942 82 22\n942 98 28\n942 99 15\n942 125 44\n942 138 33\n942 201 28\n942 239 13\n942 247 46\n942 268 14\n942 318 40\n942 327 44\n942 329 12\n942 350 12\n942 453 49\n942 535 16\n942 558 20\n942 582 35\n942 613 33\n942 642 28\n942 654 42\n942 671 41\n942 687 16\n942 700 32\n942 706 20\n942 714 40\n942 733 50\n942 746 13\n942 755 32\n942 768 29\n942 775 42\n942 800 28\n942 802 17\n942 806 34\n942 834 11\n942 862 44\n942 876 1\n942 931 1\n942 933 44\n942 953 5\n942 978 7\n943 18 48\n943 32 23\n943 45 23\n943 47 17\n943 73 17\n943 80 5\n943 143 37\n943 161 19\n943 171 8\n943 241 19\n943 256 21\n943 353 40\n943 360 43\n943 365 27\n943 388 16\n943 414 12\n943 487 8\n943 499 38\n943 542 36\n943 551 22\n943 567 34\n943 583 40\n943 601 25\n943 687 12\n943 716 4\n943 734 3\n943 747 5\n943 748 49\n943 759 9\n943 781 41\n943 786 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49\n971 995 50\n972 35 16\n972 77 7\n972 78 42\n972 92 37\n972 127 50\n972 133 19\n972 143 49\n972 155 28\n972 180 45\n972 184 4\n972 250 33\n972 302 32\n972 312 12\n972 342 40\n972 352 20\n972 353 3\n972 363 26\n972 395 47\n972 398 24\n972 411 28\n972 416 29\n972 419 34\n972 496 22\n972 504 14\n972 512 24\n972 522 1\n972 542 22\n972 563 19\n972 565 41\n972 567 31\n972 575 13\n972 606 23\n972 650 23\n972 678 7\n972 683 17\n972 765 37\n972 777 3\n972 780 33\n972 789 45\n972 809 14\n972 852 5\n972 859 33\n972 882 11\n972 906 35\n972 909 10\n972 931 8\n972 964 30\n972 983 13\n972 988 11\n973 12 9\n973 16 21\n973 24 10\n973 28 8\n973 58 47\n973 64 45\n973 66 43\n973 88 46\n973 150 49\n973 155 43\n973 175 17\n973 183 40\n973 189 5\n973 195 8\n973 237 18\n973 269 29\n973 271 18\n973 276 28\n973 339 12\n973 346 28\n973 349 28\n973 352 7\n973 359 32\n973 368 44\n973 399 32\n973 423 21\n973 446 37\n973 641 19\n973 662 4\n973 664 50\n973 678 46\n973 679 15\n973 734 6\n973 740 12\n973 741 30\n973 747 50\n973 756 27\n973 757 43\n973 791 34\n973 825 50\n973 843 30\n973 948 30\n973 963 22\n973 974 18\n973 984 50\n974 59 28\n974 66 14\n974 74 48\n974 86 40\n974 90 28\n974 114 17\n974 131 40\n974 212 42\n974 231 37\n974 314 5\n974 412 47\n974 435 20\n974 446 39\n974 454 18\n974 474 13\n974 498 32\n974 524 6\n974 525 50\n974 539 9\n974 544 30\n974 545 32\n974 574 37\n974 581 39\n974 602 41\n974 617 38\n974 626 23\n974 685 48\n974 709 42\n974 715 31\n974 723 12\n974 738 47\n974 741 3\n974 758 31\n974 770 3\n974 797 30\n974 814 48\n974 831 20\n974 833 18\n974 852 50\n974 857 12\n974 978 41\n975 40 13\n975 47 29\n975 51 17\n975 82 5\n975 142 16\n975 143 41\n975 144 14\n975 156 33\n975 173 38\n975 205 10\n975 214 23\n975 334 48\n975 337 50\n975 341 47\n975 342 40\n975 347 21\n975 366 33\n975 372 6\n975 402 35\n975 476 19\n975 494 28\n975 513 28\n975 519 32\n975 522 2\n975 532 2\n975 557 24\n975 560 37\n975 578 27\n975 587 22\n975 621 32\n975 624 34\n975 668 8\n975 674 11\n975 675 27\n975 800 30\n975 817 31\n975 823 5\n975 832 21\n975 871 32\n975 928 -1\n975 966 12\n976 14 44\n976 53 36\n976 74 23\n976 128 49\n976 162 20\n976 221 16\n976 290 42\n976 314 5\n976 392 34\n976 401 22\n976 403 47\n976 405 21\n976 411 49\n976 449 22\n976 460 25\n976 485 8\n976 511 6\n976 536 20\n976 546 28\n976 549 9\n976 595 35\n976 645 32\n976 702 37\n976 712 6\n976 747 7\n976 779 29\n976 813 50\n976 836 34\n976 886 22\n976 895 39\n976 914 17\n976 917 37\n976 947 41\n976 961 28\n976 966 22\n976 973 38\n976 974 7\n976 988 5\n976 989 30\n977 8 37\n977 12 22\n977 20 40\n977 67 23\n977 94 46\n977 98 21\n977 114 20\n977 202 9\n977 210 45\n977 240 11\n977 260 7\n977 262 29\n977 268 48\n977 287 30\n977 382 33\n977 414 32\n977 428 32\n977 478 6\n977 496 31\n977 510 9\n977 525 7\n977 532 45\n977 564 22\n977 626 17\n977 633 37\n977 638 14\n977 659 23\n977 670 28\n977 694 19\n977 695 14\n977 701 16\n977 715 21\n977 728 40\n977 729 25\n977 732 7\n977 768 0\n977 773 32\n977 808 23\n977 830 24\n977 891 11\n977 954 43\n977 982 -1\n977 991 11\n977 999 1\n978 9 39\n978 12 10\n978 24 36\n978 42 41\n978 64 12\n978 82 45\n978 112 50\n978 122 25\n978 125 30\n978 126 37\n978 127 8\n978 158 48\n978 181 13\n978 184 35\n978 226 10\n978 231 33\n978 243 31\n978 303 8\n978 342 10\n978 351 26\n978 369 44\n978 413 14\n978 429 11\n978 481 4\n978 502 36\n978 508 7\n978 543 0\n978 561 16\n978 570 13\n978 572 45\n978 580 28\n978 592 21\n978 609 30\n978 630 15\n978 631 46\n978 679 9\n978 690 10\n978 691 30\n978 709 37\n978 710 28\n978 765 7\n978 785 13\n978 840 49\n978 886 3\n978 925 -1\n978 934 10\n978 945 -1\n978 964 16\n979 18 18\n979 40 19\n979 71 39\n979 86 43\n979 108 35\n979 110 38\n979 111 9\n979 121 49\n979 122 50\n979 129 42\n979 162 44\n979 171 32\n979 177 43\n979 259 39\n979 276 48\n979 329 25\n979 358 35\n979 391 15\n979 402 26\n979 416 32\n979 421 8\n979 500 28\n979 531 36\n979 535 20\n979 542 14\n979 550 23\n979 620 50\n979 638 10\n979 639 50\n979 644 31\n979 689 44\n979 699 34\n979 704 20\n979 739 39\n979 743 20\n979 770 17\n979 776 26\n979 887 23\n979 898 50\n979 931 46\n979 943 11\n979 968 39\n979 991 4\n980 19 44\n980 23 7\n980 53 26\n980 88 50\n980 134 42\n980 152 17\n980 174 12\n980 187 16\n980 188 40\n980 279 39\n980 282 46\n980 321 32\n980 362 47\n980 407 40\n980 409 45\n980 443 6\n980 447 38\n980 461 50\n980 471 36\n980 526 49\n980 527 39\n980 541 34\n980 550 20\n980 571 16\n980 576 37\n980 580 47\n980 603 7\n980 608 12\n980 632 18\n980 655 21\n980 692 44\n980 699 4\n980 710 9\n980 714 35\n980 729 44\n980 742 14\n980 743 20\n980 768 28\n980 795 18\n980 831 42\n980 859 30\n980 863 1\n980 890 38\n980 919 10\n980 923 16\n980 929 27\n980 953 46\n980 978 7\n980 989 9\n981 67 29\n981 118 15\n981 139 13\n981 159 25\n981 167 36\n981 192 17\n981 210 31\n981 285 10\n981 329 28\n981 330 27\n981 363 16\n981 371 48\n981 380 28\n981 418 35\n981 436 4\n981 441 17\n981 442 26\n981 446 33\n981 488 40\n981 498 43\n981 505 31\n981 547 16\n981 563 48\n981 606 18\n981 610 13\n981 612 14\n981 626 6\n981 632 44\n981 633 27\n981 692 42\n981 704 35\n981 738 38\n981 752 42\n981 818 48\n981 836 31\n981 857 26\n981 870 16\n981 882 26\n981 889 41\n981 917 23\n981 969 9\n981 984 7\n982 16 50\n982 17 26\n982 18 6\n982 21 33\n982 60 30\n982 72 20\n982 114 36\n982 136 20\n982 166 13\n982 183 40\n982 198 48\n982 290 19\n982 340 33\n982 342 15\n982 352 19\n982 357 35\n982 370 17\n982 419 33\n982 429 42\n982 431 22\n982 495 32\n982 504 16\n982 551 13\n982 558 46\n982 596 35\n982 609 25\n982 690 49\n982 699 30\n982 706 4\n982 757 29\n982 763 22\n982 767 8\n982 802 36\n982 856 7\n982 926 28\n982 979 30\n982 985 30\n982 995 8\n983 4 42\n983 24 29\n983 35 18\n983 39 45\n983 43 9\n983 59 18\n983 81 38\n983 96 20\n983 108 34\n983 134 23\n983 154 48\n983 167 45\n983 178 21\n983 222 23\n983 279 26\n983 283 33\n983 299 40\n983 326 39\n983 346 21\n983 359 22\n983 379 42\n983 382 14\n983 438 17\n983 456 6\n983 461 20\n983 482 37\n983 565 31\n983 579 50\n983 585 45\n983 587 16\n983 606 10\n983 607 29\n983 626 8\n983 697 29\n983 723 30\n983 732 32\n983 736 37\n983 739 11\n983 747 39\n983 758 39\n983 772 50\n983 792 32\n983 843 8\n983 857 17\n983 875 12\n983 880 6\n983 936 35\n983 937 32\n983 945 9\n983 946 31\n983 996 16\n984 8 36\n984 11 43\n984 62 6\n984 99 39\n984 114 16\n984 138 42\n984 196 28\n984 222 31\n984 231 42\n984 263 17\n984 311 27\n984 371 39\n984 378 12\n984 386 40\n984 412 7\n984 492 3\n984 519 25\n984 546 20\n984 574 29\n984 595 33\n984 615 23\n984 667 2\n984 701 48\n984 702 26\n984 732 43\n984 794 15\n984 802 43\n984 825 45\n984 875 44\n984 881 14\n984 899 31\n984 917 45\n984 956 46\n984 958 24\n984 987 9\n984 994 49\n985 92 39\n985 99 24\n985 121 19\n985 124 20\n985 166 28\n985 201 41\n985 205 36\n985 221 21\n985 227 32\n985 230 48\n985 250 27\n985 271 47\n985 279 27\n985 312 41\n985 329 19\n985 330 8\n985 360 29\n985 362 32\n985 378 27\n985 425 29\n985 455 24\n985 466 17\n985 484 46\n985 487 29\n985 497 15\n985 512 34\n985 515 17\n985 576 15\n985 587 40\n985 634 40\n985 646 16\n985 651 33\n985 663 26\n985 667 48\n985 670 8\n985 676 5\n985 703 20\n985 713 9\n985 730 22\n985 747 9\n985 750 48\n985 753 10\n985 783 30\n985 796 46\n985 810 34\n985 819 18\n985 828 45\n985 841 36\n985 849 50\n985 866 3\n985 905 34\n985 922 41\n985 929 20\n985 933 22\n985 956 14\n985 961 28\n985 970 18\n985 974 6\n986 48 17\n986 64 19\n986 81 10\n986 87 37\n986 142 36\n986 167 32\n986 174 47\n986 210 50\n986 240 27\n986 241 50\n986 242 30\n986 252 25\n986 257 24\n986 290 36\n986 317 19\n986 346 46\n986 367 28\n986 372 49\n986 427 22\n986 441 33\n986 449 23\n986 481 48\n986 499 47\n986 503 16\n986 523 22\n986 540 20\n986 546 35\n986 589 11\n986 605 33\n986 614 8\n986 652 47\n986 691 11\n986 698 24\n986 712 36\n986 724 11\n986 725 26\n986 788 16\n986 808 9\n986 811 47\n986 817 24\n986 855 20\n986 857 1\n986 892 25\n986 895 26\n986 951 5\n986 983 19\n987 4 34\n987 39 37\n987 76 31\n987 82 21\n987 96 16\n987 156 32\n987 195 21\n987 252 29\n987 294 47\n987 312 29\n987 323 38\n987 337 35\n987 408 36\n987 412 20\n987 416 15\n987 432 11\n987 466 29\n987 471 21\n987 492 9\n987 495 19\n987 513 21\n987 541 13\n987 546 35\n987 567 9\n987 584 29\n987 598 42\n987 607 28\n987 662 43\n987 682 37\n987 713 5\n987 722 12\n987 779 16\n987 785 27\n987 796 36\n987 872 12\n987 895 14\n987 919 16\n987 922 26\n987 931 3\n987 976 18\n987 1000 11\n988 45 33\n988 90 33\n988 103 16\n988 111 43\n988 116 29\n988 172 41\n988 195 17\n988 225 20\n988 227 32\n988 322 34\n988 326 5\n988 329 5\n988 330 36\n988 332 15\n988 336 38\n988 364 4\n988 368 7\n988 396 25\n988 399 11\n988 403 47\n988 459 11\n988 467 6\n988 481 10\n988 495 1\n988 552 35\n988 584 25\n988 681 33\n988 701 35\n988 761 44\n988 773 35\n988 780 1\n988 828 35\n988 832 21\n988 865 39\n988 875 38\n988 899 15\n988 909 44\n988 916 40\n988 927 9\n989 12 47\n989 24 42\n989 37 7\n989 42 49\n989 47 22\n989 54 29\n989 112 9\n989 158 35\n989 206 37\n989 213 45\n989 227 50\n989 232 28\n989 240 47\n989 266 46\n989 275 19\n989 324 35\n989 330 13\n989 363 30\n989 382 24\n989 433 30\n989 443 50\n989 447 35\n989 483 26\n989 492 37\n989 498 41\n989 535 37\n989 548 16\n989 551 6\n989 564 23\n989 571 38\n989 584 40\n989 599 37\n989 728 33\n989 751 16\n989 760 0\n989 780 7\n989 786 31\n989 855 28\n989 856 8\n989 882 0\n989 888 25\n989 902 17\n989 913 3\n989 918 47\n989 947 34\n989 966 12\n990 33 25\n990 65 28\n990 76 23\n990 82 9\n990 84 16\n990 108 50\n990 130 27\n990 153 45\n990 154 29\n990 157 41\n990 166 11\n990 178 49\n990 214 15\n990 232 38\n990 249 8\n990 275 11\n990 283 41\n990 294 20\n990 295 5\n990 365 23\n990 369 39\n990 385 18\n990 387 30\n990 459 27\n990 524 6\n990 538 27\n990 582 42\n990 596 13\n990 621 46\n990 636 37\n990 656 36\n990 670 35\n990 723 25\n990 738 11\n990 744 17\n990 768 41\n990 776 43\n990 836 9\n990 856 5\n990 869 13\n990 877 17\n990 916 32\n990 921 0\n990 935 1\n990 948 -2\n990 977 29\n991 5 39\n991 28 15\n991 96 27\n991 106 31\n991 132 40\n991 134 24\n991 142 27\n991 147 36\n991 208 16\n991 219 49\n991 292 19\n991 316 23\n991 325 25\n991 387 20\n991 391 47\n991 433 43\n991 452 18\n991 477 45\n991 490 48\n991 491 44\n991 524 29\n991 530 23\n991 547 8\n991 560 25\n991 571 42\n991 597 37\n991 623 23\n991 630 31\n991 691 32\n991 692 33\n991 710 33\n991 730 21\n991 751 31\n991 754 8\n991 775 39\n991 779 4\n991 785 23\n991 793 21\n991 802 14\n991 808 45\n991 821 39\n991 837 45\n991 867 12\n991 887 44\n991 916 23\n991 945 25\n991 983 37\n991 992 0\n991 993 4\n992 12 35\n992 28 36\n992 60 6\n992 77 31\n992 92 50\n992 94 39\n992 100 27\n992 111 9\n992 170 41\n992 178 25\n992 180 34\n992 205 31\n992 307 26\n992 329 30\n992 342 25\n992 350 23\n992 391 42\n992 394 48\n992 411 47\n992 413 10\n992 429 37\n992 478 15\n992 486 15\n992 530 24\n992 548 44\n992 555 42\n992 581 50\n992 602 8\n992 611 7\n992 614 24\n992 616 50\n992 618 43\n992 631 16\n992 651 9\n992 653 8\n992 675 11\n992 676 31\n992 677 30\n992 705 18\n992 711 10\n992 754 37\n992 773 12\n992 777 34\n992 787 10\n992 809 34\n992 840 42\n992 886 14\n992 926 30\n992 933 24\n992 972 35\n992 974 23\n992 978 16\n992 985 41\n992 1000 3\n993 10 12\n993 15 32\n993 78 17\n993 137 17\n993 175 31\n993 202 12\n993 227 14\n993 229 41\n993 236 7\n993 252 10\n993 267 41\n993 272 21\n993 318 33\n993 365 31\n993 368 25\n993 369 36\n993 375 32\n993 381 41\n993 389 6\n993 391 25\n993 393 44\n993 438 47\n993 468 25\n993 480 39\n993 483 30\n993 518 34\n993 522 43\n993 587 22\n993 588 15\n993 656 15\n993 659 10\n993 660 7\n993 692 41\n993 727 27\n993 741 32\n993 751 4\n993 803 36\n993 808 40\n993 813 50\n993 838 39\n993 839 34\n993 842 41\n993 845 39\n993 872 45\n993 909 19\n993 910 49\n993 913 20\n993 935 21\n993 949 17\n993 951 23\n993 981 42\n993 1000 0\n994 6 19\n994 30 14\n994 77 31\n994 116 37\n994 128 29\n994 149 38\n994 194 29\n994 203 42\n994 253 46\n994 267 49\n994 273 26\n994 300 50\n994 316 44\n994 332 47\n994 361 48\n994 379 24\n994 380 30\n994 390 29\n994 398 18\n994 429 39\n994 444 45\n994 447 36\n994 509 24\n994 535 11\n994 616 8\n994 658 12\n994 669 21\n994 671 31\n994 685 19\n994 738 14\n994 743 45\n994 784 7\n994 790 18\n994 803 17\n994 825 27\n994 840 34\n994 878 23\n994 889 28\n994 946 29\n994 947 35\n994 956 31\n994 968 39\n995 12 46\n995 19 9\n995 23 36\n995 30 24\n995 49 43\n995 51 27\n995 62 7\n995 79 30\n995 85 46\n995 99 16\n995 112 46\n995 119 32\n995 120 24\n995 124 16\n995 149 36\n995 163 15\n995 233 19\n995 242 49\n995 284 19\n995 293 45\n995 345 50\n995 432 12\n995 435 5\n995 436 38\n995 443 24\n995 445 30\n995 489 11\n995 553 12\n995 597 29\n995 642 46\n995 652 8\n995 714 40\n995 744 3\n995 777 42\n995 780 45\n995 787 29\n995 791 41\n995 823 19\n995 888 24\n995 898 37\n995 939 19\n995 954 34\n995 997 12\n996 21 47\n996 34 23\n996 37 12\n996 62 15\n996 125 21\n996 171 16\n996 188 44\n996 249 31\n996 281 34\n996 309 25\n996 342 49\n996 372 42\n996 403 45\n996 477 14\n996 484 32\n996 521 36\n996 529 40\n996 614 45\n996 625 36\n996 662 47\n996 667 50\n996 672 10\n996 691 29\n996 711 30\n996 725 15\n996 738 24\n996 742 30\n996 745 27\n996 759 43\n996 806 50\n996 837 45\n996 878 7\n996 949 42\n997 18 12\n997 40 27\n997 81 2\n997 133 32\n997 137 34\n997 158 33\n997 203 5\n997 246 12\n997 249 11\n997 286 11\n997 297 35\n997 339 14\n997 360 46\n997 397 39\n997 472 36\n997 480 31\n997 508 39\n997 516 19\n997 519 16\n997 529 5\n997 565 12\n997 597 17\n997 602 48\n997 622 2\n997 642 34\n997 655 26\n997 685 27\n997 695 42\n997 764 12\n997 768 3\n997 772 13\n997 784 32\n997 805 49\n997 809 9\n997 861 17\n997 881 14\n997 944 29\n997 960 6\n997 986 42\n997 990 4\n998 10 47\n998 50 37\n998 55 25\n998 56 50\n998 77 49\n998 87 26\n998 93 31\n998 120 49\n998 131 45\n998 134 20\n998 140 49\n998 148 19\n998 151 44\n998 155 45\n998 159 24\n998 223 39\n998 225 11\n998 242 49\n998 263 12\n998 303 32\n998 310 35\n998 331 16\n998 336 41\n998 361 12\n998 369 45\n998 387 10\n998 428 12\n998 431 50\n998 434 10\n998 494 48\n998 506 28\n998 515 1\n998 538 34\n998 542 36\n998 548 6\n998 567 39\n998 572 14\n998 574 16\n998 587 30\n998 605 10\n998 606 23\n998 632 14\n998 685 13\n998 719 4\n998 736 9\n998 740 13\n998 741 9\n998 750 41\n998 755 30\n998 768 32\n998 790 21\n998 804 37\n998 807 50\n998 811 27\n998 836 -2\n998 888 35\n998 890 9\n998 930 3\n998 949 13\n998 972 10\n998 975 41\n998 982 32\n998 988 19\n999 51 9\n999 107 45\n999 122 15\n999 151 33\n999 155 34\n999 166 50\n999 209 41\n999 221 11\n999 239 14\n999 255 25\n999 259 16\n999 267 12\n999 269 30\n999 294 29\n999 301 32\n999 316 9\n999 370 37\n999 373 21\n999 379 9\n999 386 15\n999 391 10\n999 454 10\n999 471 20\n999 490 17\n999 498 49\n999 512 19\n999 553 41\n999 559 3\n999 584 48\n999 585 17\n999 625 48\n999 629 18\n999 631 9\n999 639 43\n999 667 46\n999 702 43\n999 703 33\n999 731 45\n999 732 50\n999 787 50\n999 792 39\n999 822 39\n999 917 18\n999 926 26\n999 937 31\n999 995 12\n1000 3 42\n1000 9 45\n1000 37 39\n1000 40 17\n1000 183 24\n1000 217 31\n1000 231 49\n1000 234 10\n1000 252 20\n1000 321 25\n1000 329 19\n1000 339 49\n1000 398 42\n1000 401 27\n1000 451 40\n1000 496 35\n1000 506 24\n1000 527 21\n1000 541 12\n1000 559 22\n1000 560 25\n1000 642 49\n1000 718 14\n1000 772 1\n1000 786 43\n1000 847 46\n1000 852 48\n1000 864 44\n1000 874 37\n1000 926 48\n1000 946 39\n1000 951 16\n1000 958 23\n1000 961 18\n1000 977 33\n1000 979 1\n"
  },
  {
    "path": "floyd_warshall/problem18.8test1.txt",
    "content": "5 8\n1 2 2\n1 5 3\n2 4 -2\n3 1 1\n4 1 4\n4 3 1\n4 5 2\n5 3 -1"
  },
  {
    "path": "floyd_warshall/problem18.8test2.txt",
    "content": "5 8\n1 2 2\n1 5 3\n2 4 -2\n3 1 1\n4 1 4\n4 3 1\n4 5 -1\n5 3 -1"
  },
  {
    "path": "greedy_scheduling/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(greedy_scheduling)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(greedy_scheduling main.cpp)"
  },
  {
    "path": "greedy_scheduling/main.cpp",
    "content": "#include <iostream>\n#include <fstream>\n#include <vector>\n#include <numeric>\n\nusing namespace std;\n\nusing LL = long long;\nstruct Job {\n    LL weight, length;\n    Job(LL weight, LL length) : weight{ weight }, length{ length } {}\n};\nusing Jobs = vector<Job>;\n\nclass Solution {\npublic:\n    using Pair = pair<LL, LL>; // sub-optimal, optimal\n    Pair minSum(Jobs& jobs) {\n        auto diff = [](auto& a, auto& b) {\n            auto first = a.weight - a.length,\n                 second = b.weight - b.length;\n            return first == second ? b.weight < a.weight : second < first; // sort by descending difference, break ties in favor of jobs with larger weights\n        };\n        auto ratio = [](auto& a, auto& b) {\n            auto first = double(a.weight) / a.length,\n                 second = double(b.weight) / b.length;\n            return first == second ? b.weight < a.weight : second < first; // sort by descending ratio, break ties in favor of jobs with larger weights\n        };\n        return { calcSum(jobs, diff), calcSum(jobs, ratio) };\n    }\nprivate:\n    template<typename Comp>\n    LL calcSum(Jobs& jobs, Comp comp, LL time = 0LL) {\n        sort(jobs.begin(), jobs.end(), comp);\n        return accumulate(jobs.begin(), jobs.end(), 0LL, [&](LL total, auto& job) {\n            return total += job.weight * (time += job.length);\n        });\n    }\n};\n\nvoid run(const string& filename) {\n    Jobs jobs;\n    LL N, weight, length;\n    fstream fin{ filename };\n    for (fin >> N; fin >> weight >> length; jobs.emplace_back(Job{ weight, length }));\n    auto [diff, ratio] = Solution().minSum(jobs);\n    cout << diff << \", \" << ratio << endl;\n}\n\nint main() {\n    run(\"problem13.4test1.txt\"); // 23, 22\n    run(\"problem13.4test2.txt\"); // 68615, 67247\n    run(\"problem13.4.txt\");      // 69119377652, 67311454237\n    return 0;\n}\n"
  },
  {
    "path": "greedy_scheduling/main.js",
    "content": "let LineByLine = require('n-readlines');\n\nclass Job {\n    constructor(weight, length) {\n        this.weight = weight;\n        this.length = length;\n    }\n}\n\nclass Solution {\n    minSum(jobs) {\n        let diff = (a, b) => {\n            let first = a.weight - a.length,\n                second = b.weight - b.length;\n            return first == second ? b.weight - a.weight : second - first; // sort by descending difference, break ties in favor of jobs with larger weights\n        };\n        let ratio = (a, b) => {\n            let first = a.weight / a.length,\n                second = b.weight / b.length;\n            return first == second ? b.weight - a.weight : second - first; // sort by descending ratio, break ties in favor of jobs with larger weights\n        };\n        return [ this._calcSum(jobs, diff), this._calcSum(jobs, ratio) ];\n    }\n    _calcSum(jobs, comp, time = 0) {\n        jobs.sort((a, b) => comp(a, b));\n        return jobs.reduce((total, job) => total + job.weight * (time += job.length), 0);\n    }\n}\n\nlet run = filename => {\n    let jobs = [];\n    let input = new LineByLine(filename);\n    let line = input.next(); // N\n    while (line = input.next()) {\n        let words = String.fromCharCode(...line).trim().split(' ');\n        let [weight, length] = words.map(Number);\n        jobs.push(new Job(weight, length));\n    }\n    let [diff, ratio] = new Solution().minSum(jobs);\n    console.log(`${diff}, ${ratio}`); // sub-optimal, optimal\n};\n\nrun('problem13.4test1.txt'); // 23, 22\nrun('problem13.4test2.txt'); // 68615, 67247\nrun('problem13.4.txt');      // 69119377652, 67311454237\n"
  },
  {
    "path": "greedy_scheduling/main.kt",
    "content": "import java.io.File\n\ndata class Job(val weight: Long, val length: Long)\n\nclass Solution {\n    fun minSum(jobs: Array<Job>): Pair<Long, Long> {\n        class Diff: Comparator<Job> {\n            override fun compare(a: Job?, b: Job?): Int {\n                if (a == null || b == null)\n                    return 0\n                var first = a.weight - a.length\n                var second = b.weight - b.length\n                return if (first == second) b.weight.compareTo(a.weight) else second.compareTo(first) // sort by descending difference, break ties in favor of jobs with larger weights\n            }\n        }\n        class Ratio: Comparator<Job> {\n            override fun compare(a: Job?, b: Job?): Int {\n                if (a == null || b == null)\n                    return 0\n                var first = a.weight.toDouble() / a.length\n                var second = b.weight.toDouble() / b.length\n                return if (first == second) b.weight.compareTo(a.weight) else second.compareTo(first) // sort by descending difference, break ties in favor of jobs with larger weights\n            }\n        }\n        return Pair(calcSum(jobs, Diff()), calcSum(jobs, Ratio()))\n    }\n    private fun calcSum(jobs: Array<Job>, comp: Comparator<Job>): Long {\n        jobs.sortWith(comp)\n        var time: Long = 0\n        var total: Long = 0\n        jobs.forEach { job ->\n            time += job.length\n            total += job.weight * time\n        }\n        return total\n    }\n}\n\nfun run(filename: String) {\n    var jobs = mutableListOf<Job>()\n    var first = true\n    File(filename).forEachLine {\n        if (!first) {\n            var words = it.trim().split(\" \").map{ it.toLong() }\n            var (weight, length) = words\n            jobs.add(Job(weight, length))\n        } else {\n            first = false\n        }\n    }\n    var (diff, ratio) = Solution().minSum(jobs.toTypedArray())\n    println(\"$diff, $ratio\") // sub-optimal, optimal\n}\n\nfun main() {\n    run(\"problem13.4test1.txt\") // 23, 22\n    run(\"problem13.4test2.txt\") // 68615, 67247\n    run(\"problem13.4.txt\")      // 69119377652, 67311454237\n}\n"
  },
  {
    "path": "greedy_scheduling/main.py",
    "content": "from functools import cmp_to_key\n\nclass Job:\n    def __init__(self, weight, length):\n        self.weight = weight\n        self.length = length\n\nclass Solution:\n    def minSum(self, jobs):\n        def diff(a, b):\n            first = a.weight - a.length\n            second = b.weight - b.length\n            return b.weight - a.weight if first == second else second - first # sort by descending difference, break ties in favor of jobs with larger weights\n        def ratio(a, b):\n            first = a.weight / a.length\n            second = b.weight / b.length\n            return b.weight - a.weight if first == second else second - first # sort by descending difference, break ties in favor of jobs with larger weights\n        return [ self._calcSum(jobs, diff), self._calcSum(jobs, ratio) ]\n    def _calcSum(self, jobs, comp, time = 0, total = 0):\n        jobs.sort(key = cmp_to_key(lambda a, b: comp(a, b)))\n        for job in jobs:\n            time += job.length\n            total += job.weight * time\n        return total\n\ndef run(filename):\n    jobs = []\n    with open(filename) as fin:\n        line = fin.readline() # N\n        while True:\n            line = fin.readline().strip()\n            if not line:\n                break\n            words = line.split()\n            weight, length = [int(x) for x in words]\n            jobs.append(Job(weight, length))\n    diff, ratio = Solution().minSum(jobs)\n    print(f'{diff}, {ratio}') # sub-optimal, optimal\n\nrun('problem13.4test1.txt') # 23, 22\nrun('problem13.4test2.txt') # 68615, 67247\nrun('problem13.4.txt')      # 69119377652, 67311454237\n"
  },
  {
    "path": "greedy_scheduling/package.json",
    "content": "{\n  \"name\": \"greedy_scheduling\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"Clayton Wong\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "greedy_scheduling/problem13.4.txt",
    "content": "10000\n8 50\n74 59\n31 73\n45 79\n24 10\n41 66\n93 43\n88 4\n28 30\n41 13\n4 70\n10 58\n61 34\n100 79\n17 36\n98 27\n13 68\n11 34\n80 50\n80 22\n68 73\n94 37\n86 46\n29 92\n95 58\n2 54\n9 45\n69 91\n25 97\n31 4\n23 67\n50 25\n2 54\n78 9\n29 34\n99 82\n36 14\n66 15\n64 37\n26 70\n16 95\n30 2\n18 96\n6 5\n52 99\n89 24\n6 83\n53 67\n17 38\n39 45\n2 98\n72 29\n38 59\n78 98\n95 5\n10 32\n46 76\n36 99\n43 100\n69 13\n61 58\n95 9\n96 69\n14 31\n7 63\n43 66\n83 53\n68 22\n96 13\n72 2\n91 32\n39 58\n17 91\n41 80\n36 7\n73 99\n96 20\n55 24\n90 61\n6 27\n24 7\n14 71\n39 95\n21 45\n67 35\n27 95\n64 39\n45 91\n51 60\n24 48\n86 18\n73 40\n48 86\n97 86\n24 21\n45 69\n36 16\n26 35\n43 12\n80 53\n45 96\n19 97\n93 16\n92 34\n70 98\n54 48\n26 11\n63 12\n9 78\n62 26\n36 69\n96 77\n68 40\n75 32\n57 2\n73 61\n95 85\n56 90\n8 16\n94 70\n81 56\n56 7\n64 3\n77 9\n50 32\n45 39\n9 98\n52 50\n4 32\n32 15\n20 76\n10 81\n30 24\n55 61\n38 46\n18 26\n1 57\n65 98\n49 5\n51 51\n77 13\n55 98\n5 82\n49 66\n79 100\n10 30\n54 84\n48 8\n74 23\n6 77\n54 25\n31 67\n1 45\n71 86\n17 99\n56 34\n58 77\n79 67\n58 12\n79 15\n20 38\n34 92\n21 63\n34 98\n32 89\n90 74\n78 5\n59 1\n55 61\n16 48\n81 31\n56 47\n8 39\n1 27\n36 58\n14 15\n94 61\n55 19\n58 86\n30 16\n64 3\n18 44\n20 68\n48 70\n96 4\n74 4\n49 86\n59 60\n7 31\n25 33\n74 4\n98 21\n51 32\n81 4\n1 21\n34 59\n4 77\n51 35\n81 80\n33 75\n50 43\n50 72\n11 80\n84 71\n41 24\n51 72\n30 19\n47 100\n31 22\n77 25\n45 59\n97 72\n65 61\n99 52\n41 4\n52 2\n6 81\n19 75\n50 14\n21 26\n13 84\n89 18\n9 51\n25 96\n58 12\n91 67\n11 94\n54 66\n61 43\n4 53\n8 42\n11 1\n100 28\n72 88\n15 26\n42 18\n49 43\n16 75\n46 74\n21 12\n40 55\n6 30\n54 90\n67 57\n5 61\n99 93\n21 17\n81 68\n53 40\n99 2\n12 17\n92 72\n29 72\n62 46\n21 41\n59 54\n28 51\n12 64\n95 34\n28 28\n96 32\n43 17\n7 16\n25 2\n98 62\n4 25\n9 37\n82 16\n11 17\n6 74\n82 21\n92 70\n66 28\n37 29\n26 85\n68 50\n77 47\n77 67\n68 21\n85 92\n11 59\n12 45\n19 19\n35 26\n68 90\n19 15\n26 19\n29 30\n35 28\n41 55\n41 97\n36 84\n49 66\n12 53\n65 77\n38 76\n46 11\n16 93\n11 48\n38 100\n48 16\n94 80\n30 65\n80 2\n26 90\n59 34\n1 90\n71 18\n47 39\n44 39\n37 22\n20 97\n48 89\n60 88\n36 36\n13 85\n90 85\n35 68\n20 16\n46 77\n62 26\n20 32\n4 99\n99 40\n5 4\n80 66\n92 8\n25 66\n22 55\n7 51\n4 33\n33 42\n55 78\n18 1\n90 66\n48 23\n80 18\n17 49\n63 30\n40 9\n4 58\n62 53\n67 22\n58 97\n56 31\n95 56\n22 13\n94 28\n33 45\n92 99\n53 57\n71 4\n40 15\n100 67\n36 22\n44 53\n87 20\n51 11\n24 70\n6 44\n12 32\n93 17\n100 72\n40 71\n37 92\n58 34\n29 78\n11 84\n77 90\n92 35\n12 5\n27 92\n91 23\n65 91\n85 14\n42 28\n80 85\n38 71\n62 82\n66 3\n33 33\n55 60\n48 78\n63 11\n20 51\n78 42\n37 21\n100 13\n60 57\n91 53\n49 15\n45 19\n51 2\n96 22\n32 2\n46 62\n58 11\n29 6\n74 38\n70 97\n4 22\n76 19\n1 90\n63 55\n64 44\n90 51\n36 16\n65 95\n64 59\n53 93\n17 15\n21 61\n51 69\n42 48\n97 88\n2 35\n29 72\n49 76\n54 72\n30 94\n20 72\n21 65\n80 31\n11 81\n14 43\n39 83\n45 29\n94 76\n81 1\n97 48\n71 88\n44 34\n53 62\n25 1\n81 79\n58 24\n99 15\n46 63\n10 11\n50 19\n91 56\n44 56\n86 35\n76 22\n52 27\n52 60\n84 15\n38 80\n99 1\n38 86\n79 85\n43 16\n61 68\n41 8\n67 29\n63 64\n70 91\n24 79\n14 62\n11 41\n79 1\n95 8\n57 52\n87 32\n45 40\n77 85\n53 9\n15 55\n20 29\n72 71\n64 48\n25 44\n55 9\n82 53\n89 64\n60 20\n80 57\n62 88\n54 100\n89 45\n81 67\n84 75\n37 10\n68 35\n40 85\n52 50\n67 68\n11 90\n28 74\n82 96\n37 75\n36 32\n73 29\n99 71\n88 98\n90 47\n91 12\n13 64\n13 82\n52 31\n22 14\n29 51\n1 60\n55 93\n95 31\n33 60\n78 80\n33 73\n84 82\n54 23\n22 57\n19 92\n1 97\n21 5\n100 30\n45 76\n71 17\n100 81\n19 89\n53 29\n1 63\n41 50\n86 84\n16 60\n79 60\n62 83\n49 55\n41 82\n71 29\n52 45\n70 96\n70 11\n73 24\n26 20\n51 32\n44 47\n70 71\n95 11\n93 65\n25 62\n20 21\n63 62\n26 35\n50 91\n23 61\n94 29\n23 82\n67 69\n24 23\n40 18\n94 65\n79 57\n72 42\n56 37\n90 29\n21 3\n13 17\n48 47\n52 73\n12 24\n37 6\n8 34\n67 54\n13 26\n41 54\n58 34\n96 40\n52 59\n95 61\n39 30\n76 99\n93 34\n63 77\n37 47\n74 65\n85 93\n20 43\n29 60\n63 46\n17 28\n73 49\n1 71\n99 93\n46 29\n1 44\n93 64\n84 73\n2 10\n22 87\n14 70\n32 58\n20 87\n57 17\n55 55\n15 16\n38 67\n98 78\n61 13\n92 32\n75 64\n78 25\n85 34\n51 28\n100 30\n10 45\n65 52\n13 80\n35 8\n84 1\n60 11\n54 92\n22 26\n54 30\n97 54\n62 59\n92 64\n21 69\n88 27\n73 20\n42 5\n52 93\n46 71\n75 63\n77 18\n27 14\n45 72\n80 36\n30 89\n49 79\n18 24\n39 9\n30 27\n69 7\n100 56\n30 77\n89 97\n20 65\n38 17\n19 92\n84 99\n21 49\n62 52\n19 78\n47 62\n79 29\n64 36\n7 9\n69 80\n20 24\n78 93\n54 79\n54 96\n72 76\n5 63\n33 20\n32 36\n69 69\n11 35\n71 79\n66 46\n80 76\n28 88\n64 38\n67 35\n84 76\n85 56\n57 100\n65 94\n87 34\n25 48\n95 31\n68 66\n11 83\n6 15\n53 42\n86 92\n7 61\n61 13\n4 31\n86 1\n86 68\n85 89\n1 87\n1 96\n100 3\n29 84\n18 37\n3 90\n79 26\n90 23\n96 6\n20 92\n22 75\n15 63\n7 84\n27 20\n2 31\n45 76\n59 63\n32 37\n21 9\n25 48\n9 12\n98 1\n15 97\n100 46\n34 63\n40 55\n22 87\n37 11\n63 74\n94 36\n89 72\n39 22\n92 14\n61 58\n93 44\n76 69\n14 16\n37 92\n48 70\n33 35\n29 44\n80 7\n55 8\n38 4\n22 48\n35 50\n17 60\n39 51\n84 87\n97 86\n25 23\n64 82\n13 52\n3 96\n37 55\n9 81\n32 31\n96 15\n13 37\n38 10\n86 20\n82 11\n9 10\n40 68\n20 67\n100 21\n16 78\n23 43\n81 82\n86 31\n26 37\n95 46\n3 34\n81 57\n35 18\n82 82\n59 6\n93 61\n52 2\n43 45\n36 56\n73 44\n23 14\n42 82\n80 19\n61 30\n56 83\n65 33\n14 96\n29 5\n56 12\n82 11\n5 52\n17 62\n65 6\n23 14\n44 37\n19 95\n89 44\n40 3\n44 71\n20 13\n18 33\n83 98\n60 74\n91 20\n11 12\n16 79\n43 46\n71 63\n9 84\n100 10\n14 51\n52 66\n3 18\n54 100\n17 85\n70 43\n4 16\n30 58\n83 65\n53 55\n27 28\n56 60\n53 87\n23 30\n87 50\n80 99\n91 4\n87 44\n28 86\n99 88\n18 32\n77 62\n64 15\n84 33\n23 12\n92 72\n43 34\n54 31\n81 5\n16 88\n11 82\n59 87\n34 41\n60 37\n63 39\n55 27\n27 13\n96 22\n78 42\n59 55\n21 98\n28 52\n63 33\n38 5\n58 6\n8 44\n59 40\n44 98\n82 66\n58 6\n18 13\n25 85\n60 100\n17 41\n52 47\n23 94\n16 50\n62 50\n32 97\n24 97\n45 51\n39 32\n60 36\n66 2\n88 38\n49 21\n25 95\n76 4\n90 87\n46 44\n58 33\n62 79\n5 3\n32 21\n87 31\n44 68\n49 45\n18 50\n26 74\n64 17\n81 49\n80 58\n15 6\n90 8\n6 28\n15 16\n9 98\n50 96\n30 27\n67 99\n86 63\n19 54\n80 4\n84 24\n60 22\n75 35\n76 3\n37 80\n16 51\n14 51\n93 49\n84 82\n48 9\n7 79\n7 68\n15 11\n71 59\n18 47\n5 57\n64 38\n99 35\n57 9\n13 14\n81 25\n5 14\n74 63\n80 78\n70 48\n32 54\n34 40\n21 95\n98 25\n72 59\n21 49\n19 2\n18 93\n14 81\n57 41\n95 69\n71 64\n50 35\n26 72\n92 51\n18 11\n55 26\n2 95\n93 35\n71 47\n88 22\n66 90\n72 66\n61 11\n76 10\n95 24\n35 75\n15 95\n24 76\n78 58\n28 23\n75 73\n40 40\n84 18\n31 91\n7 97\n13 96\n39 17\n22 85\n28 79\n61 73\n88 36\n82 27\n95 31\n96 59\n20 13\n44 13\n7 29\n94 27\n27 27\n34 82\n97 93\n62 10\n78 25\n23 41\n53 16\n81 93\n52 53\n74 78\n18 27\n66 62\n40 50\n8 20\n31 77\n26 82\n28 60\n98 94\n26 30\n23 49\n54 80\n69 28\n25 32\n78 7\n1 73\n2 31\n99 78\n50 95\n28 53\n60 78\n71 52\n25 85\n21 16\n20 78\n96 96\n65 1\n19 18\n24 18\n55 69\n88 76\n14 23\n58 17\n83 43\n63 9\n41 6\n71 7\n2 20\n21 63\n18 36\n53 95\n36 11\n32 64\n52 48\n52 11\n50 48\n35 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63\n64 70\n38 2\n15 31\n6 39\n68 22\n98 70\n30 2\n70 6\n75 92\n81 17\n52 95\n32 59\n15 45\n14 30\n70 54\n60 74\n98 24\n44 83\n61 36\n37 100\n48 6\n6 66\n29 91\n85 89\n69 60\n9 35\n16 96\n59 29\n90 36\n81 18\n95 72\n54 89\n84 79\n27 92\n11 59\n67 38\n59 92\n62 35\n48 61\n68 74\n55 18\n98 96\n22 6\n22 25\n71 87\n23 95\n48 23\n9 40\n28 68\n16 31\n98 82\n60 95\n55 35\n70 21\n59 85\n14 67\n98 4\n33 55\n5 82\n74 80\n30 70\n87 52\n8 95\n26 38\n6 33\n68 93\n16 35\n76 53\n4 87\n22 94\n51 52\n74 85\n22 29\n8 99\n2 27\n99 45\n26 12\n19 93\n2 17\n15 85\n82 88\n45 7\n67 87\n83 11\n2 47\n86 45\n80 60\n55 70\n59 74\n24 61\n73 29\n40 79\n67 83\n35 58\n8 30\n30 34\n70 33\n4 77\n53 82\n84 25\n20 57\n75 72\n85 17\n71 21\n24 85\n88 67\n49 84\n89 70\n22 15\n56 48\n84 17\n100 50\n55 68\n42 95\n15 76\n38 22\n84 45\n68 3\n35 88\n16 78\n95 18\n63 32\n30 88\n53 12\n3 23\n73 81\n87 20\n78 47\n21 31\n22 23\n59 74\n50 7\n84 22\n67 70\n17 93\n24 94\n71 64\n39 76\n93 86\n31 51\n71 91\n67 77\n76 20\n38 23\n74 44\n47 71\n82 83\n98 40\n92 71\n53 26\n25 71\n55 55\n95 61\n40 29\n78 32\n93 79\n69 82\n73 28\n15 65\n63 75\n65 41\n92 95\n43 5\n7 36\n97 87\n89 74\n78 42\n79 60\n91 89\n53 26\n27 5\n19 89\n87 55\n36 87\n16 49\n48 91\n81 41\n86 23\n92 57\n36 31\n36 30\n9 36\n77 93\n89 39\n23 63\n93 69\n36 92\n64 46\n68 11\n78 81\n68 92\n24 95\n38 36\n9 81\n100 88\n9 77\n85 22\n1 36\n6 98\n46 32\n80 35\n43 88\n25 95\n37 96\n86 6\n98 89\n65 23\n2 11\n97 48\n55 90\n77 52\n6 93\n73 35\n62 31\n84 1\n93 11\n100 46\n72 60\n98 2\n28 74\n87 7\n67 9\n78 10\n93 48\n86 63\n82 37\n66 33\n50 11\n52 47\n11 16\n35 63\n55 94\n27 94\n5 79\n2 3\n39 3\n15 2\n31 38\n67 53\n81 91\n33 60\n19 91\n3 26\n18 59\n82 24\n58 87\n92 3\n90 87\n48 2\n64 30\n95 63\n61 41\n3 21\n100 94\n51 3\n94 85\n94 13\n30 52\n74 60\n66 29\n7 9\n73 25\n50 4\n89 60\n45 4\n12 25\n30 46\n43 49\n42 80\n55 80\n55 48\n1 67\n57 91\n40 70\n100 34\n14 23\n56 10\n38 86\n10 68\n2 97\n16 45\n19 25\n59 75\n44 35\n85 73\n96 22\n100 100\n33 28\n76 45\n66 25\n44 99\n37 12\n71 78\n10 70\n99 79\n71 42\n82 27\n56 53\n26 73\n77 57\n93 14\n63 41\n71 17\n70 12\n94 5\n56 4\n57 96\n89 51\n9 78\n44 43\n12 20\n93 57\n6 49\n91 50\n93 8\n73 96\n70 27\n9 87\n71 10\n1 94\n88 92\n100 6\n32 23\n58 2\n62 1\n57 50\n82 6\n79 12\n77 65\n47 7\n67 2\n97 36\n44 15\n55 43\n10 75\n23 99\n66 64\n14 15\n96 64\n96 2\n99 70\n64 35\n95 72\n3 92\n50 59\n57 83\n43 31\n16 89\n85 33\n55 15\n10 43\n46 57\n64 81\n6 49\n55 81\n13 30\n83 22\n36 36\n85 90\n30 87\n79 5\n61 74\n24 27\n13 3\n87 89\n87 16\n23 49\n60 69\n80 68\n88 98\n12 96\n23 28\n27 100\n17 78\n87 58\n33 69\n16 20\n49 10\n3 88\n53 99\n87 65\n26 60\n42 51\n69 98\n77 15\n29 80\n55 30\n32 53\n56 88\n43 62\n94 97\n6 98\n31 95\n8 10\n9 81\n95 25\n9 81\n2 33\n78 18\n8 60\n23 15\n85 12\n81 26\n81 12\n100 10\n55 39\n78 53\n58 5\n55 78\n9 94\n9 44\n58 66\n56 71\n16 28\n40 18\n40 89\n71 3\n41 16\n28 6\n32 28\n63 62\n40 17\n95 45\n25 1\n10 89\n86 46\n41 98\n5 69\n8 98\n20 16\n13 70\n62 23\n99 91\n53 48\n23 69\n94 87\n48 35\n91 39\n7 80\n25 93\n26 99\n66 9\n69 46\n48 87\n62 9\n60 37\n71 55\n3 85\n4 72\n42 38\n85 29\n68 75\n98 38\n23 18\n100 48\n21 52\n74 81\n42 73\n97 95\n84 84\n37 30\n24 44\n53 14\n89 51\n58 80\n73 17\n82 77\n39 57\n23 22\n26 37\n19 98\n82 44\n25 68\n38 56\n46 92\n45 11\n7 15\n86 82\n61 98\n41 86\n95 29\n85 64\n59 24\n25 88\n61 12\n33 53\n38 39\n21 71\n97 98\n76 43\n10 55\n98 47\n92 9\n97 61\n84 61\n92 36\n87 1\n89 39\n17 36\n71 10\n41 85\n72 17\n46 63\n95 1\n83 7\n14 13\n22 42\n75 79\n33 22\n37 44\n80 46\n6 51\n47 7\n11 72\n52 67\n43 23\n4 48\n82 14\n15 67\n76 100\n29 74\n22 100\n5 60\n74 56\n53 78\n16 48\n24 64\n74 1\n38 9\n88 77\n39 27\n98 3\n37 15\n33 57\n96 40\n41 71\n66 54\n87 54\n74 16\n61 65\n51 97\n98 3\n57 38\n78 76\n79 92\n42 35\n86 87\n94 14\n67 80\n15 94\n15 94\n14 49\n78 82\n46 6\n45 59\n71 5\n83 40\n78 12\n68 93\n85 81\n13 80\n86 37\n34 80\n49 47\n34 15\n58 57\n46 94\n44 80\n68 84\n58 1\n62 22\n44 16\n94 12\n79 100\n1 93\n100 17\n83 67\n75 41\n44 52\n61 13\n92 50\n29 21\n49 25\n12 70\n95 98\n22 8\n53 52\n25 76\n20 6\n3 76\n64 77\n61 64\n86 28\n87 62\n86 85\n57 27\n55 99\n77 95\n60 89\n60 99\n21 26\n15 58\n9 27\n69 16\n86 2\n49 81\n53 2\n91 45\n61 40\n89 60\n56 75\n61 50\n40 94\n74 31\n1 7\n72 90\n62 55\n13 24\n54 80\n89 65\n33 22\n81 34\n93 39\n22 74\n54 99\n55 90\n94 11\n43 74\n86 49\n50 58\n58 59\n89 57\n74 74\n7 94\n56 47\n9 68\n59 49\n4 59\n44 81\n50 89\n97 50\n43 23\n10 54\n24 27\n89 33\n7 34\n88 75\n70 67\n62 88\n57 10\n74 7\n16 15\n43 94\n45 93\n99 87\n79 66\n38 38\n19 22\n49 63\n21 8\n98 19\n50 38\n47 86\n29 45\n92 64\n62 75\n1 91\n4 35\n43 15\n71 10\n19 27\n59 9\n100 90\n12 43\n33 75\n41 73\n47 29\n48 57\n17 82\n55 65\n79 12\n80 100\n23 96\n11 30\n94 32\n60 24\n73 69\n71 66\n76 68\n84 5\n29 56\n84 21\n66 85\n47 34\n78 98\n4 99\n59 100\n55 62\n47 39\n15 22\n17 18\n78 60\n70 80\n73 11\n75 76\n68 56\n90 57\n92 5\n36 19\n8 61\n48 49\n69 51\n8 43\n48 79\n99 54\n54 75\n86 58\n52 78\n67 58\n100 44\n46 69\n38 93\n16 95\n69 34\n63 47\n71 48\n68 8\n19 62\n87 74\n27 88\n54 56\n85 93\n71 63\n31 38\n21 7\n27 15\n29 53\n31 80\n28 39\n91 67\n5 35\n67 26\n24 32\n5 10\n99 45\n76 75\n60 57\n89 30\n31 85\n86 95\n59 90\n89 42\n83 77\n69 87\n38 1\n69 50\n30 60\n46 8\n2 96\n34 94\n40 99\n66 99\n78 65\n81 8\n37 81\n22 32\n74 31\n13 15\n74 7\n8 18\n1 97\n17 83\n54 100\n63 86\n78 17\n36 28\n64 51\n100 9\n14 92\n8 23\n78 26\n32 63\n10 84\n41 55\n4 23\n43 72\n38 92\n83 25\n56 99\n100 47\n100 26\n24 17\n24 34\n32 10\n22 99\n71 98\n96 59\n99 74\n2 75\n70 54\n24 36\n75 15\n75 93\n98 82\n52 9\n42 82\n38 3\n5 20\n70 19\n56 92\n96 8\n48 66\n77 66\n30 13\n96 24\n75 74\n8 70\n99 63\n99 16\n72 93\n24 3\n15 86\n55 4\n90 55\n69 52\n22 37\n79 75\n51 60\n42 33\n47 9\n50 84\n5 32\n35 62\n53 97\n70 51\n88 3\n33 61\n60 65\n40 68\n100 96\n7 44\n54 100\n79 2\n79 90\n11 99\n51 66\n10 91\n44 16\n2 46\n44 8\n28 9\n70 56\n20 25\n13 53\n70 38\n43 23\n37 70\n97 59\n50 48\n14 75\n79 59\n75 65\n38 73\n18 37\n19 30\n94 52\n61 20\n57 76\n100 37\n11 39\n50 28\n34 78\n28 14\n98 55\n70 39\n96 76\n47 59\n40 86\n21 14\n36 98\n86 6\n59 45\n80 99\n39 61\n2 23\n30 51\n93 96\n84 71\n36 36\n72 4\n89 64\n8 89\n8 58\n79 53\n80 47\n10 42\n63 14\n49 18\n55 39\n96 47\n42 26\n90 6\n60 52\n42 85\n28 17\n68 9\n10 33\n45 11\n2 53\n74 33\n36 16\n21 27\n57 89\n55 40\n9 96\n61 2\n44 97\n91 90\n7 69\n84 4\n9 62\n46 50\n6 49\n93 33\n66 23\n30 75\n5 27\n83 11\n19 18\n14 89\n87 45\n56 48\n34 54\n11 82\n6 77\n95 44\n16 27\n73 53\n71 83\n92 97\n34 63\n25 38\n57 88\n51 40\n69 25\n85 17\n15 35\n91 23\n50 49\n99 64\n17 74\n74 9\n95 9\n37 53\n60 54\n56 63\n4 38\n68 15\n"
  },
  {
    "path": "greedy_scheduling/problem13.4test1.txt",
    "content": "2\n3 5\n1 2\n"
  },
  {
    "path": "greedy_scheduling/problem13.4test2.txt",
    "content": "12\n8 50\n74 59\n31 73\n45 79\n24 10\n41 66\n93 43\n88 4\n28 30\n41 13\n4 70\n10 58\n"
  },
  {
    "path": "huffman/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(huffman)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(huffman main.cpp)"
  },
  {
    "path": "huffman/main.cpp",
    "content": "/*\n * Programming Problem 14.6: Huffman Codes\n *\n * In this problem the file format is:\n * [number_of_symbols]\n * [weight of symbol #1]\n * [weight of symbol #2]\n * ...\n */\n\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <queue>\n#include <list>\n\n#define PRIORITY_QUEUE    // O(N * logN)\n#ifndef PRIORITY_QUEUE\n#define TWO_QUEUES        // O(N)\n#endif\n\nusing namespace std;\nusing LL = long long;\nusing Weight = LL;\nusing Weights = vector<Weight>;\n\nstruct Tree;\nusing TreePtr = shared_ptr<Tree>;\nstruct Tree {\n    Weight weight;\n    TreePtr left, right;\n    Tree(Weight weight, TreePtr left = nullptr, TreePtr right = nullptr) :\n            weight{ weight }, left{ left }, right{ right } {}\n};\nusing TreePtrs = vector<TreePtr>;\n\n#ifdef PRIORITY_QUEUE\nstruct Comp {\n    size_t operator()(const TreePtr& a, const TreePtr& b) const {\n        return b->weight < a->weight;\n    }\n};\nusing Queue = priority_queue<TreePtr, TreePtrs, Comp>;\nTreePtr encode(const Weights& A, Queue q = {}) {\n    for (auto weight: A)\n        q.emplace(make_shared<Tree>(weight));\n    while (1 < q.size()) {\n        auto a = q.top(); q.pop();\n        auto b = q.top(); q.pop();\n        auto c = make_shared<Tree>(a->weight + b->weight, a, b);\n        q.emplace(c);\n    }\n    return q.top();\n}\n#else // TWO_QUEUES\n/*\n * Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n * of a sorting subroutine, followed by a linear amount of additional work.\n */\nusing Queue = queue<TreePtr>;\nTreePtr encode(Weights& A, Queue first = {}, Queue second = {}) {\n    sort(A.begin(), A.end());\n    for (auto weight: A)\n        first.push(make_shared<Tree>(weight));\n    TreePtrs next;\n    auto takeFirst = [&]() { next.push_back(first.front()), first.pop(); };\n    auto takeSecond = [&]() { next.push_back(second.front()), second.pop(); };\n    while (1 < first.size() + second.size()) {\n        next.clear();\n        do {\n            if (first.size() && second.size()) {\n                if (first.front()->weight < second.front()->weight) takeFirst(); else takeSecond();\n            }\n            else if (first.size()) takeFirst();\n            else if (second.size()) takeSecond();\n        } while (next.size() < 2);\n        auto [a, b] = tie(next[0], next[1]);\n        auto c = make_shared<Tree>(a->weight + b->weight, a, b);\n        second.emplace(c);\n    }\n    return second.front();\n}\n#endif\n\nusing MinMax = pair<LL, LL>;\nconstexpr auto Min = numeric_limits<LL>::min();\nconstexpr auto Max = numeric_limits<LL>::max();\nMinMax run(const string& filename) {\n    Weights A; // weight of each symbol\n    fstream fin{ filename };\n    LL N, weight;\n    for (fin >> N; fin >> weight; A.push_back(weight));\n    auto tree = encode(A);\n    LL lo = Max,\n       hi = Min;\n    using fun = function<void(TreePtr, int)>;\n    fun go = [&](auto root, LL depth) {\n        if (!root)\n            return;\n        auto isLeaf = [](auto root) { return !root->left && !root->right; };\n        if (isLeaf(root))\n            lo = min(lo, depth),\n            hi = max(hi, depth);\n        else\n            go(root->left, depth + 1),\n            go(root->right, depth + 1);\n    };\n    go(tree, 0);\n    return make_pair(lo, hi);\n}\n\nint main() {\n    for (auto& filename: { \"problem14.6test1.txt\", \"problem14.6test2.txt\", \"problem14.6.txt\" }) {\n        auto [lo, hi] = run(filename);\n        cout << filename << \": \" << lo << \", \" << hi << endl; // min, max encoding length in the corresponding optimal prefix-free tree\n    }\n//    problem14.6test1.txt: 2, 5\n//    problem14.6test2.txt: 3, 6\n//    problem14.6.txt: 9, 19\n    return 0;\n}\n"
  },
  {
    "path": "huffman/main.js",
    "content": "/*\n * Programming Problem 14.6: Huffman Codes\n *\n * In this problem the file format is:\n * [number_of_symbols]\n * [weight of symbol #1]\n * [weight of symbol #2]\n * ...\n */\n\nlet LineByLine = require('n-readlines');\n\nclass Tree {\n    constructor(weight, left = null, right = null) {\n        this.weight = weight;\n        this.left = left;\n        this.right = right;\n    }\n}\n\n/*\nlet key = x => Array.isArray(x) ? x[0] : x;\nlet heappush = (A, x, f = Math.min) => {\n    let P = i => Math.floor((i - 1) / 2);  // parent\n    A.push(x);\n    let N = A.length,\n        i = N - 1;\n    while (0 < i && key(A[i]) == f(key(A[i]), key(A[P(i)]))) {\n        [A[i], A[P(i)]] = [A[P(i)], A[i]];\n        i = P(i);\n    }\n};\nlet heappop = (A, f = Math.min) => {\n    let L = i => 2 * i + 1,  // children\n        R = i => 2 * i + 2;\n    let N = A.length,\n        i = 0;\n    let top = A[0];\n    [A[0], A[N - 1]] = [A[N - 1], A[0]], A.pop(), --N;\n    let ok;\n    do {\n        ok = true;\n        let left = f == Math.min ? Infinity : -Infinity,\n            right = left;\n        if (L(i) < N && key(A[i]) != f(key(A[i]), key(A[L(i)]))) ok = false, left  = key(A[L(i)]);\n        if (R(i) < N && key(A[i]) != f(key(A[i]), key(A[R(i)]))) ok = false, right = key(A[R(i)]);\n        if (!ok) {\n            let j = left == f(left, right) ? L(i) : R(i);\n            [A[i], A[j]] = [A[j], A[i]];\n            i = j;\n        }\n    } while (!ok);\n    return top;\n};\n\nlet encode = A => {\n    let T = [];\n    for (let weight of A)\n        heappush(T, [ weight, new Tree(weight) ]);\n    while (1 < T.length) {\n        let [ a, b ] = [ heappop(T), heappop(T) ];\n        let c = [ a[0] + b[0], new Tree(a[0] + b[0], a[1], b[1]) ];\n        heappush(T, c);\n    }\n    return T[0][1];\n};\n*/\n\n/*\n * Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n * of a sorting subroutine, followed by a linear amount of additional work.\n */\nlet encode = A => {\n    A.sort((a, b) => a - b)\n    let first = A.map(weight => new Tree(weight)),\n        second = [];\n    while (1 < first.length + second.length) {\n        let next = [];\n        while (next.length < 2) {\n            if (first.length && second.length) {\n                next.push(first[0].weight < second[0].weight ? first.shift() : second.shift());\n            }\n            else if (first.length) next.push(first.shift());\n            else if (second.length) next.push(second.shift());\n        }\n        let [a, b] = next;\n        let c = new Tree(a.weight + b.weight, a, b);\n        second.push(c);\n    }\n    return second.shift();\n};\n\nlet run = filename => {\n    let A = [];\n    let input = new LineByLine(filename);\n    let line;\n    line = input.next(); // N\n    while (line = input.next()) {\n        let weight = Number(String.fromCharCode(...line).trim());\n        A.push(weight);\n    }\n    let tree = encode(A);\n    let [lo, hi] = [Infinity, -Infinity];\n    let go = (root = tree, depth = 0) => {\n        if (!root)\n            return;\n        let isLeaf = root => !root.left && !root.right;\n        if (isLeaf(root))\n            lo = Math.min(lo, depth),\n            hi = Math.max(hi, depth);\n        else\n            go(root.left, depth + 1),\n            go(root.right, depth + 1);\n    };\n    go();\n    return [ lo, hi ];\n}\n\nfor (let filename of [ 'problem14.6test1.txt', 'problem14.6test2.txt', 'problem14.6.txt' ]) {\n    let [lo, hi] = run(filename);\n    console.log(`${filename}: ${lo}, ${hi}`); // min, max encoding length in the corresponding optimal prefix-free tree\n}\n\n//    problem14.6test1.txt: 2, 5\n//    problem14.6test2.txt: 3, 6\n//    problem14.6.txt: 9, 19\n"
  },
  {
    "path": "huffman/main.kt",
    "content": "/*\n * Programming Problem 14.6: Huffman Codes\n *\n * In this problem the file format is:\n * [number_of_symbols]\n * [weight of symbol #1]\n * [weight of symbol #2]\n * ...\n */\n\nimport java.io.File\nimport java.util.PriorityQueue\nimport java.util.Queue\nimport java.util.LinkedList\n\nvar INF = (1e9 + 7).toInt()\n\ndata class Tree(val weight: Int, val left: Tree? = null, val right: Tree? = null)\n\n/*\nfun encode(A: List<Int>): Tree {\n    var q = PriorityQueue<Tree>(Comparator{ a: Tree, b: Tree -> a.weight.compareTo(b.weight) })\n    for (weight in A)\n        q.add(Tree(weight))\n    while (1 < q.size) {\n        var a = q.poll()\n        var b = q.poll()\n        var c = Tree(a.weight + b.weight, a, b)\n        q.add(c)\n    }\n    return q.poll()\n}\n*/\n\n/*\n * Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n * of a sorting subroutine, followed by a linear amount of additional work.\n */\nfun encode(A: MutableList<Int>): Tree {\n    A.sort()\n    var first: Queue<Tree> = LinkedList<Tree>(A.map{ weight -> Tree(weight) }.toList())\n    var second: Queue<Tree> = LinkedList<Tree>()\n    var next = mutableListOf<Tree>()\n    while (1 < first.size + second.size) {\n        next.clear()\n        do {\n            if (0 < first.size && 0 < second.size) {\n                if (first.peek().weight < second.peek().weight) next.add(first.poll()) else next.add(second.poll())\n            }\n            else if (0 < first.size) next.add(first.poll())\n            else if (0 < second.size) next.add(second.poll())\n        } while (next.size < 2)\n        var (a, b) = next\n        var c = Tree(a.weight + b.weight, a, b)\n        second.add(c)\n    }\n    return second.poll()\n}\n\nfun run(filename: String): Pair<Int, Int> {\n    var A = mutableListOf<Int>()\n    var first = true\n    File(filename).forEachLine {\n        if (!first) {\n            var weight = it.trim().toInt()\n            A.add(weight)\n        } else {\n            first = false\n        }\n    }\n    var tree = encode(A.toMutableList())\n    var lo = INF\n    var hi = -INF\n    fun go(root: Tree? = tree, depth: Int = 0) {\n        if (root == null)\n            return\n        var isLeaf = { node: Tree? -> node?.left == null && node?.right == null }\n        if (isLeaf(root)) {\n            lo = Math.min(lo, depth)\n            hi = Math.max(hi, depth)\n        } else {\n            go(root.left, depth + 1)\n            go(root.right, depth + 1)\n        }\n    }\n    go()\n    return Pair(lo, hi)\n}\n\nfun main() {\n    for (filename in listOf(\"problem14.6test1.txt\", \"problem14.6test2.txt\", \"problem14.6.txt\")) {\n        var (lo, hi) = run(filename)\n        println(\"$filename: $lo, $hi\") // min, max encoding length in the corresponding optimal prefix-free tree\n    }\n}\n\n//    problem14.6test1.txt: 2, 5\n//    problem14.6test2.txt: 3, 6\n//    problem14.6.txt: 9, 19\n"
  },
  {
    "path": "huffman/main.py",
    "content": "#\n# Programming Problem 14.6: Huffman Codes\n#\n# In this problem the file format is:\n# [number_of_symbols]\n# [weight of symbol #1]\n# [weight of symbol #2]\n# ...\n#\n\nclass Tree:\n    def __init__(self, weight, left = None, right = None):\n        self.weight = weight\n        self.left = left\n        self.right = right\n    def __lt__(self, other):\n        return self.weight < other.weight\n\n#\n# priority queue\n#\n\n# from heapq import heappush\n# from heapq import heappop\n# def encode(A):\n#     T = []\n#     for weight in A:\n#         heappush(T, Tree(weight))\n#     while 1 < len(T):\n#         a, b = heappop(T), heappop(T)\n#         c = Tree(a.weight + b.weight, a, b)\n#         heappush(T, c)\n#     return heappop(T)\n\n#\n# Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n# of a sorting subroutine, followed by a linear amount of additional work.\n#\nfrom collections import deque\ndef encode(A):\n    A.sort()\n    first, second = deque([Tree(weight) for weight in A]), deque()\n    while 1 < len(first) + len(second):\n        next = []\n        while len(next) < 2:\n            if len(first) and len(second):\n                next.append(first.popleft() if first[0].weight < second[0].weight else second.popleft())\n            elif len(first): next.append(first.popleft())\n            elif len(second): next.append(second.popleft())\n        a, b = next\n        c = Tree(a.weight + b.weight, a, b)\n        second.append(c)\n    return second.popleft()\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        N = int(fin.readline())\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            weight = int(line.strip())\n            A.append(weight)\n    tree = encode(A)\n    lo, hi = float('inf'), float('-inf')\n    def go(root = tree, depth = 0):\n        nonlocal lo, hi\n        if not root:\n            return\n        isLeaf = lambda root: not root.left and not root.right\n        if isLeaf(root):\n            lo = min(lo, depth)\n            hi = max(hi, depth)\n        else:\n            go(root.left, depth + 1)\n            go(root.right, depth + 1)\n    go()\n    return [ lo, hi ]\n\nfor filename in [ 'problem14.6test1.txt', 'problem14.6test2.txt', 'problem14.6.txt' ]:\n    lo, hi = run(filename)\n    print(f'{filename}: {lo}, {hi}') # min, max encoding length in the corresponding optimal prefix-free tree\n\n#    problem14.6test1.txt: 2, 5\n#    problem14.6test2.txt: 3, 6\n#    problem14.6.txt: 9, 19\n"
  },
  {
    "path": "huffman/package.json",
    "content": "{\n  \"name\": \"huffman\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"clayton wong\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "huffman/problem14.6.txt",
    "content": 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  },
  {
    "path": "huffman/problem14.6test1.txt",
    "content": "10\n37\n59\n43\n27\n30\n96\n96\n71\n8\n76"
  },
  {
    "path": "huffman/problem14.6test2.txt",
    "content": "15\n895\n121\n188\n953\n378\n849\n153\n579\n144\n727\n589\n301\n442\n327\n930"
  },
  {
    "path": "karatsuba/main.jl",
    "content": "#\n# Karatsuba Multiplication\n#\n# Input: two n-digit positive integers x and y\n# Output: the product x * y\n# Assumption: n is a power of 2\n#\nusing Test, Random\n\nfunction go(x, y)\n  if x < 10 || y < 10\n    return x * y\n  end\n\n  n = max(length(string(x)), length(string(y)))\n  if isodd(n)\n    n += 1\n  end\n\n  m = 10 ^ div(n, 2) # middle decimal value\n  a, b = div(x, m), mod(x, m)\n  c, d = div(y, m), mod(y, m)\n  p, q = a + b, c + d\n\n  ac = go(a, c)\n  bd = go(b, d)\n  pq = go(p, q)\n  adbc = pq - ac - bd\n  return 10^n * ac + 10^div(n, 2) * adbc + bd\nend\n\nRandom.seed!(123456789)\n\n@testset \"Karatsuba Multiplication tests\" begin\n    for _ in 1:100\n        n = rand((1, 2, 4, 8, 16))\n\n        lo = 10^(n-1)\n        hi = 10^n - 1\n\n        x = rand(lo:hi)\n        y = rand(lo:hi)\n\n        expect, actual = x * y, go(x, y)\n        @test expect == actual\n        println(\"($x x $y)\\nexpect: $expect\\nactual: $actual\\n\")\n    end\nend\n\n@testset \"Challenge Problem\" begin\n    x = 3141592653589793238462643383279502884197169399375105820974944592\n    y = 2718281828459045235360287471352662497757247093699959574966967627\n\n    expect, actual = x * y, go(x, y)\n    @test expect == actual\n    println(\"($x x $y)\\nexpect: $expect\\nactual: $actual\\n\")\nend\n"
  },
  {
    "path": "karatsuba/main.py",
    "content": "def go(x, y):\n    if x < 10 or y < 10:\n        return x * y\n    n = max(len(str(x)), len(str(y)))\n    if n & 1:\n        n += 1  # +1 is n is odd\n    m = 10 ** (n // 2)\n    a, b = x // m, x % m\n    c, d = y // m, y % m\n    p, q = a + b, c + d\n\n    ac = go(a, c)\n    bd = go(b, d)\n    pq = go(p, q)\n    adbc = pq - ac - bd\n    return 10**n * ac + 10**(n//2) * adbc + bd\n\nx = 3141592653589793238462643383279502884197169399375105820974944592\ny = 2718281828459045235360287471352662497757247093699959574966967627\nassert(x * y == go(x, y))\nprint(x * y)\nprint(go(x, y))\n\n# 8539734222673567065463550869546574495034888535765114961879601127067743044893204848617875072216249073013374895871952806582723184\n# 8539734222673567065463550869546574495034888535765114961879601127067743044893204848617875072216249073013374895871952806582723184\n"
  },
  {
    "path": "knapsack/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(knapsack)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(knapsack main.cpp)"
  },
  {
    "path": "knapsack/main.cpp",
    "content": "#include <iostream>\n#include <fstream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n\nusing namespace std;\nusing Pair = pair<int, int>;  // value, weight\nusing Pairs = vector<Pair>;\nusing fun = function<int(int, int)>;\nusing Map = unordered_map<string, int>;\n\nint INF = 1e9 + 7;\n\nint top_down(Pairs& A, int K, Map m = {}) {\n    auto N = A.size();\n    fun go = [&](auto i, auto k) {\n        if (i == N)                                                             // 🛑 empty set\n            return 0;\n        stringstream key; key << i << \",\" << k;\n        if (m.find(key.str()) != m.end())                                       // 🤔 memo\n            return m[key.str()];\n        auto [value, weight] = A[i];\n        auto include = 0 <= k - weight ? go(i + 1, k - weight) + value : -INF,  // ✅ include A[i]\n             exclude = go(i + 1, k);                                            // 🚫 exclude A[i]\n        return m[key.str()] = max(include, exclude);                            // 🎯 best\n    };\n    return go(0, K);\n}\n\nint bottom_up(Pairs& A, int K) {\n    auto N = A.size();\n    using VI = vector<int>;\n    using VVI = vector<VI>;\n    VVI dp(N + 1, VI(K + 1, -INF));                                                 // 🤔 memo\n    for (auto k{ 0 }; k < K; dp[0][k++] = 0);                                      // 🛑 empty set\n    for (auto i{ 1 }; i <= N; ++i) {\n        for (auto k{ 0 }; k <= K; ++k) {\n            auto [value, weight] = A[i - 1];\n            auto include = 0 <= k - weight ? dp[i - 1][k - weight] +value : -INF,  // ✅ include A[i]\n                 exclude = dp[i - 1][k];                                           // 🚫 exclude A[i]\n            dp[i][k] = max(include, exclude);                                      // 🎯 best\n        }\n    }\n    return dp[N][K];\n}\n\nint bottom_up_memopt(Pairs& A, int K) {\n    auto N = A.size();\n    using VI = vector<int>;\n    VI pre(K + 1, 0);                                                        // 🤔 memo + 🛑 empty set\n    for (auto i{ 1 }; i <= N; ++i) {\n        VI cur(K + 1, -INF);\n        for (auto k{ 0 }; k <= K; ++k) {\n            auto [value, weight] = A[i - 1];\n            auto include = 0 <= k - weight ? pre[k - weight] +value : -INF,  // ✅ include A[i]\n            exclude = pre[k];                                                // 🚫 exclude A[i]\n            cur[k] = max(include, exclude);                                  // 🎯 best\n        }\n        swap(pre, cur);\n    }\n    return pre[K];\n}\n\nvoid run(const string& filename) {\n    Pairs A;\n    fstream fin{ filename };\n    int K, N;                // K capacity, N items\n    fin >> K >> N;\n    for (int value, weight; fin >> value >> weight; A.emplace_back(value, weight));\n    auto a = top_down(A, K),\n         b = bottom_up(A, K),\n         c = bottom_up_memopt(A, K);\n    assert(a == b && b == c); // 💩 sanity check\n    cout << filename << \": \" << a << endl;\n}\n\nint main() {\n    run(\"problem16.7test.txt\");  // problem16.7test.txt: 2493893\n    return 0;\n}\n"
  },
  {
    "path": "knapsack/main.js",
    "content": "const assert = require('assert');\nconst LineByLine = require('n-readlines');\n\nlet top_down = (A, K, m = new Map()) => {\n    let N = A.length;\n    let go = (i = 0, k = K) => {\n        if (i == N)                                                                 // 🛑 empty set\n            return 0;\n        let key = `${i},${k}`;\n        if (m.has(key))                                                             // 🤔 memo\n            return m.get(key);\n        let [value, weight] = A[i];\n        let include = 0 <= k - weight ? go(i + 1, k - weight) + value : -Infinity,  // ✅ include A[i]\n            exclude = go(i + 1, k);                                                 // 🚫 exclude A[i]\n        return m.set(key, Math.max(include, exclude))                               // 🎯 best\n                .get(key);\n    };\n    return go();\n};\n\nlet bottom_up = (A, K) => {\n    let N = A.length;\n    let dp = [...Array(N + 1)].map(_ => Array(K + 1).fill(-Infinity));                  // 🤔 memo\n    for (let k = 0; k < K; dp[0][k++] = 0);                                             // 🛑 empty set\n    for (let i = 1; i <= N; ++i) {\n        for (let k = 0; k <= K; ++k) {\n            let [value, weight] = A[i - 1];\n            let include = 0 <= k - weight ? dp[i - 1][k - weight] + value : -Infinity,  // ✅ include A[i]\n                exclude = dp[i - 1][k];                                                 // 🚫 exclude A[i]\n            dp[i][k] = Math.max(include, exclude);                                      // 🎯 best\n        }\n    }\n    return dp[N][K];\n};\n\nlet bottom_up_memopt = (A, K) => {\n    let N = A.length;\n    let pre = Array(K + 1).fill(0);                                               // 🤔 memo + 🛑 empty set\n    for (let i = 1; i <= N; ++i) {\n        let cur = Array(K + 1).fill(-Infinity);\n        for (let k = 0; k <= K; ++k) {\n            let [value, weight] = A[i - 1];\n            let include = 0 <= k - weight ? pre[k - weight] + value : -Infinity,  // ✅ include A[i]\n                exclude = pre[k];                                                 // 🚫 exclude A[i]\n            cur[k] = Math.max(include, exclude);                                  // 🎯 best\n        }\n        [pre, cur] = [cur, pre];\n    }\n    return pre[K];\n};\n\nlet run = filename => {\n    let A = [];\n    const input = new LineByLine(filename)\n    let [K, N] = input.next().toString().split(' ').map(Number);  // K capacity, N items\n    let line;\n    while (line = input.next()) {\n        let [value, weight] = line.toString().split(' ').map(Number);\n        A.push([value, weight]);\n    }\n    let a = top_down(A, K),\n        b = bottom_up(A, K),\n        c = bottom_up_memopt(A, K);\n    assert(a == b && b == c); // 💩 sanity check\n    console.log(`${filename}: ${a}`);\n};\n\nrun('problem16.7test.txt')  // problem16.7test.txt: 2493893\n"
  },
  {
    "path": "knapsack/main.kt",
    "content": "import java.io.File\n\nvar INF = (1e9 + 7).toInt()\n\nfun top_down(A: List<Pair<Int, Int>>, K: Int): Int {\n    var N = A.size\n    var m = mutableMapOf<String, Int>()\n    fun go(i: Int = 0, k: Int = K): Int {\n        if (i == N)                                                                 // 🛑 empty set\n            return 0\n        var key = \"$i,$k\"\n        if (m.contains(key))                                                        // 🤔 memo\n            return m[key]!!\n        var (value, weight) = A[i]\n        var include = if (0 <= k - weight) go(i + 1, k - weight) + value else -INF  // ✅ include A[i]\n        var exclude = go(i + 1, k)                                                  // 🚫 exclude A[i]\n        m[key] = Math.max(include, exclude)                                         // 🎯 best\n        return m[key]!!\n    }\n    return go()\n}\n\nfun bottom_up(A: List<Pair<Int, Int>>, K: Int): Int {\n    var N = A.size\n    var dp = Array(N + 1){ Array(K + 1){ -INF } }                                       // 🤔 memo\n    for (k in 0..K)                                                                     // 🛑 empty set\n        dp[0][k] = 0\n    for (i in 1..N) {\n        for (k in 0..K) {\n            var (value, weight) = A[i - 1]\n            var include = if (0 <= k - weight) dp[i - 1][k - weight] + value else -INF  // ✅ include A[i]\n            var exclude = dp[i - 1][k]                                                  // 🚫 exclude A[i]\n            dp[i][k] = Math.max(include, exclude)                                       // 🎯 best\n        }\n    }\n    return dp[N][K]\n}\n\nfun bottom_up_memopt(A: List<Pair<Int, Int>>, K: Int): Int {\n    var N = A.size\n    var pre = Array(K + 1) { 0 }                                                  // 🤔 memo + 🛑 empty set\n    for (i in 1..N) {\n        var cur = Array(K + 1) { -INF }\n        for (k in 0..K) {\n            var (value, weight) = A[i - 1]\n            var include = if (0 <= k - weight) pre[k - weight] + value else -INF  // ✅ include A[i]\n            var exclude = pre[k]                                                  // 🚫 exclude A[i]\n            cur[k] = Math.max(include, exclude)                                   // 🎯 best\n        }\n        pre = cur.also { cur = pre }\n    }\n    return pre[K]\n}\n\nfun run(filename: String) {\n    var A = mutableListOf<Pair<Int, Int>>()\n    var K = 0\n    var N = 0\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (value, weight) = line.trim().split(\" \").map{ it -> it.toInt() }\n            A.add(Pair(value, weight))\n        } else {\n            var (a, b) = line.trim().split(\" \").map{ it -> it.toInt() }\n            K = a\n            N = b\n            first = false\n        }\n    }\n    var a = top_down(A, K)\n    var b = bottom_up(A, K)\n    var c = bottom_up_memopt(A, K)\n    assert(a == b && b == c) // 💩 sanity check\n    println(\"$filename: $a\")\n}\n\nfun main() {\n    run(\"problem16.7test.txt\")  // problem16.7test.txt: 2493893\n}\n"
  },
  {
    "path": "knapsack/main.py",
    "content": "from functools import lru_cache\n\ndef top_down(A, K):\n    N = len(A)\n    total = [0] * N\n    @lru_cache(maxsize = None)                                                          # 🤔 memo\n    def go(i = 0, k = K):\n        if i == N:                                                                      # 🛑 empty set\n            return 0\n        value, weight = A[i]\n        include = go(i + 1, k - weight) + value if 0 <= k - weight else float('-inf')  # ✅ include A[i]\n        exclude = go(i + 1, k)                                                         # 🚫 exclude A[i]\n        return max(include, exclude)                                                   # 🎯 best\n    return go()\n\ndef bottom_up(A, K):\n    N = len(A)\n    dp = [[float('-inf')] * (K + 1) for _ in range(N + 1)]                                 # 🤔 memo\n    for j in range(K):                                                                     # 🛑 empty set\n        dp[0][j] = 0\n    for i in range(1, N + 1):\n        for k in range(1, K + 1):\n            value, weight = A[i - 1]\n            include = dp[i - 1][k - weight] + value if 0 <= k - weight else float('-inf')  # ✅ include A[i]\n            exclude = dp[i - 1][k]                                                         # 🚫 exclude A[i]\n            dp[i][k] = max(include, exclude)                                               # 🎯 best\n    return dp[N][K]\n\ndef bottom_up_memopt(A, K):\n    N = len(A)\n    pre = [0] * (K + 1)                                                              # 🤔 memo + 🛑 empty set\n    for i in range(1, N + 1):\n        cur = [float('-inf')] * (K + 1)\n        for k in range(1, K + 1):\n            value, weight = A[i - 1]\n            include = pre[k - weight] + value if 0 <= k - weight else float('-inf')  # ✅ include A[i]\n            exclude = pre[k]                                                         # 🚫 exclude A[i]\n            cur[k] = max(include, exclude)                                           # 🎯 best\n        pre, cur = cur, pre\n    return pre[K]\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        line = fin.readline()\n        [K, N] = [int(word) for word in line.split()]  # K capacity, N items\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            value, weight = [int(word) for word in line.split()]\n            A.append([value, weight])\n    a = top_down(A, K)\n    b = bottom_up(A, K)\n    c = bottom_up_memopt(A, K)\n    assert(a == b and b == c) # 💩 sanity check\n    print(f'{filename}: {a}')\n\nrun('problem16.7test.txt')  # problem16.7test.txt: 2493893\n"
  },
  {
    "path": "knapsack/package.json",
    "content": "{\n  \"name\": \"knapsack\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"clayton wong\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"assert\": \"^2.0.0\",\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "knapsack/problem16.7.txt",
    "content": "2000000 2000\n16808 241486\n50074 834558\n8931 738037\n27545 212860\n77924 494349\n64441 815107\n84493 723724\n7988 421316\n82328 652893\n78841 402599\n44304 631607\n17710 318556\n29561 608119\n93100 429390\n51817 431959\n99098 365899\n13513 90282\n23811 467558\n80980 743542\n36580 896948\n11968 883369\n1394 604449\n25486 562244\n25229 333236\n40195 157443\n35002 696933\n16709 539123\n15669 202584\n88125 759690\n9531 69730\n27723 110467\n28550 651058\n97802 231944\n40978 186803\n8229 572887\n60299 797491\n28636 692529\n23866 503157\n39064 243688\n39426 182032\n24116 262772\n75630 246257\n46518 605917\n30106 685556\n19452 522241\n82189 419114\n99506 622799\n6753 512332\n36717 489578\n54439 869423\n51502 771067\n83872 884103\n11138 450309\n53178 444804\n22295 405168\n21610 527012\n59746 255432\n53636 702071\n98143 264607\n27969 227173\n261 471962\n41595 807033\n16396 471595\n19114 520773\n71007 21653\n97943 882635\n42083 801161\n30768 806299\n85696 402599\n73672 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  },
  {
    "path": "knapsack/problem16.7test.txt",
    "content": "10000 100\n16808 250\n50074 659\n8931 273\n27545 879\n77924 710\n64441 166\n84493 43\n7988 504\n82328 730\n78841 613\n44304 170\n17710 158\n29561 934\n93100 279\n51817 336\n99098 827\n13513 268\n23811 634\n80980 150\n36580 822\n11968 673\n1394 337\n25486 746\n25229 92\n40195 358\n35002 154\n16709 945\n15669 491\n88125 197\n9531 904\n27723 667\n28550 25\n97802 854\n40978 409\n8229 934\n60299 982\n28636 14\n23866 815\n39064 537\n39426 670\n24116 95\n75630 502\n46518 196\n30106 405\n19452 299\n82189 124\n99506 883\n6753 567\n36717 338\n54439 145\n51502 898\n83872 829\n11138 359\n53178 398\n22295 905\n21610 232\n59746 176\n53636 299\n98143 400\n27969 413\n261 558\n41595 9\n16396 969\n19114 531\n71007 963\n97943 366\n42083 853\n30768 822\n85696 713\n73672 902\n48591 832\n14739 58\n31617 791\n55641 680\n37336 7\n97973 99\n49096 320\n83455 224\n12290 761\n48906 127\n36124 507\n45814 771\n35239 95\n96221 845\n12367 535\n25227 395\n41364 739\n7845 591\n36551 160\n8624 948\n97386 218\n95273 540\n99248 386\n13497 886\n40624 421\n28145 969\n35736 916\n61626 535\n46043 12\n54680 153\n"
  },
  {
    "path": "kosaraju/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(kosaraju)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(kosaraju main.cpp)"
  },
  {
    "path": "kosaraju/main.cpp",
    "content": "#include <iostream>\n#include <fstream>\n#include <vector>\n#include <unordered_map>\n#include <unordered_set>\n#include <queue>\n\nusing namespace std;\n\nusing List = deque<int>;\nusing Lists = deque<List>;\nusing AdjList = unordered_map<int, List>;\nusing Set = unordered_set<int>;\nusing Map = unordered_map<int, int>;\n\nnamespace Base {\n    class Solution {\n    protected:\n        AdjList adj, rev;\n    public:\n        Solution(AdjList& adj, AdjList& rev) : adj{ adj }, rev{ rev } {}\n    };\n}\nnamespace Recursive {\n    struct Solution : public Base::Solution {\n        Solution(AdjList& adj, AdjList& rev) : Base::Solution{ adj, rev } {}\n        Lists kosaraju() {\n            Lists lists;\n            Set seen;\n            using fun = function<void(int, List&)>;\n            fun go = [&](auto u, auto& list) {\n                if (!seen.insert(u).second)\n                    return;\n                list.push_back(u);\n                for (auto v: adj[u])\n                    go(v, list);\n            };\n            for (auto u: topo_sort()) {\n                List list;\n                go(u, list);\n                lists.emplace_back(list);\n            }\n            sort(lists.begin(), lists.end(), [](auto& a, auto& b) { return b.size() < a.size(); });\n            return lists;\n        }\n        List topo_sort() {\n            List list;\n            Set seen;\n            using fun = function<void(int)>;\n            fun go = [&](auto u) {\n                if (!seen.insert(u).second)\n                    return;\n                for (auto v: rev[u])\n                    go(v);\n                list.push_front(u);\n            };\n            for (auto [u, _]: rev)\n                go(u);\n            return list;\n        }\n    };\n}\nnamespace Iterative {\n    struct Solution : public Base::Solution {\n        Solution(AdjList& adj, AdjList& rev) : Base::Solution{ adj, rev } {}\n        Lists kosaraju() {\n            Lists lists;\n            Set seen;\n            for (auto u: topo_sort()) {\n                if (seen.find(u) != seen.end())\n                    continue;\n                List list;\n                List stack{ u }; seen.insert(u);\n                while (stack.size()) {\n                    auto u = stack.back();\n                    for (auto v: adj[u])\n                        if (seen.insert(v).second)\n                            stack.push_back(v);\n                    if (u == stack.back())\n                        list.push_back(u), stack.pop_back();\n                }\n                lists.emplace_back(list);\n            }\n            sort(lists.begin(), lists.end(), [](auto& a, auto& b) { return b.size() < a.size(); });\n            return lists;\n        }\n        List topo_sort() {\n            List list;\n            Set seen;\n            for (auto [u, _]: rev) {\n                if (seen.find(u) != seen.end())\n                    continue;\n                List stack{ u }; seen.insert(u);\n                while (stack.size()) {\n                    auto u = stack.back();\n                    for (auto v: rev[u])\n                        if (seen.insert(v).second)\n                            stack.push_back(v);\n                    if (u == stack.back())\n                        list.push_front(stack.back()), stack.pop_back();\n                }\n            }\n            return list;\n        }\n    };\n}\n\nvoid run(string filename) {\n    int u, v;\n    AdjList adj, rev;\n    fstream fin{ filename };\n    for (string line; fin >> u >> v;) {\n        adj[u].push_back(v);\n        rev[v].push_back(u);\n    }\n    auto A = Iterative::Solution{ adj, rev }.kosaraju();\n    A.resize(min(A.size(), size_t(5)));\n    cout << filename << \": \";\n    for (auto i{ 0 }; i < A.size(); cout << A[i++].size() << \" \");\n    cout << endl;\n}\n\nint main() {\n    run(\"section8.6.5page64.txt\");  // Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\n    run(\"problem8.10test1.txt\");    // Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\n    run(\"problem8.10test2.txt\");    // Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\n    run(\"problem8.10test3.txt\");    // Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\n    run(\"problem8.10test4.txt\");    // Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\n    run(\"problem8.10test5.txt\");    // Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\n    run(\"problem8.10.txt\");         // Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n//    section8.6.5page64.txt: 4 3 3 1\n//    problem8.10test1.txt: 3 3 3\n//    problem8.10test2.txt: 3 3 2\n//    problem8.10test3.txt: 3 3 1 1\n//    problem8.10test4.txt: 7 1\n//    problem8.10test5.txt: 6 3 2 1\n//    problem8.10.txt: 434821 968 459 313 211\n\n    return 0;\n}\n"
  },
  {
    "path": "kosaraju/main.js",
    "content": "class BaseSolution {\n    constructor(adj, rev) {\n        this.adj = adj;\n        this.rev = rev;\n    }\n}\n\nclass RecursiveSolution extends BaseSolution {\n    constructor(adj, rev) {\n        super(adj, rev);\n    }\n    topo_sort() {\n        let list = [];\n        let seen = new Set();\n        let go = u => {\n            if (seen.has(u))\n                return;\n            seen.add(u);\n            for (let v of [...this.rev.get(u)])\n                go(v);\n            list.unshift(u);\n        };\n        for (let [u, _] of [...this.rev])\n            go(u);\n        return list;\n    }\n    kosaraju() {\n        let lists = [];\n        let seen = new Set();\n        let go = (u, list) => {\n            if (seen.has(u))\n                return;\n            seen.add(u);\n            list.push(u);\n            for (let v of [...this.adj.get(u)])\n                go(v, list);\n        };\n        for (let u of this.topo_sort()) {\n            let list = [];\n            go(u, list);\n            lists.push([...list]);\n        }\n        lists.sort((a, b) => b.length - a.length);\n        return lists;\n    }\n}\n\nclass IterativeSolution extends BaseSolution {\n    constructor(adj, rev) {\n        super(adj, rev);\n    }\n    topo_sort() {\n        let list = [];\n        let seen = new Set();\n        for (let [u, _] of [...this.rev]) {\n            if (seen.has(u))\n                continue;\n            let stack = [ u ]; seen.add(u);\n            stack.back = () => stack[stack.length - 1];\n            while (stack.length) {\n                let u = stack.back();\n                for (let v of [...this.rev.get(u)])\n                    if (!seen.has(v))\n                        stack.push(v), seen.add(v);\n                if (u == stack.back())\n                    list.unshift(stack.pop());\n            }\n        }\n        return list;\n    }\n    kosaraju() {\n        let lists = [];\n        let seen = new Set();\n        for (let u of this.topo_sort()) {\n            if (seen.has(u))\n                continue;\n            let list = [];\n            let stack = [ u ]; seen.add(u);\n            stack.back = () => stack[stack.length - 1];\n            while (stack.length) {\n                let u = stack.back();\n                for (let v of [...this.adj.get(u)])\n                    if (!seen.has(v))\n                        stack.push(v), seen.add(v);\n                if (u == stack.back())\n                    list.push(stack.pop());\n            }\n            lists.push([...list]);\n        }\n        lists.sort((a, b) => b.length - a.length);\n        return lists;\n    }\n}\n\nlet run = filename => {\n    let adj = new Map(),\n        rev = new Map();\n    let LineByLine = require('n-readlines');\n    let input = new LineByLine(filename);\n    let line;\n    while (line = input.next()) {\n        let [u, v] = String.fromCharCode(...line).split(' ').map(Number);\n        if (!adj.has(u)) adj.set(u, []); if (!adj.has(v)) adj.set(v, []);\n        if (!rev.has(u)) rev.set(u, []); if (!rev.has(v)) rev.set(v, []);\n        adj.get(u).push(v);\n        rev.get(v).push(u);\n    }\n    // let A = new RecursiveSolution(adj, rev).kosaraju();\n    let A = new IterativeSolution(adj, rev).kosaraju();\n    console.log(`${filename}: ${A.slice(0, Math.min(A.length, 5)).map(scc => scc.length).join(' ')}`);\n};\n\nrun('section8.6.5page64.txt')  // Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\nrun('problem8.10test1.txt')    // Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\nrun('problem8.10test2.txt')    // Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\nrun('problem8.10test3.txt')    // Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\nrun('problem8.10test4.txt')    // Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\nrun('problem8.10test5.txt')    // Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\nrun('problem8.10.txt')         // Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n\n//    section8.6.5page64.txt: 4 3 3 1\n//    problem8.10test1.txt: 3 3 3\n//    problem8.10test2.txt: 3 3 2\n//    problem8.10test3.txt: 3 3 1 1\n//    problem8.10test4.txt: 7 1\n//    problem8.10test5.txt: 6 3 2 1\n//    problem8.10.txt: 434821 968 459 313 211\n"
  },
  {
    "path": "kosaraju/main.kt",
    "content": "import java.util.Stack\nimport java.io.File\n\nclass RecursiveSolution(var adj: MutableMap<Int, MutableList<Int>>, var rev: MutableMap<Int, MutableList<Int>>) {\n    fun topo_sort(): MutableList<Int> {\n        var list = mutableListOf<Int>()\n        var seen = mutableSetOf<Int>()\n        fun go(u: Int) {\n            if (seen.contains(u))\n                return\n            seen.add(u)\n            for (v in rev[u]!!)\n                go(v)\n            list.add(0, u)\n        }\n        for ((u, _) in rev)\n            go(u)\n        return list\n    }\n    fun kosaraju(): MutableList<List<Int>> {\n        var lists = mutableListOf<List<Int>>()\n        var seen = mutableSetOf<Int>()\n        fun go(u: Int, list: MutableList<Int>) {\n            if (seen.contains(u))\n                return\n            list.add(u); seen.add(u)\n            for (v in adj[u]!!)\n                go(v, list)\n        }\n        for (u in topo_sort()) {\n            if (seen.contains(u))\n                continue\n            var list = mutableListOf<Int>()\n            go(u, list)\n            lists.add(list.toList())\n        }\n        return lists\n    }\n}\n\nclass IterativeSolution(var adj: MutableMap<Int, MutableList<Int>>, var rev: MutableMap<Int, MutableList<Int>>) {\n    fun topo_sort(): MutableList<Int> {\n        var list = mutableListOf<Int>()\n        var seen = mutableSetOf<Int>()\n        for ((u, _) in rev) {\n            if (seen.contains(u))\n                continue\n            var stack = Stack<Int>()\n            stack.push(u); seen.add(u)\n            while (!stack.empty()) {\n                var u = stack.last()\n                for (v in rev[u]!!) {\n                    if (!seen.contains(v)) {\n                        stack.push(v); seen.add(v)\n                    }\n                }\n                if (u == stack.last())\n                    list.add(0, stack.pop())\n            }\n        }\n        return list\n    }\n    fun kosaraju(): MutableList<List<Int>> {\n        var lists = mutableListOf<List<Int>>()\n        var seen = mutableSetOf<Int>()\n        for (u in topo_sort()) {\n            if (seen.contains(u))\n                continue\n            var list = mutableListOf<Int>()\n            var stack = Stack<Int>()\n            stack.push(u); seen.add(u)\n            while (!stack.empty()) {\n                var u = stack.last()\n                for (v in adj[u]!!) {\n                    if (!seen.contains(v)) {\n                        stack.push(v); seen.add(v)\n                    }\n                }\n                if (u == stack.last())\n                    list.add(stack.pop())\n            }\n            lists.add(list.toList())\n        }\n        return lists\n    }\n}\n\nfun run(filename: String) {\n    var adj = mutableMapOf<Int, MutableList<Int>>()\n    var rev = mutableMapOf<Int, MutableList<Int>>()\n    File(filename).forEachLine {\n        var (u, v) = it.trim().split(\" \").map{ it.toInt() }\n        if (!adj.contains(u)) adj[u] = mutableListOf(); if (!adj.contains(v)) adj[v] = mutableListOf()\n        if (!rev.contains(u)) rev[u] = mutableListOf(); if (!rev.contains(v)) rev[v] = mutableListOf()\n        adj[u]!!.add(v)\n        rev[v]!!.add(u)\n    }\n    // var solution = RecursiveSolution(adj, rev)\n    var solution = IterativeSolution(adj, rev)\n    var A = solution.kosaraju()\n    A.sortWith(Comparator{ a: List<Int>, b: List<Int> -> b.size - a.size })\n    println(filename + \": \" + A.map{ it.size }.slice(0 until Math.min(A.size, 5)).joinToString(\" \"))\n}\n\nfun main() {\n    run(\"section8.6.5page64.txt\");  // Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\n    run(\"problem8.10test1.txt\");    // Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\n    run(\"problem8.10test2.txt\");    // Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\n    run(\"problem8.10test3.txt\");    // Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\n    run(\"problem8.10test4.txt\");    // Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\n    run(\"problem8.10test5.txt\");    // Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\n    run(\"problem8.10.txt\");         // Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n//    section8.6.5page64.txt: 4 3 3 1\n//    problem8.10test1.txt: 3 3 3\n//    problem8.10test2.txt: 3 3 2\n//    problem8.10test3.txt: 3 3 1 1\n//    problem8.10test4.txt: 7 1\n//    problem8.10test5.txt: 6 3 2 1\n//    problem8.10.txt: 434821 968 459 313 211\n\n}\n"
  },
  {
    "path": "kosaraju/main.py",
    "content": "from collections import deque\nfrom functools import cmp_to_key\n\nclass BaseSolution:\n    def __init__(self, adj, rev):\n        self.adj = adj\n        self.rev = rev\n\nclass RecursiveSolution(BaseSolution):\n    def topo_sort(self):\n        list = deque()\n        seen = set()\n        def go(u):\n            if u in seen:\n                return\n            seen.add(u)\n            for v in self.rev[u]:\n                go(v)\n            list.appendleft(u)\n        for u in self.rev.keys():\n            go(u)\n        return list\n\n    def kosaraju(self):\n        lists = []\n        seen = set()\n        def go(u, list):\n            if u in seen:\n                return\n            seen.add(u)\n            list.append(u)\n            for v in self.adj[u]:\n                go(v, list)\n        for u in self.topo_sort():\n            list = []\n            go(u, list)\n            lists.append(list.copy())\n        lists.sort(key = cmp_to_key(lambda a, b: len(b) - len(a)))\n        return lists\n\nclass IterativeSolution(BaseSolution):\n    def topo_sort(self):\n        list = deque()\n        seen = set()\n        for u in self.rev.keys():\n            if u in seen:\n                continue\n            stack = [ u ]; seen.add(u)\n            while len(stack):\n                u = stack[-1]\n                for v in self.rev[u]:\n                    if v not in seen:\n                        stack.append(v); seen.add(v)\n                if u == stack[-1]:\n                    list.appendleft(stack.pop())\n        return list\n\n    def kosaraju(self):\n        lists = []\n        seen = set()\n        for u in self.topo_sort():\n            if u in seen:\n                continue\n            list = deque()\n            stack = [ u ]; seen.add(u)\n            while len(stack):\n                u = stack[-1]\n                for v in self.adj[u]:\n                    if v not in seen:\n                        stack.append(v); seen.add(v)\n                if u == stack[-1]:\n                    list.appendleft(stack.pop())\n            lists.append(list.copy())\n        lists.sort(key = cmp_to_key(lambda a, b: len(b) - len(a)))\n        return lists\n\ndef run(filename):\n    adj, rev = {}, {}\n    with open(filename) as fin:\n        while True:\n            line = fin.readline().strip()\n            if not line:\n                break\n            u, v = [int(x) for x in line.split()]\n            if u not in adj: adj[u] = []\n            if v not in adj: adj[v] = []\n            if u not in rev: rev[u] = []\n            if v not in rev: rev[v] = []\n            adj[u].append(v)\n            rev[v].append(u)\n    # solution = RecursiveSolution(adj, rev)\n    solution = IterativeSolution(adj, rev)\n    A = solution.kosaraju()\n    print(filename + ': ' + ' '.join(str(len(scc)) for scc in A[:5]))\n\nrun('section8.6.5page64.txt')  # Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\nrun('problem8.10test1.txt')    # Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\nrun('problem8.10test2.txt')    # Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\nrun('problem8.10test3.txt')    # Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\nrun('problem8.10test4.txt')    # Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\nrun('problem8.10test5.txt')    # Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\nrun('problem8.10.txt')         # Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n#    section8.6.5page64.txt: 4 3 3 1\n#    problem8.10test1.txt: 3 3 3\n#    problem8.10test2.txt: 3 3 2\n#    problem8.10test3.txt: 3 3 1 1\n#    problem8.10test4.txt: 7 1\n#    problem8.10test5.txt: 6 3 2 1\n#    problem8.10.txt: 434821 968 459 313 211\n"
  },
  {
    "path": "kosaraju/package.json",
    "content": "{\n  \"name\": \"kosaraju\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"clayton wong\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "kosaraju/problem8.10test1.txt",
    "content": "1 4\n2 8\n3 6\n4 7\n5 2\n6 9\n7 1\n8 5\n8 6\n9 7\n9 3\n"
  },
  {
    "path": "kosaraju/problem8.10test2.txt",
    "content": "1 2\n2 6\n2 3\n2 4\n3 1\n3 4\n4 5\n5 4\n6 5\n6 7\n7 6\n7 8\n8 5\n8 7\n"
  },
  {
    "path": "kosaraju/problem8.10test3.txt",
    "content": "1 2\n2 3\n3 1\n3 4\n5 4\n6 4\n8 6\n6 7\n7 8\n"
  },
  {
    "path": "kosaraju/problem8.10test4.txt",
    "content": "1 2\n2 3\n3 1\n3 4\n5 4\n6 4\n8 6\n6 7\n7 8\n4 3\n4 6\n"
  },
  {
    "path": "kosaraju/problem8.10test5.txt",
    "content": "1 2\n2 3\n2 4\n2 5\n3 6\n4 5\n4 7\n5 2\n5 6\n5 7\n6 3\n6 8\n7 8\n7 10\n8 7\n9 7\n10 9\n10 11\n11 12\n12 10\n"
  },
  {
    "path": "kosaraju/section8.6.5page64.txt",
    "content": "1 5\n2 9\n3 1\n4 2\n4 9\n5 3\n6 8\n6 11\n7 4\n7 5\n8 9\n8 10\n8 11\n9 5\n9 7\n10 2\n10 6\n11 3\n"
  },
  {
    "path": "kotlin/dijkstra.kt",
    "content": "import java.io.File\nimport java.util.PriorityQueue\n\nvar INF = (1e9 + 7).toInt()\n\ninterface BaseSolution {\n    fun run(filename: String, queries: Array<Int>): String\n}\n\nclass NaiveSolution : BaseSolution {\n    fun dijkstra(E: List<Triple<Int, Int, Int>>): MutableMap<Int, Int> {\n        var dist = mutableMapOf<Int, Int>()\n        var seen = mutableSetOf<Int>()\n        var start = 1\n        dist[start] = 0; seen.add(start)\n        var found: Boolean;\n        do {\n            found = false\n            var best_v = INF\n            var best_w = INF\n            for ((u, v, w) in E) {\n                if (!seen.contains(u) || seen.contains(v))\n                    continue\n                found = true\n                if (best_w > dist[u]!! + w) {\n                    best_v = v\n                    best_w = dist[u]!! + w\n                }\n            }\n            var v = best_v\n            var w = best_w\n            dist[v] = w; seen.add(v)\n        } while (found)\n        return dist\n    }\n    override fun run(filename: String, queries: Array<Int>): String {\n        var E = mutableListOf<Triple<Int, Int, Int>>()\n        File(filename).forEachLine {\n            var words = it.trim().split(\"\\t\")\n            var u = words[0].toInt()\n            for (i in 1 until words.size) {\n                var (v, w) = words[i].split(\",\").map{ it.toInt() }\n                E.add(Triple(u, v, w))\n            }\n        }\n        var dist = dijkstra(E.toList())\n        return queries.map{ dist[it] }.joinToString(\" \")\n    }\n}\n\nclass HeapSolution : BaseSolution {\n    fun dijkstra(adj: MutableMap<Int, MutableList<Pair<Int, Int>>>): MutableMap<Int, Int> {\n        var dist = mutableMapOf<Int, Int>()\n        var seen = mutableSetOf<Int>()\n        var start = 1\n        dist[start] = 0\n        var q = PriorityQueue<Pair<Int, Int>>(Comparator{ a: Pair<Int, Int>, b: Pair<Int, Int> -> a.first.compareTo(b.first) })\n        q.add(Pair(0, start))\n        while (0 < q.size) {\n            var (cost, u) = q.poll()\n            if (seen.contains(u))\n                continue\n            dist[u] = cost; seen.add(u)\n            for ((w, v) in adj[u]!!) {\n                if (seen.contains(v))\n                    continue\n                q.add(Pair(cost + w, v))\n            }\n        }\n        return dist\n    }\n    override fun run(filename: String, queries: Array<Int>): String {\n        var adj = mutableMapOf<Int, MutableList<Pair<Int, Int>>>()\n        File(filename).forEachLine {\n            var words = it.trim().split(\"\\t\")\n            var u = words[0].toInt()\n            if (!adj.contains(u))\n                adj[u] = mutableListOf()\n            for (i in 1 until words.size) {\n                var (v, w) = words[i].split(\",\").map{ it.toInt() }\n                adj[u]!!.add(Pair(w, v))\n            }\n        }\n        var dist = dijkstra(adj)\n        return queries.map{ dist[it] }.joinToString(\" \")\n    }\n}\n\nfun run(solution: BaseSolution) {\n    println(solution.run(\"problem9.8test.txt\", arrayOf(1, 2, 3, 4, 5, 6, 7, 8)))\n    println(solution.run(\"problem9.8.txt\", arrayOf(7, 37, 59, 82, 99, 115, 133, 165, 188, 197)))\n}\n\nfun main() {\n    run(NaiveSolution())\n    //    0 1 2 3 4 4 3 2\n    //    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n    run(HeapSolution())\n    //    0 1 2 3 4 4 3 2\n    //    2599 2610 2947 2052 2367 2399 2029 2442 2505 3068\n}\n"
  },
  {
    "path": "kotlin/greedy_scheduling.kt",
    "content": "import java.io.File\n\ndata class Job(val weight: Long, val length: Long)\n\nclass Solution {\n    fun minSum(jobs: Array<Job>): Pair<Long, Long> {\n        class Diff: Comparator<Job> {\n            override fun compare(a: Job?, b: Job?): Int {\n                if (a == null || b == null)\n                    return 0\n                var first = a.weight - a.length\n                var second = b.weight - b.length\n                return if (first == second) b.weight.compareTo(a.weight) else second.compareTo(first) // sort by descending difference, break ties in favor of jobs with larger weights\n            }\n        }\n        class Ratio: Comparator<Job> {\n            override fun compare(a: Job?, b: Job?): Int {\n                if (a == null || b == null)\n                    return 0\n                var first = a.weight.toDouble() / a.length\n                var second = b.weight.toDouble() / b.length\n                return if (first == second) b.weight.compareTo(a.weight) else second.compareTo(first) // sort by descending difference, break ties in favor of jobs with larger weights\n            }\n        }\n        return Pair(calcSum(jobs, Diff()), calcSum(jobs, Ratio()))\n    }\n    private fun calcSum(jobs: Array<Job>, comp: Comparator<Job>): Long {\n        jobs.sortWith(comp)\n        var time: Long = 0\n        var total: Long = 0\n        jobs.forEach { job ->\n            time += job.length\n            total += job.weight * time\n        }\n        return total\n    }\n}\n\nfun run(filename: String) {\n    var jobs = mutableListOf<Job>()\n    var first = true\n    File(filename).forEachLine {\n        if (!first) {\n            var words = it.trim().split(\" \").map{ it.toLong() }\n            var (weight, length) = words\n            jobs.add(Job(weight, length))\n        } else {\n            first = false\n        }\n    }\n    var (diff, ratio) = Solution().minSum(jobs.toTypedArray())\n    println(\"$diff, $ratio\") // sub-optimal, optimal\n}\n\nfun main() {\n    run(\"problem13.4test1.txt\") // 23, 22\n    run(\"problem13.4test2.txt\") // 68615, 67247\n    run(\"problem13.4.txt\")      // 69119377652, 67311454237\n}\n"
  },
  {
    "path": "kotlin/huffman.kt",
    "content": "/*\n * Programming Problem 14.6: Huffman Codes\n *\n * In this problem the file format is:\n * [number_of_symbols]\n * [weight of symbol #1]\n * [weight of symbol #2]\n * ...\n */\n\nimport java.io.File\nimport java.util.PriorityQueue\nimport java.util.Queue\nimport java.util.LinkedList\n\nvar INF = (1e9 + 7).toInt()\n\ndata class Tree(val weight: Int, val left: Tree? = null, val right: Tree? = null)\n\n/*\nfun encode(A: List<Int>): Tree {\n    var q = PriorityQueue<Tree>(Comparator{ a: Tree, b: Tree -> a.weight.compareTo(b.weight) })\n    for (weight in A)\n        q.add(Tree(weight))\n    while (1 < q.size) {\n        var a = q.poll()\n        var b = q.poll()\n        var c = Tree(a.weight + b.weight, a, b)\n        q.add(c)\n    }\n    return q.poll()\n}\n*/\n\n/*\n * Problem 14.5: Give an implementation of Huffman's greedy algorithm that uses a single invocation\n * of a sorting subroutine, followed by a linear amount of additional work.\n */\nfun encode(A: MutableList<Int>): Tree {\n    A.sort()\n    var first: Queue<Tree> = LinkedList<Tree>(A.map{ weight -> Tree(weight) }.toList())\n    var second: Queue<Tree> = LinkedList<Tree>()\n    var next = mutableListOf<Tree>()\n    while (1 < first.size + second.size) {\n        next.clear()\n        do {\n            if (0 < first.size && 0 < second.size) {\n                if (first.peek().weight < second.peek().weight) next.add(first.poll()) else next.add(second.poll())\n            }\n            else if (0 < first.size) next.add(first.poll())\n            else if (0 < second.size) next.add(second.poll())\n        } while (next.size < 2)\n        var (a, b) = next\n        var c = Tree(a.weight + b.weight, a, b)\n        second.add(c)\n    }\n    return second.poll()\n}\n\nfun run(filename: String): Pair<Int, Int> {\n    var A = mutableListOf<Int>()\n    var first = true\n    File(filename).forEachLine {\n        if (!first) {\n            var weight = it.trim().toInt()\n            A.add(weight)\n        } else {\n            first = false\n        }\n    }\n    var tree = encode(A.toMutableList())\n    var lo = INF\n    var hi = -INF\n    fun go(root: Tree? = tree, depth: Int = 0) {\n        if (root == null)\n            return\n        var isLeaf = { node: Tree? -> node?.left == null && node?.right == null }\n        if (isLeaf(root)) {\n            lo = Math.min(lo, depth)\n            hi = Math.max(hi, depth)\n        } else {\n            go(root.left, depth + 1)\n            go(root.right, depth + 1)\n        }\n    }\n    go()\n    return Pair(lo, hi)\n}\n\nfun main() {\n    for (filename in listOf(\"problem14.6test1.txt\", \"problem14.6test2.txt\", \"problem14.6.txt\")) {\n        var (lo, hi) = run(filename)\n        println(\"$filename: $lo, $hi\") // min, max encoding length in the corresponding optimal prefix-free tree\n    }\n}\n\n//    problem14.6test1.txt: 2, 5\n//    problem14.6test2.txt: 3, 6\n//    problem14.6.txt: 9, 19\n"
  },
  {
    "path": "kotlin/knapsack.kt",
    "content": "import java.io.File\n\nvar INF = (1e9 + 7).toInt()\n\nfun top_down(A: List<Pair<Int, Int>>, K: Int): Int {\n    var N = A.size\n    var m = mutableMapOf<String, Int>()\n    fun go(i: Int = 0, k: Int = K): Int {\n        if (i == N)                                                                 // 🛑 empty set\n            return 0\n        var key = \"$i,$k\"\n        if (m.contains(key))                                                        // 🤔 memo\n            return m[key]!!\n        var (value, weight) = A[i]\n        var include = if (0 <= k - weight) go(i + 1, k - weight) + value else -INF  // ✅ include A[i]\n        var exclude = go(i + 1, k)                                                  // 🚫 exclude A[i]\n        m[key] = Math.max(include, exclude)                                         // 🎯 best\n        return m[key]!!\n    }\n    return go()\n}\n\nfun bottom_up(A: List<Pair<Int, Int>>, K: Int): Int {\n    var N = A.size\n    var dp = Array(N + 1){ Array(K + 1){ -INF } }                                       // 🤔 memo\n    for (k in 0..K)                                                                     // 🛑 empty set\n        dp[0][k] = 0\n    for (i in 1..N) {\n        for (k in 0..K) {\n            var (value, weight) = A[i - 1]\n            var include = if (0 <= k - weight) dp[i - 1][k - weight] + value else -INF  // ✅ include A[i]\n            var exclude = dp[i - 1][k]                                                  // 🚫 exclude A[i]\n            dp[i][k] = Math.max(include, exclude)                                       // 🎯 best\n        }\n    }\n    return dp[N][K]\n}\n\nfun run(filename: String) {\n    var A = mutableListOf<Pair<Int, Int>>()\n    var K = 0\n    var N = 0\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (value, weight) = line.trim().split(\" \").map{ it -> it.toInt() }\n            A.add(Pair(value, weight))\n        } else {\n            var (a, b) = line.trim().split(\" \").map{ it -> it.toInt() }\n            K = a\n            N = b\n            first = false\n        }\n    }\n    var a = top_down(A, K)\n    var b = bottom_up(A, K)\n    assert(a == b) // 💩 sanity check\n    println(\"$filename: $a\")\n}\n\nfun main() {\n    run(\"problem16.7test.txt\")  // problem16.7test.txt: 2493893\n}\n"
  },
  {
    "path": "kotlin/kosaraju.kt",
    "content": "import java.util.Stack\nimport java.io.File\n\nclass RecursiveSolution(var adj: MutableMap<Int, MutableList<Int>>, var rev: MutableMap<Int, MutableList<Int>>) {\n    fun topo_sort(): MutableList<Int> {\n        var list = mutableListOf<Int>()\n        var seen = mutableSetOf<Int>()\n        fun go(u: Int) {\n            if (seen.contains(u))\n                return\n            seen.add(u)\n            for (v in rev[u]!!)\n                go(v)\n            list.add(0, u)\n        }\n        for ((u, _) in rev)\n            go(u)\n        return list\n    }\n    fun kosaraju(): MutableList<List<Int>> {\n        var lists = mutableListOf<List<Int>>()\n        var seen = mutableSetOf<Int>()\n        fun go(u: Int, list: MutableList<Int>) {\n            if (seen.contains(u))\n                return\n            list.add(u); seen.add(u)\n            for (v in adj[u]!!)\n                go(v, list)\n        }\n        for (u in topo_sort()) {\n            if (seen.contains(u))\n                continue\n            var list = mutableListOf<Int>()\n            go(u, list)\n            lists.add(list.toList())\n        }\n        return lists\n    }\n}\n\nclass IterativeSolution(var adj: MutableMap<Int, MutableList<Int>>, var rev: MutableMap<Int, MutableList<Int>>) {\n    fun topo_sort(): MutableList<Int> {\n        var list = mutableListOf<Int>()\n        var seen = mutableSetOf<Int>()\n        for ((u, _) in rev) {\n            if (seen.contains(u))\n                continue\n            var stack = Stack<Int>()\n            stack.push(u); seen.add(u)\n            while (!stack.empty()) {\n                var u = stack.last()\n                for (v in rev[u]!!) {\n                    if (!seen.contains(v)) {\n                        stack.push(v); seen.add(v)\n                    }\n                }\n                if (u == stack.last())\n                    list.add(0, stack.pop())\n            }\n        }\n        return list\n    }\n    fun kosaraju(): MutableList<List<Int>> {\n        var lists = mutableListOf<List<Int>>()\n        var seen = mutableSetOf<Int>()\n        for (u in topo_sort()) {\n            if (seen.contains(u))\n                continue\n            var list = mutableListOf<Int>()\n            var stack = Stack<Int>()\n            stack.push(u); seen.add(u)\n            while (!stack.empty()) {\n                var u = stack.last()\n                for (v in adj[u]!!) {\n                    if (!seen.contains(v)) {\n                        stack.push(v); seen.add(v)\n                    }\n                }\n                if (u == stack.last())\n                    list.add(stack.pop())\n            }\n            lists.add(list.toList())\n        }\n        return lists\n    }\n}\n\nfun run(filename: String) {\n    var adj = mutableMapOf<Int, MutableList<Int>>()\n    var rev = mutableMapOf<Int, MutableList<Int>>()\n    File(filename).forEachLine {\n        var (u, v) = it.trim().split(\" \").map{ it.toInt() }\n        if (!adj.contains(u)) adj[u] = mutableListOf(); if (!adj.contains(v)) adj[v] = mutableListOf()\n        if (!rev.contains(u)) rev[u] = mutableListOf(); if (!rev.contains(v)) rev[v] = mutableListOf()\n        adj[u]!!.add(v)\n        rev[v]!!.add(u)\n    }\n    // var solution = RecursiveSolution(adj, rev)\n    var solution = IterativeSolution(adj, rev)\n    var A = solution.kosaraju()\n    A.sortWith(Comparator{ a: List<Int>, b: List<Int> -> b.size - a.size })\n    println(filename + \": \" + A.map{ it.size }.slice(0 until Math.min(A.size, 5)).joinToString(\" \"))\n}\n\nfun main() {\n    run(\"section8.6.5page64.txt\");  // Graph from section 8.6.5 on page 64 of Algorithms Illuminated: Part 2\n    run(\"problem8.10test1.txt\");    // Test case #1: A 9-vertex 11-edge graph. Top 5 SCC sizes: 3,3,3,0,0\n    run(\"problem8.10test2.txt\");    // Test case #2: An 8-vertex 14-edge graph. Top 5 SCC sizes: 3,3,2,0,0\n    run(\"problem8.10test3.txt\");    // Test case #3: An 8-vertex 9-edge graph. Top 5 SCC sizes: 3,3,1,1,0\n    run(\"problem8.10test4.txt\");    // Test case #4: An 8-vertex 11-edge graph. Top 5 SCC sizes: 7,1,0,0,0\n    run(\"problem8.10test5.txt\");    // Test case #5: A 12-vertex 20-edge graph. Top 5 SCC sizes: 6,3,2,1,0\n    run(\"problem8.10.txt\");         // Challenge data set: Vertices are labeled as positive integers from 1 to 875714\n\n//    section8.6.5page64.txt: 4 3 3 1\n//    problem8.10test1.txt: 3 3 3\n//    problem8.10test2.txt: 3 3 2\n//    problem8.10test3.txt: 3 3 1 1\n//    problem8.10test4.txt: 7 1\n//    problem8.10test5.txt: 6 3 2 1\n//    problem8.10.txt: 434821 968 459 313 211\n\n}\n"
  },
  {
    "path": "kotlin/kruskal.kt",
    "content": "import java.io.File\n\nfun kruskal(E: MutableList<Triple<Int, Int, Int>>): Int {\n    var total: Int = 0\n    var M = E.size\n    var P = IntArray(M) { it } // 🙂 parent representatives of 1..M disjoint sets\n    fun find(x: Int): Int {\n        P[x] = if (P[x] == x) x else find(P[x])\n        return P[x]\n    }\n    fun union(a: Int, b: Int): Boolean {\n        var x = find(a)\n        var y = find(b)\n        if (x == y)\n            return false\n        P[x] = y // 🎲 arbitrary choice\n        return true\n    }\n    E.sortWith(Comparator{ a, b -> a.third.compareTo(b.third) }) // sort edges by nondecreasing weight\n    for ((u, v, w) in E)\n        if (union(u, v))\n            total += w\n    return total\n}\n\nfun run(filename: String) {\n    var E = mutableListOf<Triple<Int, Int, Int>>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (u, v, w) = line.trim().split(\" \").map{ it.toInt() }\n            E.add(Triple(u, v, w))\n        } else {\n            first = false // ignore first line with N vertices and M edges\n        }\n    }\n    var cost = kruskal(E)\n    println(\"$filename: $cost\")\n}\n\nfun main() {\n    run(\"problem15.9test.txt\") // problem15.9test.txt: 14\n    run(\"problem15.9.txt\")     // problem15.9.txt: -3612829\n}\n"
  },
  {
    "path": "kotlin/merge_sort.kt",
    "content": "fun sort(A: IntArray): IntArray {\n    fun merge(A: IntArray, B: IntArray): IntArray {\n        var C = mutableListOf<Int>()\n        var i = 0\n        var j = 0\n        while (i < A.size && j < B.size)\n            if (A[i] < B[j])\n                C.add(A[i++])\n            else\n                C.add(B[j++])\n        A.slice(i..A.lastIndex).forEach { C.add(it) }\n        B.slice(j..B.lastIndex).forEach { C.add(it) }\n        return C.toIntArray()\n    }\n    fun go(A: IntArray): IntArray {\n        var N = A.size\n        if (N < 2)\n            return A\n        var half = Math.floor(N / 2.0).toInt()\n        var first  = go(A.slice(0 until half).toIntArray())\n        var second = go(A.slice(half until N).toIntArray())\n        return merge(first, second)\n    }\n    return go(A)\n}\n\nfun main(args: Array<String>) {\n    sort(intArrayOf(5,3,8,9,1,7,0,2,6,4)).forEach { print(\"$it \") }  // 0 1 2 3 4 5 6 7 8 9\n    println()\n}\n"
  },
  {
    "path": "kotlin/merge_sort_inversions.kt",
    "content": "import java.io.File\n\nfun sort(A: IntArray): Pair<IntArray, Long> {\n    fun merge(A: IntArray, B: IntArray): Pair<IntArray, Long> {\n        var C = mutableListOf<Int>()\n        var inv: Long = 0\n        var i = 0\n        var j = 0\n        while (i < A.size && j < B.size)\n            if (A[i] < B[j]) {\n                C.add(A[i++])\n            } else {\n                inv += A.size - i  // ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.add(B[j++])\n            }\n        A.slice(i..A.lastIndex).forEach { C.add(it) }\n        B.slice(j..B.lastIndex).forEach { C.add(it) }\n        return Pair(C.toIntArray(), inv)\n    }\n    fun go(A: IntArray): Pair<IntArray, Long> {\n        var N = A.size\n        if (N < 2)\n            return Pair(A, 0)\n        var half = Math.floor(N / 2.0).toInt()\n        var (first,  inv1) = go(A.slice(0 until half).toIntArray())\n        var (second, inv2) = go(A.slice(half until N).toIntArray())\n        var (third,  inv3) = merge(first, second)\n        return Pair(third, inv1 + inv2 + inv3)\n    }\n    return go(A)\n}\n\nfun run(filename: String): Long {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    var (_, inv) = sort(A.toIntArray())\n    return inv\n}\n\nfun main() {\n    println(\"problem3.5test.txt: \" + run(\"problem3.5test.txt\"))  // problem3.5test.txt: 28\n    println(\"problem3.5.txt: \"     + run(\"problem3.5.txt\"))      // problem3.5.txt: 2407905288\n}"
  },
  {
    "path": "kotlin/prim.kt",
    "content": "import java.io.File\nimport java.util.PriorityQueue\nimport java.util.Random\n\nfun prim(N: Int, adj: MutableMap<Int, MutableList<Pair<Int, Int>>>): Int {\n    var total: Int = 0\n    var start = Random().nextInt(N) + 1\n    var q = PriorityQueue<Pair<Int, Int>>(Comparator{ a: Pair<Int, Int>, b: Pair<Int, Int> -> a.first.compareTo(b.first) })\n    var seen = mutableSetOf<Int>(start)\n    for ((w, v) in adj[start]!!)\n        q.add(Pair(w, v))\n    while (0 < q.size) {\n        var (cost, u) = q.poll()\n        if (seen.contains(u))\n            continue\n        total += cost; seen.add(u)\n        for ((w, v) in adj[u]!!)\n            if (!seen.contains(v))\n                q.add(Pair(w, v))\n    }\n    return total\n}\n\nfun run(filename: String) {\n    var N: Int = 0\n    var adj = mutableMapOf<Int, MutableList<Pair<Int, Int>>>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (u, v, w) = line.split(\" \").map{ it.toInt() }\n            if (!adj.contains(u)) adj[u] = mutableListOf<Pair<Int, Int>>()\n            if (!adj.contains(v)) adj[v] = mutableListOf<Pair<Int, Int>>()\n            adj[u]!!.add(Pair(w, v))\n            adj[v]!!.add(Pair(w, u))\n        } else {\n            var (numVertex, _) = line.split(\" \").map{ it.toInt() }\n            N = numVertex\n            first = false\n        }\n    }\n    var cost = prim(N, adj)\n    println(\"$filename: $cost\")\n}\n\nfun main() {\n    run(\"problem15.9test.txt\") // problem15.9test.txt: 14\n    run(\"problem15.9.txt\")     // problem15.9.txt: -3612829\n}\n"
  },
  {
    "path": "kotlin/quick_sort.kt",
    "content": "import java.io.File\n\ntypealias PivotFunc = (A: MutableList<Int>, L: Int, R: Int) -> (Int)\nvar pivotLeft: PivotFunc = { _: MutableList<Int>, L: Int, _: Int -> L }\nvar pivotRight: PivotFunc = { _: MutableList<Int>, _: Int, R: Int -> R }\nfun _pivotMedian(A: MutableList<Int>, L: Int, R: Int): Int {\n    var M = L + (R - L) / 2\n    var cand = intArrayOf(A[L], A[M], A[R])\n    cand.sort()\n    var target = cand[1]\n    if (target == A[L]) return L\n    if (target == A[M]) return M\n    if (target == A[R]) return R\n    return -1\n}\nvar pivotMedian: PivotFunc = { A: MutableList<Int>, L: Int, R: Int -> _pivotMedian(A, L, R) }\n\nfun partition(A: MutableList<Int>, L: Int, R: Int, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    var i = L + 1\n    var j = L + 1\n    var k = choosePivot(A, L, R)\n    A[k] = A[L].also { A[L] = A[k] }          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                    // maintain loop invariant A[i] < pivot < A[j]\n            A[i] = A[j].also { A[j] = A[i] }\n            ++i\n        }\n        ++j\n    }\n    A[L] = A[i - 1].also { A[i - 1] = A[L] }  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n}\n\nfun quicksort(A: MutableList<Int>, L: Int, R: Int, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    if (R <= L)\n        return 0\n    var k = partition(A, L, R, choosePivot)\n    return (R - L) + quicksort(A, L, k - 1, choosePivot) + quicksort(A, k + 1, R, choosePivot)\n}\n\nfun run(filename: String, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    return quicksort(A, 0, A.size - 1, choosePivot)\n}\n\nfun main() {\n    var filename = \"problem5.6.txt\"\n    println(\"  left: ${run(filename, pivotLeft)}\")    //   left: 162085\n    println(\" right: ${run(filename, pivotRight)}\")   //  right: 164123\n    println(\"median: ${run(filename, pivotMedian)}\")  // median: 138382\n}\n"
  },
  {
    "path": "kotlin/rselect.kt",
    "content": "import java.io.File\nimport kotlin.random.Random\n\nfun partition(A: MutableList<Int>, L: Int, R: Int): Int {\n    var i = L + 1\n    var j = L + 1\n    var k = Random.nextInt(L, R + 1)          // +1 for L..R inclusive\n    A[L] = A[k].also { A[k] = A[L] }          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                    // maintain loop invariant A[i] < pivot < A[j]\n            A[i] = A[j].also { A[j] = A[i] }\n            ++i\n        }\n        ++j\n    }\n    A[L] = A[i - 1].also { A[i - 1] = A[L] }  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n}\n\nfun rselect(A: MutableList<Int>, i: Int, L_: Int, R_: Int): Int {\n    var L = L_\n    var R = R_\n    var k = partition(A, L, R)\n    if (i == k)\n        return A[k]  // 🎯 lucky guess\n    if (i < k)\n        R = k - 1\n    else\n        L = k + 1\n    return rselect(A, i, L, R)\n}\n\nfun run(filename: String, i: Int): Int {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    var N = A.size\n    return rselect(A, i - 1, 0 , N - 1)  // -1 for 0-based indexing\n}\n\nfun main() {\n    println(\"problem6.5test1.txt: \" + run(\"problem6.5test1.txt\", 5))   // problem6.5test1.txt: 5469\n    println(\"problem6.5test2.txt: \" + run(\"problem6.5test2.txt\", 50))  // problem6.5test2.txt: 4715\n}\n"
  },
  {
    "path": "kotlin/topo_sort.kt",
    "content": "import java.util.Queue\nimport java.util.LinkedList\n\nclass Solution(val adj: MutableMap<Char, List<Char>>) {\n\n    var N: Int\n    var color: Int\n    var m = mutableMapOf<Char, Int>()\n    var seen = mutableSetOf<Char>()\n\n    init {\n        N = adj.size\n        color = 0\n    }\n\n    fun init(start: Int) {\n        color = start\n        m.clear()\n        seen.clear()\n    }\n\n    fun topoSortBFS(): String {\n        init(1)  // 👉 color forward from 1..N\n        bfs()\n        return toString()\n    }\n\n    fun topoSortDFS(): String {\n        init(N)  // 👈 color reverse from N..1 (as the recursive stack unwinds)\n        adj.forEach{ (u, _) -> dfs(u) }\n        return toString()\n    }\n\n    fun bfs() {\n        var degree = mutableMapOf<Char, Int>()\n        adj.forEach{ (_, neighbors) ->\n            neighbors.forEach{ v ->\n                degree[v] = 1 + degree.getOrDefault(v, 0)\n            }\n        }\n        var q: Queue<Char> = LinkedList(adj.map{ (u, _) -> u }.filter{ !degree.contains(it) })\n        while (0 < q.size) {\n            var u = q.poll()\n            m[u] = color++\n            adj[u]!!.forEach{ v ->\n                degree[v] = degree[v]!!.minus(1)\n                if (degree[v] == 0 && !seen.contains(v)) {\n                    q.add(v); seen.add(v)\n                }\n            }\n        }\n    }\n\n    fun dfs(u: Char) {\n        if (seen.contains(u))\n            return\n        seen.add(u)\n        adj[u]!!.forEach{ v ->\n            dfs(v)\n        }\n        m[u] = color--\n    }\n\n    override fun toString(): String {\n        var s = mutableListOf<String>()\n        adj.forEach{ (u, _) ->\n            s.add(\"$u: ${m[u]}\")\n        }\n        return s.joinToString(\"\\n\")\n    }\n}\n\nfun main() {\n    var adj = mutableMapOf<Char, List<Char>>(\n        's' to listOf<Char>('v', 'w'),\n        'v' to listOf<Char>('t'),\n        'w' to listOf<Char>('t'),\n        't' to listOf<Char>()\n    )\n    var solution = Solution(adj)\n    println(\"BFS:\\n${solution.topoSortBFS()}\\n\\nDFS:\\n${solution.topoSortDFS()}\")\n\n//    BFS:\n//    s: 1\n//    v: 2\n//    w: 3\n//    t: 4\n\n//    DFS:\n//    s: 1\n//    v: 3\n//    w: 2\n//    t: 4\n\n}\n"
  },
  {
    "path": "kotlin/weighted_independent_set.kt",
    "content": "/*\n * In this problem, each file describes the weights of vertices in a path graph and has the format:\n * [number_of_vertices_in_path_graph]\n * [weight of first vertex]\n * [weight of second vertex]\n * ...\n * Test case: (contributed by Logan Travis) What is the value of a maximum-weight independent set of the 10-vertex path graph described in this file, and which vertices belong to the MWIS? (Answer: 2617, and the vertices 2, 4, 7, and 10).\n * Challenge data set: Repeat the previous problem for the 1000-vertex path graph described in this file.\n */\n\nimport java.io.File\n\nfun topDown(A: MutableList<Long>): Long {\n    var N = A.size\n    var m = mutableMapOf<Int, Long>()\n    fun go(i: Int = N - 1): Long {\n        if (m.contains(i))                    // 🤔 memo\n            return m[i]!!\n        if (i < 0) {                          // 🛑 empty set\n            m[i] = 0\n            return 0\n        }\n        if (i == 0) {                         // 🛑 single set\n            m[i] = A[0]\n            return A[0]\n        }\n        var include = go(i - 2) + A[i]        // ✅ include A[i]\n        var exclude = go(i - 1)               // 🚫 exclude A[i]\n        m[i] = Math.max(include, exclude)     // 🎯 best\n        return m[i]!!\n    }\n    return go()\n}\n\nfun bottomUp(A: MutableList<Long>): Long {\n    var N = A.size\n    var dp = LongArray(N + 1)                 // 🤔 memo\n    dp[0] = 0                                 // 🛑 empty set\n    dp[1] = A[0]                              // 🛑 single set\n    for (i in 2..N) {\n        var include = dp[i - 2] + A[i - 1]    // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        var exclude = dp[i - 1]               // 🚫 exclude A[i]\n        dp[i] = Math.max(include, exclude)    // 🎯 best\n    }\n    return dp[N]\n}\n\nfun run(filename: String) {\n    var A = mutableListOf<Long>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            A.add(line.toLong())\n        } else {\n            first = false\n        }\n    }\n    var a = topDown(A)\n    var b = bottomUp(A)\n    assert(a == b) // 💩 sanity check\n    println(\"$filename: $a\")\n}\n\nfun main() {\n    run(\"problem16.6test.txt\")  // problem16.6test.txt: 2617\n    run(\"problem16.6.txt\")      // problem16.6.txt: 2955353732\n}\n"
  },
  {
    "path": "kruskal/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(prim)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(prim main.cpp)"
  },
  {
    "path": "kruskal/main.cpp",
    "content": "#include <iostream>\n#include <fstream>\n#include <vector>\n#include <unordered_map>\n#include <numeric>\n\nusing namespace std;\nusing Edge = tuple<int, int, int>;\nusing Edges = vector<Edge>;\nusing Parents = vector<int>;\nusing fun = function<int(int)>;\n\nint kruskal(Edges& E, int total = 0) {\n    auto M = E.size();\n    Parents P(M); iota(P.begin(), P.end(), 0); // 🙂 parent representatives of 1..M disjoint sets \n    fun find = [&](auto x) {\n         return P[x] = P[x] == x ? x : find(P[x]);\n    };\n    auto join = [&](auto a, auto b) {\n        a = find(a);\n        b = find(b);\n        if (a == b)\n            return false;\n        P[a] = b; // 🎲 arbitrary choice\n        return true;\n    };\n    sort(E.begin(), E.end(), [](auto& first, auto& second) { // sort edges by nondecreasing weight\n        auto [u1, v1, w1] = first;\n        auto [u2, v2, w2] = second;\n        return w1 < w2;\n    });\n    for (auto [u, v, w]: E)\n        if (join(u, v))\n            total += w;\n    return total;\n}\n\nvoid run(const string& filename, Edges E = {}) {\n    fstream fin{ filename };\n    int N, M; fin >> N >> M; // ignore first line with N vertices and M edges\n    int u, v, w;             // edge u -> v of weight w\n    while (fin >> u >> v >> w)\n        E.emplace_back(u, v, w);\n    auto cost = kruskal(E);\n    cout << filename << \": \" << cost << endl;\n}\n\nint main() {\n    run(\"problem15.9test.txt\"); // problem15.9test.txt: 14\n    run(\"problem15.9.txt\");     // problem15.9.txt: -3612829\n    return 0;\n}\n"
  },
  {
    "path": "kruskal/main.js",
    "content": "let LineByLine = require('n-readlines');\n\nlet kruskal = E => {\n    let total = 0;\n    let M = E.length;\n    let P = [...Array(M).keys()]; // 🙂 parent representatives of 1..M disjoint sets\n    let find = x => P[x] = P[x] == x ? x : find(P[x]);\n    let union = (a, b) => {\n        a = find(a);\n        b = find(b);\n        if (a == b)\n            return false;\n        P[a] = b; // 🎲 arbitrary choice\n        return true;\n    };\n    E.sort((first, second) => { // sort edges by nondecreasing weight\n        let [u1, v1, w1] = first,\n            [u2, v2, w2] = second;\n        return w1 - w2;\n    });\n    for (let [u, v, w] of E)\n        if (union(u, v))\n            total += w;\n    return total;\n};\n\nlet run = filename => {\n    let E = [];\n    let input = new LineByLine(filename);\n    let line = input.next(); // ignore first line with N vertices and M edges\n    while (line = input.next()) {\n        let [u, v, w] = String.fromCharCode(...line).trim().split(' ').map(Number);\n        E.push([ u, v, w ]);\n    }\n    let cost = kruskal(E);\n    console.log(`${filename}: ${cost}`);\n};\n\nrun('problem15.9test.txt'); // problem15.9test.txt: 14\nrun('problem15.9.txt');     // problem15.9.txt: -3612829\n"
  },
  {
    "path": "kruskal/main.kt",
    "content": "import java.io.File\n\nfun kruskal(E: MutableList<Triple<Int, Int, Int>>): Int {\n    var total: Int = 0\n    var M = E.size\n    var P = IntArray(M) { it } // 🙂 parent representatives of 1..M disjoint sets\n    fun find(x: Int): Int {\n        P[x] = if (P[x] == x) x else find(P[x])\n        return P[x]\n    }\n    fun union(a: Int, b: Int): Boolean {\n        var x = find(a)\n        var y = find(b)\n        if (x == y)\n            return false\n        P[x] = y // 🎲 arbitrary choice\n        return true\n    }\n    E.sortWith(Comparator{ a, b -> a.third.compareTo(b.third) }) // sort edges by nondecreasing weight\n    for ((u, v, w) in E)\n        if (union(u, v))\n            total += w\n    return total\n}\n\nfun run(filename: String) {\n    var E = mutableListOf<Triple<Int, Int, Int>>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (u, v, w) = line.trim().split(\" \").map{ it.toInt() }\n            E.add(Triple(u, v, w))\n        } else {\n            first = false // ignore first line with N vertices and M edges\n        }\n    }\n    var cost = kruskal(E)\n    println(\"$filename: $cost\")\n}\n\nfun main() {\n    run(\"problem15.9test.txt\") // problem15.9test.txt: 14\n    run(\"problem15.9.txt\")     // problem15.9.txt: -3612829\n}\n"
  },
  {
    "path": "kruskal/main.py",
    "content": "from functools import cmp_to_key\n\ndef kruskal(E, total = 0):\n    M = len(E)\n    P = [i for i in range(M)] # 🙂 parent representatives of 1..M disjoint sets\n    def find(x):\n        P[x] = P[x] if P[x] == x else find(P[x])\n        return P[x]\n    def union(a, b):\n        a = find(a)\n        b = find(b)\n        if a == b:\n            return False\n        P[a] = b # 🎲 arbitary choice\n        return True\n    E.sort(key = cmp_to_key(lambda first, second: first[2] - second[2])) # sort edges by nondecreasing weight\n    for u, v, w in E:\n        if union(u, v):\n            total += w\n    return total\n\ndef run(filename):\n    E = []\n    first = True\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            values = [int(x) for x in line.strip().split()]\n            if not first:\n                u, v, w = values # edge u -> v of weight w\n                E.append([ u, v, w ])\n            else:\n                first = False # ignore first line with N vertices and M edges\n    cost = kruskal(E)\n    print(f'{filename}: {cost}')\n\nrun('problem15.9test.txt') # problem15.9test.txt: 14\nrun('problem15.9.txt')     # problem15.9.txt: -3612829\n"
  },
  {
    "path": "kruskal/package.json",
    "content": "{\n  \"name\": \"kruskal\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"clayton wong\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "kruskal/problem15.9.txt",
    "content": "500 2184\n1 2 6807\n2 3 -8874\n3 4 -1055\n4 5 4414\n5 6 1728\n6 7 -2237\n7 8 -7507\n8 9 7990\n9 10 -5012\n10 11 7353\n11 12 -6736\n12 13 -7604\n13 14 5273\n14 15 9331\n15 16 -7753\n16 17 -4370\n17 18 267\n18 19 903\n19 20 7674\n20 21 5436\n21 22 9479\n22 23 9432\n23 24 4472\n24 25 7258\n25 26 8709\n26 27 4358\n27 28 -6775\n28 29 68\n29 30 -2849\n30 31 -9951\n31 32 -8643\n32 33 -4010\n33 34 -4667\n34 35 -5829\n35 36 -5222\n36 37 -7609\n37 38 3054\n38 39 7935\n39 40 173\n40 41 9596\n41 42 -4557\n42 43 -4823\n43 44 -6198\n44 45 8450\n45 46 5533\n46 47 -6059\n47 48 7411\n48 49 9102\n49 50 914\n50 51 9501\n51 52 2704\n52 53 -140\n53 54 1179\n54 55 -1572\n55 56 7095\n56 57 3613\n57 58 5888\n58 59 -4184\n59 60 1910\n60 61 4401\n61 62 591\n62 63 -9504\n63 64 3116\n64 65 -6230\n65 66 1867\n66 67 3816\n67 68 2402\n68 69 7667\n69 70 -3532\n70 71 -2985\n71 72 -3462\n72 73 7737\n73 74 8886\n74 75 -102\n75 76 -3013\n76 77 9948\n77 78 8032\n78 79 -841\n79 80 7663\n80 81 8974\n81 82 5234\n82 83 -3366\n83 84 3926\n84 85 2583\n85 86 3295\n86 87 -3398\n87 88 1058\n88 89 2518\n89 90 2141\n90 91 8894\n91 92 7151\n92 93 -1766\n93 94 -8183\n94 95 1773\n95 96 -6715\n96 97 -9266\n97 98 2472\n98 99 9986\n99 100 -4478\n100 101 -1456\n101 102 3812\n102 103 4658\n103 104 3034\n104 105 6682\n105 106 4633\n106 107 7981\n107 108 -2976\n108 109 8849\n109 110 -5089\n110 111 -5617\n111 112 9034\n112 113 -4112\n113 114 -9800\n114 115 -1462\n115 116 -3454\n116 117 5890\n117 118 -9012\n118 119 7557\n119 120 1231\n120 121 6409\n121 122 491\n122 123 -5925\n123 124 -8728\n124 125 -6474\n125 126 3510\n126 127 -244\n127 128 8413\n128 129 8772\n129 130 1584\n130 131 6869\n131 132 -7293\n132 133 5355\n133 134 -4059\n134 135 -3303\n135 136 -657\n136 137 2192\n137 138 2039\n138 139 -1128\n139 140 626\n140 141 -887\n141 142 -4769\n142 143 -7750\n143 144 5026\n144 145 7151\n145 146 -3960\n146 147 5902\n147 148 -9587\n148 149 27\n149 150 265\n150 151 -5445\n151 152 -1850\n152 153 2907\n153 154 5564\n154 155 3872\n155 156 -823\n156 157 7660\n157 158 8685\n158 159 -3164\n159 160 -7839\n160 161 9902\n161 162 -487\n162 163 8353\n163 164 -5987\n164 165 4948\n165 166 2192\n166 167 2283\n167 168 428\n168 169 2596\n169 170 636\n170 171 6480\n171 172 1141\n172 173 -9697\n173 174 1467\n174 175 -8677\n175 176 -9786\n176 177 -9636\n177 178 -620\n178 179 653\n179 180 -5463\n180 181 6062\n181 182 9858\n182 183 8655\n183 184 -1583\n184 185 5507\n185 186 -719\n186 187 9275\n187 188 -9471\n188 189 7296\n189 190 3768\n190 191 -9\n191 192 7546\n192 193 7645\n193 194 1272\n194 195 2135\n195 196 -9529\n196 197 3904\n197 198 -6105\n198 199 -1925\n199 200 -2491\n200 201 5606\n201 202 -8731\n202 203 -8100\n203 204 2830\n204 205 -2078\n205 206 6293\n206 207 752\n207 208 5289\n208 209 -5201\n209 210 1564\n210 211 4944\n211 212 -2368\n212 213 6432\n213 214 -1421\n214 215 -7142\n215 216 6331\n216 217 3374\n217 218 -2164\n218 219 7518\n219 220 -6876\n220 221 8576\n221 222 -7797\n222 223 -4499\n223 224 -1751\n224 225 5777\n225 226 -3832\n226 227 -5058\n227 228 8187\n228 229 6101\n229 230 9131\n230 231 7884\n231 232 5904\n232 233 -5000\n233 234 -8309\n234 235 -5961\n235 236 -4598\n236 237 3563\n237 238 -1734\n238 239 -9874\n239 240 6294\n240 241 -2489\n241 242 -8966\n242 243 6243\n243 244 -3343\n244 245 -9103\n245 246 1757\n246 247 792\n247 248 9403\n248 249 -3384\n249 250 5555\n250 251 6155\n251 252 7781\n252 253 -2456\n253 254 7775\n254 255 -8096\n255 256 4382\n256 257 -1\n257 258 1925\n258 259 -7340\n259 260 4493\n260 261 -1791\n261 262 9304\n262 263 -2202\n263 264 1858\n264 265 -8596\n265 266 -4101\n266 267 -2373\n267 268 -8907\n268 269 -4668\n269 270 -1966\n270 271 -202\n271 272 -4915\n272 273 5789\n273 274 -7658\n274 275 -4649\n275 276 -2753\n276 277 101\n277 278 -6763\n278 279 3542\n279 280 -9809\n280 281 4856\n281 282 -8850\n282 283 -9803\n283 284 7959\n284 285 7229\n285 286 6301\n286 287 -9632\n287 288 -9903\n288 289 -5683\n289 290 4849\n290 291 -1292\n291 292 -730\n292 293 -1806\n293 294 2480\n294 295 7872\n295 296 -4634\n296 297 3695\n297 298 7216\n298 299 7174\n299 300 -424\n300 301 -157\n301 302 5299\n302 303 -3618\n303 304 2745\n304 305 2356\n305 306 9341\n306 307 6215\n307 308 997\n308 309 6059\n309 310 -2124\n310 311 -8711\n311 312 -3721\n312 313 -5356\n313 314 6085\n314 315 3445\n315 316 7783\n316 317 -7213\n317 318 1999\n318 319 -5649\n319 320 5770\n320 321 -1747\n321 322 -2500\n322 323 5951\n323 324 -6212\n324 325 -3338\n325 326 -810\n326 327 2013\n327 328 3270\n328 329 3052\n329 330 -9595\n330 331 2329\n331 332 2798\n332 333 5123\n333 334 6680\n334 335 -675\n335 336 -1738\n336 337 9560\n337 338 -2733\n338 339 -9443\n339 340 5217\n340 341 -3316\n341 342 3352\n342 343 5124\n343 344 4775\n344 345 6317\n345 346 9720\n346 347 9802\n347 348 536\n348 349 -6018\n349 350 510\n350 351 -4579\n351 352 -4412\n352 353 9106\n353 354 -3551\n354 355 6334\n355 356 2435\n356 357 2271\n357 358 3410\n358 359 -4330\n359 360 5567\n360 361 -5118\n361 362 -2471\n362 363 -5503\n363 364 1476\n364 365 7608\n365 366 -9219\n366 367 -5581\n367 368 9122\n368 369 -8888\n369 370 -1096\n370 371 2687\n371 372 -43\n372 373 170\n373 374 -5983\n374 375 -7986\n375 376 -1601\n376 377 -2445\n377 378 -592\n378 379 -2951\n379 380 7291\n380 381 -5578\n381 382 4514\n382 383 -5091\n383 384 6887\n384 385 -3021\n385 386 -4429\n386 387 4775\n387 388 5259\n388 389 1623\n389 390 6391\n390 391 -2466\n391 392 8465\n392 393 -8912\n393 394 145\n394 395 7996\n395 396 8163\n396 397 -1734\n397 398 1603\n398 399 -8532\n399 400 9988\n400 401 9402\n401 402 2130\n402 403 -2763\n403 404 5488\n404 405 6613\n405 406 -1525\n406 407 -4215\n407 408 3378\n408 409 39\n409 410 8375\n410 411 -579\n411 412 2647\n412 413 1827\n413 414 7295\n414 415 -2987\n415 416 4052\n416 417 -5636\n417 418 9647\n418 419 -1587\n419 420 3067\n420 421 8234\n421 422 -7189\n422 423 -4343\n423 424 8612\n424 425 941\n425 426 -8875\n426 427 5422\n427 428 -4103\n428 429 -760\n429 430 5251\n430 431 -7532\n431 432 6416\n432 433 7244\n433 434 -8966\n434 435 -880\n435 436 -7818\n436 437 9097\n437 438 -2279\n438 439 7262\n439 440 -7217\n440 441 -3548\n441 442 -9851\n442 443 -7558\n443 444 -8151\n444 445 -3461\n445 446 -9813\n446 447 -1603\n447 448 -9184\n448 449 8981\n449 450 3537\n450 451 8574\n451 452 452\n452 453 -4855\n453 454 -6950\n454 455 8161\n455 456 2231\n456 457 9580\n457 458 -3644\n458 459 -9068\n459 460 -5603\n460 461 -1208\n461 462 -9989\n462 463 9734\n463 464 8650\n464 465 1534\n465 466 8194\n466 467 4613\n467 468 1867\n468 469 -3667\n469 470 -8102\n470 471 -875\n471 472 -5564\n472 473 -9211\n473 474 4696\n474 475 -7052\n475 476 -37\n476 477 -399\n477 478 2587\n478 479 7567\n479 480 1924\n480 481 129\n481 482 5965\n482 483 -9453\n483 484 8124\n484 485 -1698\n485 486 -813\n486 487 1576\n487 488 4881\n488 489 7498\n489 490 -9312\n490 491 7282\n491 492 2219\n492 493 -4854\n493 494 -421\n494 495 2927\n495 496 327\n496 497 4963\n497 498 -5404\n498 499 -6861\n499 500 8293\n1 132 -151\n1 171 8358\n1 244 6723\n1 310 9791\n1 316 569\n1 324 -1612\n1 397 -5942\n1 414 3655\n2 25 6267\n2 39 907\n2 104 -8744\n2 157 1036\n2 173 -7751\n2 309 -7230\n3 91 -8754\n3 110 504\n3 136 -4218\n3 144 -9056\n3 231 -494\n3 303 5310\n3 353 9242\n3 482 -1048\n4 43 566\n4 77 -3033\n4 82 -6069\n4 93 -2804\n4 247 2557\n4 266 1686\n4 284 8282\n4 364 -8897\n4 388 5176\n4 423 6365\n5 122 722\n5 153 8816\n6 15 -1593\n6 73 7693\n6 297 -3253\n6 343 154\n7 103 8257\n7 314 -1756\n7 416 -5246\n7 451 7495\n8 124 -5969\n8 162 7179\n8 194 -507\n8 294 -4333\n8 318 -4261\n8 359 2771\n8 432 2206\n9 17 -3864\n9 250 -1984\n9 307 -4003\n9 495 5260\n10 114 223\n10 168 4271\n10 330 7863\n10 390 -8598\n11 43 4323\n11 69 171\n11 176 -9470\n11 469 6195\n12 20 -686\n12 277 6273\n13 24 -9600\n13 61 5960\n13 152 4272\n13 164 -1175\n13 486 7432\n14 64 -1515\n14 209 9744\n14 219 -9493\n14 276 7321\n14 359 9452\n14 396 909\n14 492 5070\n15 87 -1165\n15 211 -290\n15 220 -8415\n15 242 -1132\n15 287 3395\n15 302 9956\n15 365 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284 8488\n28 458 -9550\n28 496 843\n29 61 -9929\n29 66 7663\n29 83 1029\n29 142 -5099\n30 288 8221\n30 324 -9689\n30 373 -5022\n30 490 -5396\n31 70 5151\n31 107 -9611\n31 156 -9373\n31 221 7268\n31 232 2075\n31 267 -1337\n31 272 1807\n31 414 -2222\n31 443 -1030\n31 475 5263\n32 213 4162\n32 333 -5050\n32 376 -5448\n32 433 -4768\n32 443 -4981\n32 462 2102\n33 102 3685\n33 147 -865\n33 301 -7033\n33 392 2279\n33 413 7099\n34 169 -9727\n34 211 8366\n34 268 9651\n34 357 1218\n34 375 3935\n34 417 6302\n34 439 2083\n34 456 -5727\n35 225 -9215\n35 315 6631\n35 362 8945\n35 493 3571\n36 62 -1242\n36 178 6305\n36 292 -6348\n36 301 2079\n36 497 -5712\n37 303 -562\n37 476 4790\n38 126 -761\n38 179 2305\n38 235 -1218\n38 246 3710\n38 267 8612\n38 365 6473\n38 373 -6005\n38 376 247\n38 388 -7439\n38 395 7492\n38 456 -4670\n38 471 3819\n39 122 -6276\n39 170 5316\n39 193 -3940\n39 299 -1837\n40 45 -1173\n40 81 -5474\n40 143 1350\n40 161 2640\n40 322 -5174\n40 336 -7189\n40 387 3360\n41 66 -4827\n41 100 9346\n41 183 -9848\n41 186 8129\n41 220 -1776\n41 281 5319\n41 286 1270\n41 336 6677\n41 376 608\n42 63 3020\n42 131 4949\n42 268 712\n43 123 6522\n43 154 -9305\n43 168 4635\n43 247 8258\n43 258 5745\n43 319 -1878\n43 406 -1432\n43 415 7553\n43 428 9924\n43 431 1393\n43 482 8283\n44 66 6927\n44 197 -7215\n44 231 4764\n44 249 7757\n44 297 339\n44 317 4376\n44 422 -1459\n44 456 6604\n45 68 -2951\n45 202 -8727\n45 219 1607\n45 291 -3145\n45 304 -9980\n45 353 -6425\n45 385 8454\n45 403 9929\n45 436 5789\n45 495 9024\n45 496 -5065\n46 171 -3812\n46 214 -8927\n46 259 -6561\n46 305 -4498\n46 342 -2272\n46 351 8878\n46 372 5199\n46 382 3499\n46 452 3501\n47 58 -3931\n47 71 9490\n47 88 9400\n47 103 -1551\n47 418 -4973\n48 159 -3810\n48 309 -2321\n48 372 823\n48 380 -8760\n48 396 6428\n49 95 -3905\n49 125 993\n49 196 2779\n49 251 -2191\n49 255 -2211\n49 279 -2141\n49 459 2431\n49 484 -6785\n50 65 4266\n50 177 2525\n50 194 9155\n50 228 -4294\n50 297 -1225\n51 177 1630\n51 223 6854\n51 316 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6167\n340 407 2399\n340 484 -1929\n341 343 -5565\n341 420 5265\n341 458 -6180\n342 346 8831\n342 489 1939\n343 378 4970\n343 397 -7570\n343 424 2842\n343 452 -536\n343 488 -6842\n344 356 -7281\n344 453 -8302\n345 425 -5731\n346 454 -3527\n347 392 5563\n347 418 -2386\n347 466 3771\n347 468 -4049\n348 397 6497\n348 486 -2415\n349 352 -613\n349 398 3335\n350 378 6543\n350 434 7699\n350 465 9140\n350 482 -2291\n351 409 -1048\n351 426 3612\n351 471 409\n353 395 9151\n353 412 9296\n353 419 -735\n353 436 -5275\n353 453 -1087\n353 500 8370\n354 359 -4117\n354 386 -846\n354 410 1672\n355 406 -1579\n355 420 -8857\n355 497 -895\n356 466 -8140\n357 404 -2310\n357 450 1350\n358 382 3911\n358 386 3609\n358 395 -6761\n358 436 8427\n359 495 1554\n360 459 -6735\n360 489 -9515\n361 377 4408\n361 437 -1746\n361 488 -2367\n361 499 8199\n362 422 9597\n362 427 4182\n364 375 7988\n364 415 6754\n365 426 -6930\n365 481 -3070\n366 382 -6765\n366 432 -9909\n366 454 -9405\n367 380 -5349\n367 412 3542\n368 380 6629\n368 411 -1355\n368 421 1195\n368 465 6223\n368 470 -334\n368 474 -7991\n368 493 2282\n369 376 3704\n369 450 -2512\n370 420 -9950\n371 398 -9477\n371 432 -6670\n371 448 -200\n372 387 6424\n373 380 -3592\n373 470 -8502\n375 393 9105\n375 453 -2933\n375 492 -6444\n376 427 -7114\n376 470 -4493\n377 434 9582\n378 465 3894\n379 398 8878\n379 491 9760\n380 439 -1859\n381 407 9593\n381 484 -1667\n382 405 6975\n382 499 4725\n383 466 7807\n384 442 -9312\n384 480 5442\n384 485 -3665\n385 410 -2643\n385 422 2303\n386 438 6767\n388 481 3277\n389 411 -7853\n390 417 3903\n390 463 7696\n390 479 9257\n392 465 3120\n392 493 759\n394 398 6573\n394 494 7679\n395 479 1669\n395 495 -2332\n396 459 6338\n398 450 -9491\n398 476 -8221\n398 481 -9932\n399 424 -4886\n399 445 6302\n400 433 -6294\n401 412 -662\n401 464 9064\n401 480 -8775\n402 469 -1306\n403 498 1210\n406 420 -2125\n407 488 7000\n410 459 -1638\n410 467 -1424\n410 478 -1565\n410 493 -7145\n411 445 1797\n420 464 -3068\n420 492 -1060\n421 435 -8158\n422 469 -8414\n423 440 -2764\n423 493 1392\n424 472 6518\n425 498 -57\n427 451 4970\n428 433 -4289\n428 487 896\n429 453 4573\n430 443 -3248\n433 482 -5668\n433 494 9608\n433 499 7927\n434 488 -447\n438 479 3219\n441 466 -2111\n442 454 -7877\n442 488 -4811\n445 483 -1801\n452 462 8016\n452 489 -1217\n452 497 -8325\n454 489 -9298\n454 498 -4686\n456 474 1691\n457 500 2717\n459 478 2393\n460 492 -5705\n460 499 9321\n462 471 -2894\n463 473 -5410\n463 477 1205\n464 468 -2595\n464 475 -9291\n467 473 9837\n473 500 1052\n474 491 7245\n478 480 -4790\n496 500 -1519"
  },
  {
    "path": "kruskal/problem15.9test.txt",
    "content": "6 10\n1 2 6\n1 4 5\n1 5 4\n2 4 1\n2 5 2\n2 3 5\n2 6 3\n3 6 4\n4 5 2\n5 6 4"
  },
  {
    "path": "matrix_multiplication/main.jl",
    "content": "#\n# Straightforward Matrix Multiplication\n#\n# Input: n x n integer matrices X and Y\n#\n# Output: Z = X * Y\n#\n\nN = 2\n\nX = [1 2\n     3 4]\n\nY = [5 6\n     7 8]\n\nZ = zeros(Int64, N, N)\n\nfor i in 1:N\n    for j in 1:N\n        for k in 1:N\n            Z[i, j] += X[i, k] * Y[k, j]\n        end\n    end\nend\n\nfunction pretty_print(A)\n    for row in eachrow(A)\n        println(row)\n    end\n    println()\nend\n\npretty_print(X)\npretty_print(Y)\npretty_print(Z)\n\n# ➜  matrix_multiplication git:(main) ✗ julia ./main.jl\n# [1, 2]\n# [3, 4]\n\n# [5, 6]\n# [7, 8]\n\n# [19, 22]\n# [43, 50]\n"
  },
  {
    "path": "matrix_multiplication/main.py",
    "content": "#\n# Straightforward Matrix Multiplication\n#\n# Input: n x n integer matrices X and Y\n#\n# Output: Z = X * Y\n#\n\nN = 2\n\nX = [[1, 2],\n     [3, 4]]\n\nY = [[5, 6],\n     [7, 8]]\n\nZ = [[0] * N for _ in range(N)]\n\nfor i in range(N):\n    for j in range(N):\n        for k in range(N):\n            Z[i][j] += X[i][k] * Y[k][j]\n\npretty_print = lambda A: [print(row) for row in A] and print()\n\npretty_print(X)\npretty_print(Y)\npretty_print(Z)\n\n# ➜  matrix_multiplication git:(main) ✗ python3 ./main.py\n# [1, 2]\n# [3, 4]\n\n# [5, 6]\n# [7, 8]\n\n# [19, 22]\n# [43, 50]\n"
  },
  {
    "path": "merge_sort/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.14)\nproject(mergesort)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(mergesort merge_sort.cpp)"
  },
  {
    "path": "merge_sort/merge_sort.cpp",
    "content": "#include <iostream>\n#include <vector>\n\nusing namespace std;\n\nclass Solution {\npublic:\n    using VI = vector<int>;\n    VI mergesort(VI& A) {\n        return go(move(A));\n    }\nprivate:\n    VI go(VI&& A) {\n        auto N = A.size();\n        if( N < 2 )\n            return A;\n        auto half = A.begin() + (N / 2);\n        auto first = go({ A.begin(), half }),\n             second = go({ half, A.end() });\n        return merge(first, second);\n    }\n    VI merge(VI& A, VI& B, VI C = {}) {\n        auto i{ 0 },\n             j{ 0 };\n        while (i < A.size() && j < B.size())\n            C.push_back(A[i] < B[j] ? A[i++] : B[j++]);\n        C.insert(C.end(), A.begin() + i, A.end());\n        C.insert(C.end(), B.begin() + j, B.end());\n        return C;\n    }\n};\n\nint main() {\n    Solution::VI A{ 3,5,7,1,3,9,2,0 };\n    auto ans = Solution().mergesort(A);\n    copy(ans.begin(), ans.end(), ostream_iterator<int>(cout, \" \")), cout << endl;  // 0 1 2 3 4 5 6 7 8 9\n    return 0;\n}\n"
  },
  {
    "path": "merge_sort/merge_sort.jl",
    "content": "#\n# Merge Sort\n#\n# Input: array A of n distinct integers\n# Output: array with the same integers, sorted from smallest to largest\n#\nfunction go(A)\n  N = length(A)\n  if N < 2\n    return A\n  end\n  half = div(N, 2)\n  first = go(A[begin:half])\n  second = go(A[half+1:end])\n  return merge(first, second)\nend\n\nfunction merge(A, B)\n  C = []\n  i, j, k = 1, 1, 1\n  while i <= length(A) && j <= length(B)\n    if A[i] < B[j]\n      push!(C, A[i])\n      i += 1\n    else\n      push!(C, B[j])\n      j += 1\n    end\n    k += 1\n  end\n  append!(C, @view A[i:end])\n  append!(C, @view B[j:end])\n  return C\nend\n\nprintln(go([5, 3, 8, 9, 1, 7, 0, 2, 6, 4]))  # Any[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n\n# ➜  merge_sort git:(main) ✗ julia ./merge_sort.jl\n# Any[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n"
  },
  {
    "path": "merge_sort/merge_sort.js",
    "content": "let sort = A => {\n    let go = A => {\n        let N = A.length;\n        if (N < 2)\n            return A;\n        let half = Math.floor(N / 2);\n        let first  = go([...A.slice(0, half)]),\n            second = go([...A.slice(half, N)]);\n        return merge(first, second);\n    };\n    let merge = (A, B, C = []) => {\n        let M = A.length,\n            N = B.length;\n        let i = 0,\n            j = 0;\n        while (i < M && j < N)\n            C.push(A[i] < B[j] ? A[i++] : B[j++]);\n        C.push(...A.slice(i, M));\n        C.push(...B.slice(j, N));\n        return C;\n    };\n    return go(A);\n};\n\nconsole.log(sort([5,3,8,9,1,7,0,2,6,4]));  // (10) [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n"
  },
  {
    "path": "merge_sort/merge_sort.kt",
    "content": "fun sort(A: IntArray): IntArray {\n    fun merge(A: IntArray, B: IntArray): IntArray {\n        var C = mutableListOf<Int>()\n        var i = 0\n        var j = 0\n        while (i < A.size && j < B.size)\n            if (A[i] < B[j])\n                C.add(A[i++])\n            else\n                C.add(B[j++])\n        A.slice(i..A.lastIndex).forEach { C.add(it) }\n        B.slice(j..B.lastIndex).forEach { C.add(it) }\n        return C.toIntArray()\n    }\n    fun go(A: IntArray): IntArray {\n        var N = A.size\n        if (N < 2)\n            return A\n        var half = Math.floor(N / 2.0).toInt()\n        var first  = go(A.slice(0 until half).toIntArray())\n        var second = go(A.slice(half until N).toIntArray())\n        return merge(first, second)\n    }\n    return go(A)\n}\n\nfun main(args: Array<String>) {\n    sort(intArrayOf(5,3,8,9,1,7,0,2,6,4)).forEach { print(\"$it \") }  // 0 1 2 3 4 5 6 7 8 9\n    println()\n}\n"
  },
  {
    "path": "merge_sort/merge_sort.py",
    "content": "from math import floor\n\ndef sort(A):\n    def go(A):\n        N = len(A)\n        if N < 2:\n            return A\n        half = floor(N / 2)\n        first =  go(A[:half])\n        second = go(A[half:])\n        return merge(first, second)\n    def merge(A, B):\n        C = []\n        i = 0\n        j = 0\n        while i < len(A) and j < len(B):\n            if A[i] < B[j]:\n                C.append(A[i]); i += 1\n            else:\n                C.append(B[j]); j += 1\n        C.extend(A[i:])\n        C.extend(B[j:])\n        return C\n    return go(A)\n\nprint(sort([5,3,8,9,1,7,0,2,6,4]))  # [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n"
  },
  {
    "path": "merge_sort_inversions/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(merge_sort_inversions)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(merge_sort_inversions merge_sort_inversions.cpp)"
  },
  {
    "path": "merge_sort_inversions/merge_sort_inversions.cpp",
    "content": "#include <iostream>\n#include <vector>\n#include <fstream>\n\nusing namespace std;\n\nclass Solution {\npublic:\n    using VL = vector<long>;\n    using Pair = pair<VL, long>;\n    using fun = function<Pair(VL&&)>;\n    Pair merge(VL& A, VL& B, VL C = {}, long inv = 0) {\n        auto i = 0,\n             j = 0;\n        while (i < A.size() && j < B.size()) {\n            if (A[i] < B[j]) {\n                C.push_back(A[i++]);\n            } else {\n                inv += A.size() - i; // ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.push_back(B[j++]);\n            }\n        }\n        C.insert(C.end(), A.begin() + i, A.end());\n        C.insert(C.end(), B.begin() + j, B.end());\n        return { C, inv };\n    }\n    Pair inversions(VL& A) {\n        fun go = [&](VL&& A) -> Pair {\n            int N = A.size();\n            if (N < 2)\n                return { A, 0 };\n            int half = N / 2;\n            auto [first,  inv1] = go({ A.begin(), A.begin() + half });\n            auto [second, inv2] = go({ A.begin() + half, A.end() });\n            auto [third,  inv3] = merge(first, second);\n            return { third, inv1 + inv2 + inv3 };\n        };\n        return go(move(A));\n    }\n};\n\nlong run(string filename) {\n    Solution solution;\n    Solution::VL A;\n    fstream fin{ filename };\n    for (string line; fin >> line; A.push_back(stol(line)));\n    auto [_, inv] = solution.inversions(A);\n    return inv;\n}\n\nint main() {\n    cout << \"problem3.5test.txt: \" << run(\"problem3.5test.txt\") << endl   // problem3.5test.txt: 28\n         << \"problem3.5.txt: \"     << run(\"problem3.5.txt\")     << endl;  // problem3.5.txt: 2407905288\n    return 0;\n}\n"
  },
  {
    "path": "merge_sort_inversions/merge_sort_inversions.jl",
    "content": "#\n# Merge Sort Inversions\n#\n# Input: array A of n distinct integers\n# Output: the number of inversions of A\n#\nfunction go(A)\n  N = length(A)\n  if N < 2\n    return A, 0\n  end\n  half = div(N, 2)\n  first, inv1 = go(A[begin:half])\n  second, inv2 = go(A[half+1:end])\n  third, inv3 = merge(first, second)\n  return third, inv1 + inv2 + inv3\nend\n\nfunction merge(A, B)\n  C, inv = [], 0\n  i, j, k = 1, 1, 1\n  while i <= length(A) && j <= length(B)\n    if A[i] < B[j]\n      push!(C, A[i])\n      i += 1\n    else\n      push!(C, B[j]); inv += length(A) - i + 1  # ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n      j += 1\n    end\n    k += 1\n  end\n  append!(C, @view A[i:end])\n  append!(C, @view B[j:end])\n  return C, inv\nend\n\nfunction run(filename)\n  input = Int[]\n  open(filename, \"r\") do file\n    for line in eachline(file)\n      push!(input, parse(Int, strip(line)))\n    end\n  end\n  _, inv = go(input)\n  return inv\nend\n\nprintln(run(\"problem3.5test.txt\"))  # 28\nprintln(run(\"problem3.5.txt\"))      # 2407905288\n"
  },
  {
    "path": "merge_sort_inversions/merge_sort_inversions.js",
    "content": "let sort = A => {\n    let go = A => {\n        let N = A.length;\n        if (N < 2)\n            return [A, 0];\n        let half = Math.floor(N / 2);\n        let [first,  inv1] = go([...A.slice(0, half)]),\n            [second, inv2] = go([...A.slice(half, N)]),\n            [third,  inv3] = merge(first, second);\n        return [third, inv1 + inv2 + inv3];\n    };\n    let merge = (A, B, C = [], inv = 0) => {\n        let M = A.length,\n            N = B.length;\n        let i = 0,\n            j = 0;\n        while (i < M && j < N)\n            if (A[i] < B[j])\n                C.push(A[i++]);\n            else\n                inv += M - i,      // ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.push(B[j++]);\n        C.push(...A.slice(i, M));\n        C.push(...B.slice(j, N));\n        return [C, inv];\n    };\n    return go(A);\n};\n\nlet run = filename => {\n    let A = [];\n    require('fs').readFileSync(filename, 'utf-8').split(/\\r?\\n/).forEach(line => A.push(Number(line)));\n    let [_, inv] = sort(A);\n    return inv;\n}\n\nconsole.log(`problem3.5test.txt: ${run('problem3.5test.txt')}`);  // problem3.5test.txt: 28\nconsole.log(`problem3.5.txt: ${run('problem3.5.txt')}`);          // problem3.5.txt: 2407905288\n"
  },
  {
    "path": "merge_sort_inversions/merge_sort_inversions.kt",
    "content": "import java.io.File\n\nfun sort(A: IntArray): Pair<IntArray, Long> {\n    fun merge(A: IntArray, B: IntArray): Pair<IntArray, Long> {\n        var C = mutableListOf<Int>()\n        var inv: Long = 0\n        var i = 0\n        var j = 0\n        while (i < A.size && j < B.size)\n            if (A[i] < B[j]) {\n                C.add(A[i++])\n            } else {\n                inv += A.size - i  // ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.add(B[j++])\n            }\n        A.slice(i..A.lastIndex).forEach { C.add(it) }\n        B.slice(j..B.lastIndex).forEach { C.add(it) }\n        return Pair(C.toIntArray(), inv)\n    }\n    fun go(A: IntArray): Pair<IntArray, Long> {\n        var N = A.size\n        if (N < 2)\n            return Pair(A, 0)\n        var half = Math.floor(N / 2.0).toInt()\n        var (first,  inv1) = go(A.slice(0 until half).toIntArray())\n        var (second, inv2) = go(A.slice(half until N).toIntArray())\n        var (third,  inv3) = merge(first, second)\n        return Pair(third, inv1 + inv2 + inv3)\n    }\n    return go(A)\n}\n\nfun run(filename: String): Long {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    var (_, inv) = sort(A.toIntArray())\n    return inv\n}\n\nfun main() {\n    println(\"problem3.5test.txt: \" + run(\"problem3.5test.txt\"))  // problem3.5test.txt: 28\n    println(\"problem3.5.txt: \"     + run(\"problem3.5.txt\"))      // problem3.5.txt: 2407905288\n}"
  },
  {
    "path": "merge_sort_inversions/merge_sort_inversions.py",
    "content": "from math import floor\n\ndef sort(A):\n    def go(A):\n        N = len(A)\n        if N < 2:\n            return [A, 0]\n        half = floor(N / 2)\n        first,  inv1 = go(A[:half])\n        second, inv2 = go(A[half:])\n        third,  inv3 = merge(first, second)\n        return [third, inv1 + inv2 + inv3]\n    def merge(A, B, inv = 0):\n        C = []\n        i = 0\n        j = 0\n        while i < len(A) and j < len(B):\n            if A[i] < B[j]:\n                C.append(A[i]); i += 1\n            else:\n                inv += len(A) - i        # ⭐️ B[j] comes before all remaining A[i...], thus all remaining A[i...] are inversions\n                C.append(B[j]); j += 1\n        C.extend(A[i:])\n        C.extend(B[j:])\n        return [C, inv]\n    return go(A)\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            A.append(int(line))\n    _, inv = sort(A)\n    return inv\n\nprint(f\"problem3.5test.txt: {run('problem3.5test.txt')}\")  # problem3.5test.txt: 28\nprint(f\"problem3.5.txt: {run('problem3.5.txt')}\")          # problem3.5.txt: 2407905288\n"
  },
  {
    "path": "merge_sort_inversions/problem3.5.txt",
    "content": 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  },
  {
    "path": "merge_sort_inversions/problem3.5test.txt",
    "content": "54044\r\n14108\r\n79294\r\n29649\r\n25260\r\n60660\r\n2995\r\n53777\r\n49689\r\n9083"
  },
  {
    "path": "prim/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(prim)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(prim main.cpp)"
  },
  {
    "path": "prim/main.cpp",
    "content": "#include <iostream>\n#include <fstream>\n#include <unordered_set>\n#include <unordered_map>\n#include <queue>\n#include <random>\n\nusing namespace std;\nusing Pair = pair<int, int>;\nusing Pairs = vector<Pair>;\nusing AdjList = unordered_map<int, Pairs>;\nusing Queue = priority_queue<Pair, Pairs, std::greater<Pair>>;\nusing Set = unordered_set<int>;\n\nconstexpr auto INF = int(1e9 + 7);\n\nint getRandom(int N) {\n    default_random_engine generator;\n    uniform_int_distribution<int> distribution(1, N);\n    return distribution(generator);\n}\n\nint prim(int N, AdjList& adj, Queue q = {}, Set seen = {}, int total = 0) {\n    auto start = getRandom(N);\n    seen.insert(start);\n    for (auto [w, v]: adj[start])\n        q.push({ w, v });\n    while (q.size()) {\n        auto [cost, u] = q.top(); q.pop();\n        if (!seen.insert(u).second)\n            continue;\n        total += cost;\n        for (auto [w, v]: adj[u])\n            if (seen.find(v) == seen.end())\n                q.push({ w, v });\n    }\n    return total;\n}\n\nvoid run(const string& filename) {\n    AdjList adj;\n    fstream fin{ filename };\n    int N, M; fin >> N >> M; // N vertices and M edges\n    int u, v, w;             // edge u -> v of weight w\n    while (fin >> u >> v >> w) {\n        adj[u].emplace_back(w, v);\n        adj[v].emplace_back(w, u);\n    }\n    auto cost = prim(N, adj);\n    cout << filename << \": \" << cost << endl;\n}\n\nint main() {\n    run(\"problem15.9test.txt\"); // problem15.9test.txt: 14\n    run(\"problem15.9.txt\");     // problem15.9.txt: -3612829\n    return 0;\n}\n"
  },
  {
    "path": "prim/main.js",
    "content": "let LineByLine = require('n-readlines');\n\nlet key = x => Array.isArray(x) ? x[0] : x;\nlet heappush = (A, x, f = Math.min) => {\n    let P = i => Math.floor((i - 1) / 2);  // parent\n    A.push(x);\n    let N = A.length,\n        i = N - 1;\n    while (0 < i && key(A[i]) == f(key(A[i]), key(A[P(i)]))) {\n        [A[i], A[P(i)]] = [A[P(i)], A[i]];\n        i = P(i);\n    }\n};\nlet heappop = (A, f = Math.min) => {\n    let L = i => 2 * i + 1,  // children\n        R = i => 2 * i + 2;\n    let N = A.length,\n        i = 0;\n    let top = A[0];\n    [A[0], A[N - 1]] = [A[N - 1], A[0]], A.pop(), --N;\n    let ok;\n    do {\n        ok = true;\n        let left = f == Math.min ? Infinity : -Infinity,\n            right = left;\n        if (L(i) < N && key(A[i]) != f(key(A[i]), key(A[L(i)]))) ok = false, left  = key(A[L(i)]);\n        if (R(i) < N && key(A[i]) != f(key(A[i]), key(A[R(i)]))) ok = false, right = key(A[R(i)]);\n        if (!ok) {\n            let j = left == f(left, right) ? L(i) : R(i);\n            [A[i], A[j]] = [A[j], A[i]];\n            i = j;\n        }\n    } while (!ok);\n    return top;\n};\n\nlet prim = (N, adj, q = [], seen = new Set(), total = 0) => {\n    let start = Math.ceil(N * Math.random());\n    seen.add(start);\n    for (let [w, v] of adj.get(start))\n        heappush(q, [w, v]);\n    while (q.length) {\n        let [cost, u] = heappop(q);\n        if (seen.has(u))\n            continue;\n        total += cost; seen.add(u);\n        for (let [w, v] of adj.get(u))\n            if (!seen.has(v))\n                heappush(q, [w, v]);\n    }\n    return total;\n};\n\nlet run = filename => {\n    let adj = new Map();\n    let input = new LineByLine(filename);\n    let line = input.next();\n    let [N, M] = String.fromCharCode(...line).trim().split(' ').map(Number);\n    while (line = input.next()) {\n        let [u, v, w] = String.fromCharCode(...line).trim().split(' ').map(Number);\n        if (!adj.has(u)) adj.set(u, []);\n        if (!adj.has(v)) adj.set(v, []);\n        adj.get(u).push([w, v]);\n        adj.get(v).push([w, u]);\n    }\n    let cost = prim(N, adj);\n    console.log(`${filename}: ${cost}`);\n}\n\nrun('problem15.9test.txt') // problem15.9test.txt: 14\nrun('problem15.9.txt')     // problem15.9.txt: -3612829\n"
  },
  {
    "path": "prim/main.kt",
    "content": "import java.io.File\nimport java.util.PriorityQueue\nimport java.util.Random\n\nfun prim(N: Int, adj: MutableMap<Int, MutableList<Pair<Int, Int>>>): Int {\n    var total: Int = 0\n    var start = Random().nextInt(N) + 1\n    var q = PriorityQueue<Pair<Int, Int>>(Comparator{ a: Pair<Int, Int>, b: Pair<Int, Int> -> a.first.compareTo(b.first) })\n    var seen = mutableSetOf<Int>(start)\n    for ((w, v) in adj[start]!!)\n        q.add(Pair(w, v))\n    while (0 < q.size) {\n        var (cost, u) = q.poll()\n        if (seen.contains(u))\n            continue\n        total += cost; seen.add(u)\n        for ((w, v) in adj[u]!!)\n            if (!seen.contains(v))\n                q.add(Pair(w, v))\n    }\n    return total\n}\n\nfun run(filename: String) {\n    var N: Int = 0\n    var adj = mutableMapOf<Int, MutableList<Pair<Int, Int>>>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            var (u, v, w) = line.split(\" \").map{ it.toInt() }\n            if (!adj.contains(u)) adj[u] = mutableListOf<Pair<Int, Int>>()\n            if (!adj.contains(v)) adj[v] = mutableListOf<Pair<Int, Int>>()\n            adj[u]!!.add(Pair(w, v))\n            adj[v]!!.add(Pair(w, u))\n        } else {\n            var (numVertex, _) = line.split(\" \").map{ it.toInt() }\n            N = numVertex\n            first = false\n        }\n    }\n    var cost = prim(N, adj)\n    println(\"$filename: $cost\")\n}\n\nfun main() {\n    run(\"problem15.9test.txt\") // problem15.9test.txt: 14\n    run(\"problem15.9.txt\")     // problem15.9.txt: -3612829\n}\n"
  },
  {
    "path": "prim/main.py",
    "content": "from random import randint\nfrom heapq import heappush, heappop\n\ndef prim(N, adj, total = 0):\n    q = []\n    seen = set()\n    start = randint(1, N); seen.add(start)\n    for w, v in adj[start]:\n        heappush(q, [w, v])\n    while q:\n        cost, u = heappop(q)\n        if u in seen:\n            continue\n        total += cost; seen.add(u)\n        for w, v in adj[u]:\n            if v not in seen:\n                heappush(q, [w, v])\n    return total\n\ndef run(filename):\n    adj = {}\n    first = True\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            words = line.split()\n            if not first:\n                u, v, w = [int(x) for x in words]\n                if u not in adj: adj[u] = []\n                if v not in adj: adj[v] = []\n                adj[u].append([w, v])\n                adj[v].append([w, u])\n            else:\n                N, M = [int(x) for x in words]\n                first = False\n    cost = prim(N, adj)\n    print(f'{filename}: {cost}')\n\nrun('problem15.9test.txt') # problem15.9test.txt: 14\nrun('problem15.9.txt')     # problem15.9.txt: -3612829\n"
  },
  {
    "path": "prim/package.json",
    "content": "{\n  \"name\": \"prim\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"clayton wong\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "prim/problem15.9.txt",
    "content": "500 2184\n1 2 6807\n2 3 -8874\n3 4 -1055\n4 5 4414\n5 6 1728\n6 7 -2237\n7 8 -7507\n8 9 7990\n9 10 -5012\n10 11 7353\n11 12 -6736\n12 13 -7604\n13 14 5273\n14 15 9331\n15 16 -7753\n16 17 -4370\n17 18 267\n18 19 903\n19 20 7674\n20 21 5436\n21 22 9479\n22 23 9432\n23 24 4472\n24 25 7258\n25 26 8709\n26 27 4358\n27 28 -6775\n28 29 68\n29 30 -2849\n30 31 -9951\n31 32 -8643\n32 33 -4010\n33 34 -4667\n34 35 -5829\n35 36 -5222\n36 37 -7609\n37 38 3054\n38 39 7935\n39 40 173\n40 41 9596\n41 42 -4557\n42 43 -4823\n43 44 -6198\n44 45 8450\n45 46 5533\n46 47 -6059\n47 48 7411\n48 49 9102\n49 50 914\n50 51 9501\n51 52 2704\n52 53 -140\n53 54 1179\n54 55 -1572\n55 56 7095\n56 57 3613\n57 58 5888\n58 59 -4184\n59 60 1910\n60 61 4401\n61 62 591\n62 63 -9504\n63 64 3116\n64 65 -6230\n65 66 1867\n66 67 3816\n67 68 2402\n68 69 7667\n69 70 -3532\n70 71 -2985\n71 72 -3462\n72 73 7737\n73 74 8886\n74 75 -102\n75 76 -3013\n76 77 9948\n77 78 8032\n78 79 -841\n79 80 7663\n80 81 8974\n81 82 5234\n82 83 -3366\n83 84 3926\n84 85 2583\n85 86 3295\n86 87 -3398\n87 88 1058\n88 89 2518\n89 90 2141\n90 91 8894\n91 92 7151\n92 93 -1766\n93 94 -8183\n94 95 1773\n95 96 -6715\n96 97 -9266\n97 98 2472\n98 99 9986\n99 100 -4478\n100 101 -1456\n101 102 3812\n102 103 4658\n103 104 3034\n104 105 6682\n105 106 4633\n106 107 7981\n107 108 -2976\n108 109 8849\n109 110 -5089\n110 111 -5617\n111 112 9034\n112 113 -4112\n113 114 -9800\n114 115 -1462\n115 116 -3454\n116 117 5890\n117 118 -9012\n118 119 7557\n119 120 1231\n120 121 6409\n121 122 491\n122 123 -5925\n123 124 -8728\n124 125 -6474\n125 126 3510\n126 127 -244\n127 128 8413\n128 129 8772\n129 130 1584\n130 131 6869\n131 132 -7293\n132 133 5355\n133 134 -4059\n134 135 -3303\n135 136 -657\n136 137 2192\n137 138 2039\n138 139 -1128\n139 140 626\n140 141 -887\n141 142 -4769\n142 143 -7750\n143 144 5026\n144 145 7151\n145 146 -3960\n146 147 5902\n147 148 -9587\n148 149 27\n149 150 265\n150 151 -5445\n151 152 -1850\n152 153 2907\n153 154 5564\n154 155 3872\n155 156 -823\n156 157 7660\n157 158 8685\n158 159 -3164\n159 160 -7839\n160 161 9902\n161 162 -487\n162 163 8353\n163 164 -5987\n164 165 4948\n165 166 2192\n166 167 2283\n167 168 428\n168 169 2596\n169 170 636\n170 171 6480\n171 172 1141\n172 173 -9697\n173 174 1467\n174 175 -8677\n175 176 -9786\n176 177 -9636\n177 178 -620\n178 179 653\n179 180 -5463\n180 181 6062\n181 182 9858\n182 183 8655\n183 184 -1583\n184 185 5507\n185 186 -719\n186 187 9275\n187 188 -9471\n188 189 7296\n189 190 3768\n190 191 -9\n191 192 7546\n192 193 7645\n193 194 1272\n194 195 2135\n195 196 -9529\n196 197 3904\n197 198 -6105\n198 199 -1925\n199 200 -2491\n200 201 5606\n201 202 -8731\n202 203 -8100\n203 204 2830\n204 205 -2078\n205 206 6293\n206 207 752\n207 208 5289\n208 209 -5201\n209 210 1564\n210 211 4944\n211 212 -2368\n212 213 6432\n213 214 -1421\n214 215 -7142\n215 216 6331\n216 217 3374\n217 218 -2164\n218 219 7518\n219 220 -6876\n220 221 8576\n221 222 -7797\n222 223 -4499\n223 224 -1751\n224 225 5777\n225 226 -3832\n226 227 -5058\n227 228 8187\n228 229 6101\n229 230 9131\n230 231 7884\n231 232 5904\n232 233 -5000\n233 234 -8309\n234 235 -5961\n235 236 -4598\n236 237 3563\n237 238 -1734\n238 239 -9874\n239 240 6294\n240 241 -2489\n241 242 -8966\n242 243 6243\n243 244 -3343\n244 245 -9103\n245 246 1757\n246 247 792\n247 248 9403\n248 249 -3384\n249 250 5555\n250 251 6155\n251 252 7781\n252 253 -2456\n253 254 7775\n254 255 -8096\n255 256 4382\n256 257 -1\n257 258 1925\n258 259 -7340\n259 260 4493\n260 261 -1791\n261 262 9304\n262 263 -2202\n263 264 1858\n264 265 -8596\n265 266 -4101\n266 267 -2373\n267 268 -8907\n268 269 -4668\n269 270 -1966\n270 271 -202\n271 272 -4915\n272 273 5789\n273 274 -7658\n274 275 -4649\n275 276 -2753\n276 277 101\n277 278 -6763\n278 279 3542\n279 280 -9809\n280 281 4856\n281 282 -8850\n282 283 -9803\n283 284 7959\n284 285 7229\n285 286 6301\n286 287 -9632\n287 288 -9903\n288 289 -5683\n289 290 4849\n290 291 -1292\n291 292 -730\n292 293 -1806\n293 294 2480\n294 295 7872\n295 296 -4634\n296 297 3695\n297 298 7216\n298 299 7174\n299 300 -424\n300 301 -157\n301 302 5299\n302 303 -3618\n303 304 2745\n304 305 2356\n305 306 9341\n306 307 6215\n307 308 997\n308 309 6059\n309 310 -2124\n310 311 -8711\n311 312 -3721\n312 313 -5356\n313 314 6085\n314 315 3445\n315 316 7783\n316 317 -7213\n317 318 1999\n318 319 -5649\n319 320 5770\n320 321 -1747\n321 322 -2500\n322 323 5951\n323 324 -6212\n324 325 -3338\n325 326 -810\n326 327 2013\n327 328 3270\n328 329 3052\n329 330 -9595\n330 331 2329\n331 332 2798\n332 333 5123\n333 334 6680\n334 335 -675\n335 336 -1738\n336 337 9560\n337 338 -2733\n338 339 -9443\n339 340 5217\n340 341 -3316\n341 342 3352\n342 343 5124\n343 344 4775\n344 345 6317\n345 346 9720\n346 347 9802\n347 348 536\n348 349 -6018\n349 350 510\n350 351 -4579\n351 352 -4412\n352 353 9106\n353 354 -3551\n354 355 6334\n355 356 2435\n356 357 2271\n357 358 3410\n358 359 -4330\n359 360 5567\n360 361 -5118\n361 362 -2471\n362 363 -5503\n363 364 1476\n364 365 7608\n365 366 -9219\n366 367 -5581\n367 368 9122\n368 369 -8888\n369 370 -1096\n370 371 2687\n371 372 -43\n372 373 170\n373 374 -5983\n374 375 -7986\n375 376 -1601\n376 377 -2445\n377 378 -592\n378 379 -2951\n379 380 7291\n380 381 -5578\n381 382 4514\n382 383 -5091\n383 384 6887\n384 385 -3021\n385 386 -4429\n386 387 4775\n387 388 5259\n388 389 1623\n389 390 6391\n390 391 -2466\n391 392 8465\n392 393 -8912\n393 394 145\n394 395 7996\n395 396 8163\n396 397 -1734\n397 398 1603\n398 399 -8532\n399 400 9988\n400 401 9402\n401 402 2130\n402 403 -2763\n403 404 5488\n404 405 6613\n405 406 -1525\n406 407 -4215\n407 408 3378\n408 409 39\n409 410 8375\n410 411 -579\n411 412 2647\n412 413 1827\n413 414 7295\n414 415 -2987\n415 416 4052\n416 417 -5636\n417 418 9647\n418 419 -1587\n419 420 3067\n420 421 8234\n421 422 -7189\n422 423 -4343\n423 424 8612\n424 425 941\n425 426 -8875\n426 427 5422\n427 428 -4103\n428 429 -760\n429 430 5251\n430 431 -7532\n431 432 6416\n432 433 7244\n433 434 -8966\n434 435 -880\n435 436 -7818\n436 437 9097\n437 438 -2279\n438 439 7262\n439 440 -7217\n440 441 -3548\n441 442 -9851\n442 443 -7558\n443 444 -8151\n444 445 -3461\n445 446 -9813\n446 447 -1603\n447 448 -9184\n448 449 8981\n449 450 3537\n450 451 8574\n451 452 452\n452 453 -4855\n453 454 -6950\n454 455 8161\n455 456 2231\n456 457 9580\n457 458 -3644\n458 459 -9068\n459 460 -5603\n460 461 -1208\n461 462 -9989\n462 463 9734\n463 464 8650\n464 465 1534\n465 466 8194\n466 467 4613\n467 468 1867\n468 469 -3667\n469 470 -8102\n470 471 -875\n471 472 -5564\n472 473 -9211\n473 474 4696\n474 475 -7052\n475 476 -37\n476 477 -399\n477 478 2587\n478 479 7567\n479 480 1924\n480 481 129\n481 482 5965\n482 483 -9453\n483 484 8124\n484 485 -1698\n485 486 -813\n486 487 1576\n487 488 4881\n488 489 7498\n489 490 -9312\n490 491 7282\n491 492 2219\n492 493 -4854\n493 494 -421\n494 495 2927\n495 496 327\n496 497 4963\n497 498 -5404\n498 499 -6861\n499 500 8293\n1 132 -151\n1 171 8358\n1 244 6723\n1 310 9791\n1 316 569\n1 324 -1612\n1 397 -5942\n1 414 3655\n2 25 6267\n2 39 907\n2 104 -8744\n2 157 1036\n2 173 -7751\n2 309 -7230\n3 91 -8754\n3 110 504\n3 136 -4218\n3 144 -9056\n3 231 -494\n3 303 5310\n3 353 9242\n3 482 -1048\n4 43 566\n4 77 -3033\n4 82 -6069\n4 93 -2804\n4 247 2557\n4 266 1686\n4 284 8282\n4 364 -8897\n4 388 5176\n4 423 6365\n5 122 722\n5 153 8816\n6 15 -1593\n6 73 7693\n6 297 -3253\n6 343 154\n7 103 8257\n7 314 -1756\n7 416 -5246\n7 451 7495\n8 124 -5969\n8 162 7179\n8 194 -507\n8 294 -4333\n8 318 -4261\n8 359 2771\n8 432 2206\n9 17 -3864\n9 250 -1984\n9 307 -4003\n9 495 5260\n10 114 223\n10 168 4271\n10 330 7863\n10 390 -8598\n11 43 4323\n11 69 171\n11 176 -9470\n11 469 6195\n12 20 -686\n12 277 6273\n13 24 -9600\n13 61 5960\n13 152 4272\n13 164 -1175\n13 486 7432\n14 64 -1515\n14 209 9744\n14 219 -9493\n14 276 7321\n14 359 9452\n14 396 909\n14 492 5070\n15 87 -1165\n15 211 -290\n15 220 -8415\n15 242 -1132\n15 287 3395\n15 302 9956\n15 365 -9352\n15 496 783\n16 49 2410\n16 93 4136\n16 110 221\n16 248 6820\n16 275 -7206\n16 369 -1699\n17 35 -2706\n17 69 -1754\n17 92 4535\n17 185 5372\n17 212 7481\n17 248 5899\n17 272 5930\n17 317 2595\n17 376 5972\n17 427 7949\n17 432 -2484\n18 241 3362\n18 279 2815\n18 433 -9810\n18 451 6558\n19 240 -4667\n19 328 -8231\n19 335 -7787\n19 367 -5912\n19 474 -590\n20 115 -7690\n20 129 356\n20 207 -9098\n20 237 -3298\n20 278 7668\n20 307 1045\n20 336 -1814\n20 385 904\n21 167 3714\n21 175 1947\n21 185 6092\n21 285 6656\n21 352 1462\n22 46 8371\n22 63 -7119\n22 85 -9225\n22 101 -9660\n22 156 -9282\n22 208 -7025\n22 237 -508\n22 416 -4591\n22 479 -2180\n23 117 7541\n23 198 3114\n24 42 5136\n24 89 401\n24 268 5400\n24 297 3760\n24 348 48\n25 278 6246\n25 281 -2140\n25 288 -3078\n25 315 1949\n25 328 4495\n26 80 3206\n26 94 6394\n26 226 -6114\n26 260 -6981\n26 322 -560\n26 366 -7642\n26 432 4115\n26 436 2275\n27 30 2964\n27 99 6073\n27 189 3311\n27 372 69\n28 93 1885\n28 192 -2679\n28 260 5134\n28 284 8488\n28 458 -9550\n28 496 843\n29 61 -9929\n29 66 7663\n29 83 1029\n29 142 -5099\n30 288 8221\n30 324 -9689\n30 373 -5022\n30 490 -5396\n31 70 5151\n31 107 -9611\n31 156 -9373\n31 221 7268\n31 232 2075\n31 267 -1337\n31 272 1807\n31 414 -2222\n31 443 -1030\n31 475 5263\n32 213 4162\n32 333 -5050\n32 376 -5448\n32 433 -4768\n32 443 -4981\n32 462 2102\n33 102 3685\n33 147 -865\n33 301 -7033\n33 392 2279\n33 413 7099\n34 169 -9727\n34 211 8366\n34 268 9651\n34 357 1218\n34 375 3935\n34 417 6302\n34 439 2083\n34 456 -5727\n35 225 -9215\n35 315 6631\n35 362 8945\n35 493 3571\n36 62 -1242\n36 178 6305\n36 292 -6348\n36 301 2079\n36 497 -5712\n37 303 -562\n37 476 4790\n38 126 -761\n38 179 2305\n38 235 -1218\n38 246 3710\n38 267 8612\n38 365 6473\n38 373 -6005\n38 376 247\n38 388 -7439\n38 395 7492\n38 456 -4670\n38 471 3819\n39 122 -6276\n39 170 5316\n39 193 -3940\n39 299 -1837\n40 45 -1173\n40 81 -5474\n40 143 1350\n40 161 2640\n40 322 -5174\n40 336 -7189\n40 387 3360\n41 66 -4827\n41 100 9346\n41 183 -9848\n41 186 8129\n41 220 -1776\n41 281 5319\n41 286 1270\n41 336 6677\n41 376 608\n42 63 3020\n42 131 4949\n42 268 712\n43 123 6522\n43 154 -9305\n43 168 4635\n43 247 8258\n43 258 5745\n43 319 -1878\n43 406 -1432\n43 415 7553\n43 428 9924\n43 431 1393\n43 482 8283\n44 66 6927\n44 197 -7215\n44 231 4764\n44 249 7757\n44 297 339\n44 317 4376\n44 422 -1459\n44 456 6604\n45 68 -2951\n45 202 -8727\n45 219 1607\n45 291 -3145\n45 304 -9980\n45 353 -6425\n45 385 8454\n45 403 9929\n45 436 5789\n45 495 9024\n45 496 -5065\n46 171 -3812\n46 214 -8927\n46 259 -6561\n46 305 -4498\n46 342 -2272\n46 351 8878\n46 372 5199\n46 382 3499\n46 452 3501\n47 58 -3931\n47 71 9490\n47 88 9400\n47 103 -1551\n47 418 -4973\n48 159 -3810\n48 309 -2321\n48 372 823\n48 380 -8760\n48 396 6428\n49 95 -3905\n49 125 993\n49 196 2779\n49 251 -2191\n49 255 -2211\n49 279 -2141\n49 459 2431\n49 484 -6785\n50 65 4266\n50 177 2525\n50 194 9155\n50 228 -4294\n50 297 -1225\n51 177 1630\n51 223 6854\n51 316 -1958\n51 327 -9020\n52 128 -6427\n52 163 -9821\n52 185 -8731\n52 238 -8566\n52 322 8467\n52 443 8943\n52 455 6943\n53 70 -5040\n53 414 -507\n54 208 5922\n54 298 8138\n54 367 -863\n55 74 -9806\n55 111 -3854\n55 138 -184\n55 188 -944\n55 211 7740\n56 65 9727\n56 141 3669\n56 214 1623\n56 239 1609\n56 244 7576\n56 475 -6542\n57 176 -130\n57 258 -5160\n57 365 7655\n57 421 -4680\n58 333 -6694\n59 158 -9038\n59 257 3130\n59 267 3293\n59 326 185\n59 343 -4103\n59 403 -5780\n59 424 9400\n59 445 3970\n60 75 -4458\n60 98 1851\n60 151 5579\n60 152 -5617\n60 158 5691\n60 281 -2544\n60 337 302\n60 427 2681\n60 454 632\n60 456 4219\n60 483 -953\n61 83 -7267\n61 88 -8574\n61 338 1664\n61 372 5879\n61 429 2849\n62 83 6359\n62 173 -7617\n62 235 -6507\n62 270 5311\n62 286 2939\n62 318 5306\n62 365 8961\n62 477 -4003\n62 480 9555\n63 108 9903\n63 152 -1476\n63 210 -3653\n63 267 -8209\n63 364 1907\n63 477 7451\n63 498 -5460\n64 68 5150\n64 148 -7784\n65 86 4268\n65 109 -7488\n65 128 3617\n65 200 1627\n65 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  },
  {
    "path": "prim/problem15.9test.txt",
    "content": "6 10\n1 2 6\n1 4 5\n1 5 4\n2 4 1\n2 5 2\n2 3 5\n2 6 3\n3 6 4\n4 5 2\n5 6 4"
  },
  {
    "path": "quick_sort/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(quick_sort)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(quick_sort main.cpp)"
  },
  {
    "path": "quick_sort/main.cpp",
    "content": "#include <iostream>\n#include <fstream>\n#include <vector>\n\nusing namespace std;\nusing VI = vector<int>;\nusing fun = function<int(VI&, int, int)>;\n\nfun pivotLeft = [](VI& A, int L, int R) { return L; };\nfun pivotRight = [](VI& A, int L, int R) { return R; };\nfun pivotMedian = [](VI& A, int L, int R) {\n    auto M = L + (R - L) / 2;\n    VI cand{ A[L], A[M], A[R] };\n    sort(cand.begin(), cand.end());\n    auto target = cand[1];\n    if (target == A[L]) return L;\n    if (target == A[M]) return M;\n    if (target == A[R]) return R;\n};\n\nint partition(VI& A, int L, int R, fun choosePivot) {\n    auto i = L + 1,\n         j = L + 1,\n         k = choosePivot(A, L, R);\n    swap(A[L], A[k]);           // swap pivot A[k] with first element of the subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {            // maintain loop invariant A[i] < pivot < A[j]\n            swap(A[i], A[j]);\n            ++i;\n        }\n        ++j;\n    }\n    swap(A[L], A[i - 1]);  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n}\n\nint quicksort(VI& A, int L, int R, fun choosePivot) {\n    if (R <= L)\n        return 0;\n    auto k = partition(A, L, R, choosePivot);\n    return (R - L) + quicksort(A, L, k - 1, choosePivot)\n                   + quicksort(A, k + 1, R, choosePivot);\n}\n\nint run(string& filename, fun choosePivot) {\n    VI A;\n    fstream fin{ filename };\n    for (string line; fin >> line; A.push_back(stoi(line)));\n    int N = A.size();\n    return quicksort(A, 0, N - 1, choosePivot);\n}\n\nint main() {\n    string filename{ \"problem5.6.txt\" };\n    cout << \"  left: \" << run(filename, pivotLeft)   << endl   //   left: 162085\n         << \" right: \" << run(filename, pivotRight)  << endl   //  right: 164123\n         << \"median: \" << run(filename, pivotMedian) << endl;  // median: 138382\n    return 0;\n}\n"
  },
  {
    "path": "quick_sort/main.js",
    "content": "let pivotLeft = (A, L, R) => L;\nlet pivotRight = (A, L, R) => R;\nlet pivotMedian = (A, L, R) => {\n    let M = L + Math.floor((R - L) / 2);\n    let cand = [A[L], A[M], A[R]].sort((a, b) => a - b),\n        target = cand[1];\n    if (target == A[L]) return L;\n    if (target == A[M]) return M;\n    if (target == A[R]) return R;\n};\n\nlet partition = (A, L, R, choosePivot) => {\n    let i = L + 1,\n        j = L + 1,\n        k = choosePivot(A, L, R);\n    [A[L], A[k]] = [A[k], A[L]];          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                // maintain loop invariant A[i] < pivot < A[j]\n            [A[i], A[j]] = [A[j], A[i]];\n            ++i;\n        }\n        ++j;\n    }\n    [A[L], A[i - 1]] = [A[i - 1], A[L]];  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n};\n\nlet quicksort = (A, L, R, choosePivot) => {\n    if (R <= L)\n        return 0;\n    let k = partition(A, L, R, choosePivot);\n    return (R - L) + quicksort(A, L, k - 1, choosePivot)\n                   + quicksort(A, k + 1, R, choosePivot);\n};\n\nlet run = (filename, choosePivot) => {\n    let A = [];\n    let LineByLine = require(\"n-readlines\");\n    let input = new LineByLine(filename);\n    for (let line; line = input.next(); A.push(Number(line)));\n    return quicksort(A, 0, A.length - 1, choosePivot);\n}\n\nlet filename = 'problem5.6.txt';\nconsole.log(`  left: ${run(filename, pivotLeft)}`);    //   left: 162085\nconsole.log(` right: ${run(filename, pivotRight)}`);   //  right: 164123\nconsole.log(`median: ${run(filename, pivotMedian)}`);  // median: 138382\n"
  },
  {
    "path": "quick_sort/main.kt",
    "content": "import java.io.File\n\ntypealias PivotFunc = (A: MutableList<Int>, L: Int, R: Int) -> (Int)\nvar pivotLeft: PivotFunc = { _: MutableList<Int>, L: Int, _: Int -> L }\nvar pivotRight: PivotFunc = { _: MutableList<Int>, _: Int, R: Int -> R }\nfun _pivotMedian(A: MutableList<Int>, L: Int, R: Int): Int {\n    var M = L + (R - L) / 2\n    var cand = intArrayOf(A[L], A[M], A[R])\n    cand.sort()\n    var target = cand[1]\n    if (target == A[L]) return L\n    if (target == A[M]) return M\n    if (target == A[R]) return R\n    return -1\n}\nvar pivotMedian: PivotFunc = { A: MutableList<Int>, L: Int, R: Int -> _pivotMedian(A, L, R) }\n\nfun partition(A: MutableList<Int>, L: Int, R: Int, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    var i = L + 1\n    var j = L + 1\n    var k = choosePivot(A, L, R)\n    A[k] = A[L].also { A[L] = A[k] }          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                    // maintain loop invariant A[i] < pivot < A[j]\n            A[i] = A[j].also { A[j] = A[i] }\n            ++i\n        }\n        ++j\n    }\n    A[L] = A[i - 1].also { A[i - 1] = A[L] }  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n}\n\nfun quicksort(A: MutableList<Int>, L: Int, R: Int, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    if (R <= L)\n        return 0\n    var k = partition(A, L, R, choosePivot)\n    return (R - L) + quicksort(A, L, k - 1, choosePivot) + quicksort(A, k + 1, R, choosePivot)\n}\n\nfun run(filename: String, choosePivot: (A: MutableList<Int>, L: Int, R: Int) -> (Int)): Int {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    return quicksort(A, 0, A.size - 1, choosePivot)\n}\n\nfun main() {\n    var filename = \"problem5.6.txt\"\n    println(\"  left: ${run(filename, pivotLeft)}\")    //   left: 162085\n    println(\" right: ${run(filename, pivotRight)}\")   //  right: 164123\n    println(\"median: ${run(filename, pivotMedian)}\")  // median: 138382\n}\n"
  },
  {
    "path": "quick_sort/main.py",
    "content": "def pivotLeft(A, L, R): return L\ndef pivotRight(A, L, R): return R\ndef pivotMedian(A, L, R):\n    M = L + (R - L) // 2\n    cand = sorted([A[L], A[M], A[R]])\n    target = cand[1]\n    if target == A[L]: return L\n    if target == A[M]: return M\n    if target == A[R]: return R\n\ndef partition(A, L, R, choosePivot):\n    i = L + 1\n    j = L + 1\n    k = choosePivot(A, L, R)\n    A[L], A[k] = A[k], A[L]          # swap pivot A[k] with first element of subarray A[L]\n    while j <= R:\n        if A[j] < A[L]:              # maintain loop invariant A[i] < pivot < A[j]\n            A[i], A[j] = A[j], A[i]\n            i += 1\n        j += 1\n    A[L], A[i - 1] = A[i - 1], A[L]  # swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n\ndef quicksort(A, L, R, choosePivot):\n    if R <= L:\n        return 0\n    k = partition(A, L, R, choosePivot)\n    return (R - L) + quicksort(A, L, k - 1, choosePivot) + quicksort(A, k + 1, R, choosePivot)\n\ndef run(filename, choosePivot):\n    A = []\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            A.append(int(line))\n\n    return quicksort(A, 0, len(A) - 1, choosePivot)\n\nfilename = 'problem5.6.txt'\nprint(f'  left: {run(filename, pivotLeft)}')    #   left: 162085\nprint(f' right: {run(filename, pivotRight)}')   #  right: 164123\nprint(f'median: {run(filename, pivotMedian)}')  # median: 138382\n"
  },
  {
    "path": "quick_sort/package.json",
    "content": "{\n  \"name\": \"quick_sort\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"Clayton Wong\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "quick_sort/problem5.6.txt",
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  },
  {
    "path": "quick_sort/problem5.6test1.txt",
    "content": "2148\r\n9058\r\n7742\r\n3153\r\n6324\r\n609\r\n7628\r\n5469\r\n7017\r\n504\r\n"
  },
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    "path": "quick_sort/problem5.6test2.txt",
    "content": "2148\r\n9058\r\n7742\r\n3153\r\n6324\r\n609\r\n7628\r\n5469\r\n7017\r\n504\r\n4092\r\n1582\r\n9572\r\n1542\r\n5697\r\n2081\r\n4218\r\n3130\r\n7923\r\n9595\r\n6558\r\n3859\r\n9832\r\n3062\r\n6788\r\n7578\r\n7432\r\n479\r\n8439\r\n9079\r\n7173\r\n2667\r\n2770\r\n2655\r\n972\r\n4264\r\n2014\r\n3171\r\n4715\r\n345\r\n4388\r\n3816\r\n8887\r\n3915\r\n3490\r\n2327\r\n123\r\n4596\r\n4307\r\n8737\r\n4007\r\n6798\r\n6551\r\n1627\r\n1190\r\n4984\r\n2480\r\n3404\r\n2027\r\n4778\r\n2951\r\n2795\r\n5002\r\n8121\r\n8910\r\n9593\r\n5254\r\n448\r\n6237\r\n5565\r\n1816\r\n392\r\n8143\r\n9310\r\n9293\r\n3138\r\n4869\r\n6756\r\n872\r\n6183\r\n3517\r\n3513\r\n1676\r\n5498\r\n9172\r\n5739\r\n6108\r\n7538\r\n7671\r\n5780\r\n8666\r\n540\r\n9771\r\n6837\r\n9341\r\n1590\r\n5689\r\n1605\r\n1103\r\n5859\r\n"
  },
  {
    "path": "rec_int_mult/main.jl",
    "content": "#\n# Recursive Integer Multiplication\n#\n# Input: two n-digit positive integers x and y\n# Output: the product x * y\n# Assumption: n is a power of 2\n#\nusing Test, Random\n\nfunction go(x, y)\n  if x < 10 || y < 10\n    return x * y\n  end\n\n  n = max(length(string(x)), length(string(y)))\n  if isodd(n)\n    n += 1\n  end\n\n  m = 10 ^ div(n, 2) # middle decimal value\n  a, b = div(x, m), mod(x, m)\n  c, d = div(y, m), mod(y, m)\n\n  ac = go(a, c)\n  ad = go(a, d)\n  bc = go(b, c)\n  bd = go(b, d)\n  return 10^n * ac + 10^div(n, 2) * (ad + bc) + bd\nend\n\nRandom.seed!(123456789)\n\n@testset \"Recursive Integer Multiplication tests\" begin\n    for _ in 1:100\n        n = rand((1, 2, 4, 8, 16))\n\n        lo = 10^(n-1)\n        hi = 10^n - 1\n\n        x = rand(lo:hi)\n        y = rand(lo:hi)\n\n        expect, actual = x * y, go(x, y)\n        @test expect == actual\n        println(\"($x x $y)\\nexpect: $expect\\nactual: $actual\\n\")\n    end\nend\n"
  },
  {
    "path": "rec_mat_mult/main.py",
    "content": "#\n# Standard Recursive Matrix Multiplication (RecMatMult)\n#\n# Input: n x n integer matrices X and Y\n# Output: Z = X * Y\n# Assumption: n is a power of 2\n# Complexity: O(n^3) - T(n) = 8T(n/2) + O(n^2)\n#\nimport numpy as np\n\ndef go(X, Y):\n    n = X.shape[0]\n\n    # Base case: 1x1 matrix\n    if n == 1:\n        return X * Y\n\n    # Divide: Partition A and B into n/2 x n/2 submatrices\n    k = n // 2\n\n    A, B = X[:k, :k], X[:k, k:]\n    C, D = X[k:, :k], X[k:, k:]\n\n    E, F = Y[:k, :k], Y[:k, k:]\n    G, H = Y[k:, :k], Y[k:, k:]\n\n    # Combine: Reconstruct the full matrix from quadrants\n    Z = np.zeros((n, n), dtype=X.dtype)\n    Z[:k, :k], Z[:k, k:] = go(A, E) + go(B, G), go(A, F) + go(B, H)\n    Z[k:, :k], Z[k:, k:] = go(C, E) + go(D, G), go(C, F) + go(D, H)\n    return Z\n\ndef pretty_print(A, label=''):\n    col_width = max(len(str(x)) for x in A.flat)\n    if len(label):\n        print(label)\n        n = A.shape[0]\n        spaces = n - 1\n        print('-' * (n * col_width + spaces))\n\n    fmt = f'{{:>{col_width}d}}'\n    for row in A:\n        print(' '.join(fmt.format(x) for x in row))\n    print()\n\ndef main():\n    n = 4 # n must be a power of 2 for this simple implementation\n    A = np.random.randint(0, 10, (n, n))\n    B = np.random.randint(0, 10, (n, n))\n\n    expect = A @ B\n    actual = go(A, B)\n    pretty_print(A, 'A')\n    pretty_print(B, 'B')\n    pretty_print(expect, 'A * B (expect)')\n    pretty_print(actual, 'A * B (actual)')\n    assert(np.array_equal(expect, actual))\n\nif __name__ == \"__main__\":\n    main()\n\n# ➜  rec_mat_mult git:(main) ✗ uv run ./main.py\n# A\n# -------\n# 9 0 6 8\n# 4 6 9 2\n# 0 5 9 9\n# 9 1 1 3\n\n# B\n# -------\n# 2 3 4 6\n# 5 5 4 3\n# 1 6 8 0\n# 5 2 4 2\n\n# A * B (expect)\n# ---------------\n#  64  79 116  70\n#  57 100 120  46\n#  79  97 128  33\n#  39  44  60  63\n\n# A * B (actual)\n# ---------------\n#  64  79 116  70\n#  57 100 120  46\n#  79  97 128  33\n#  39  44  60  63\n"
  },
  {
    "path": "rec_mat_mult/pyproject.toml",
    "content": "[project]\nname = \"rec-mat-mult\"\nversion = \"0.1.0\"\ndescription = \"Recursive matrix multiplication\"\nreadme = \"README.md\"\nrequires-python = \">=3.14\"\ndependencies = [\n    \"numpy>=2.4.1\",\n]\n"
  },
  {
    "path": "rselect/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(rselect)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(rselect main.cpp)"
  },
  {
    "path": "rselect/main.cpp",
    "content": "#include <iostream>\n#include <fstream>\n#include <vector>\n#include <random>\n\nusing namespace std;\nusing VI = vector<int>;\n\nint random(int L, int R) {\n    random_device rd;\n    mt19937 gen{ rd() };\n    uniform_int_distribution dist(L, R);\n    return dist(gen);\n}\n\nint partition(VI& A, int L, int R) {\n    auto i = L + 1,\n         j = L + 1,\n         k = random(L, R);\n    swap(A[L], A[k]);            // swap pivot A[k] with first element of the subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L])         // maintain loop invariant A[i] < pivot < A[j]\n            swap(A[i++], A[j]);\n        ++j;\n    }\n    swap(A[L], A[i - 1]);        // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n}\n\nint rselect(VI& A, int i, int L, int R) {\n    auto k = partition(A, L, R);\n    if (i == k)\n        return A[k];  // 🎯 lucky guess\n    if (i < k)\n        R = k - 1;\n    else\n        L = k + 1;\n    return rselect(A, i, L, R);\n}\n\nint run(string filename, int i, VI A = {}) {\n    fstream fin{ filename };\n    for (string line; fin >> line; A.push_back(stoi(line)));\n    int N = A.size();\n    return rselect(A, i - 1, 0, N - 1);  // -1 for 0-based indexing\n}\n\nint main() {\n    cout << \"problem6.5test1.txt: \" << run(\"problem6.5test1.txt\", 5)  << endl;  // problem6.5test1.txt: 5469\n    cout << \"problem6.5test2.txt: \" << run(\"problem6.5test2.txt\", 50) << endl;  // problem6.5test2.txt: 4715\n    return 0;\n}\n"
  },
  {
    "path": "rselect/main.js",
    "content": "let random = (L, R) => Math.floor(Math.random() * (R + 1 - L) + L);  // +1 for L..R inclusive\n\nlet partition = (A, L, R) => {\n    let i = L + 1,\n        j = L + 1,\n        k = random(L, R);\n    [A[L], A[k]] = [A[k], A[L]];          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                // maintain loop invariant A[i] < pivot < A[j]\n            [A[i], A[j]] = [A[j], A[i]];\n            ++i;\n        }\n        ++j;\n    }\n    [A[L], A[i - 1]] = [A[i - 1], A[L]];  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1;\n};\n\nlet rselect = (A, i, L, R) => {\n    let k = partition(A, L, R);\n    if (i == k)\n        return A[k];  // 🎯 lucky guess\n    if (i < k)\n        R = k - 1;\n    else\n        L = k + 1;\n    return rselect(A, i, L, R);\n}\n\nlet run = (filename, i) => {\n    let A = [];\n    let LineByLine = require(\"n-readlines\");\n    let input = new LineByLine(filename);\n    for (let line; line = input.next(); A.push(Number(line)));\n    let N = A.length;\n    return rselect(A, i - 1, 0, N - 1);  // -1 for 0-based indexing\n};\n\nconsole.log(`problem6.5test1.txt: ${run('problem6.5test1.txt', 5)}`);   // problem6.5test1.txt: 5469\nconsole.log(`problem6.5test2.txt: ${run('problem6.5test2.txt', 50)}`);  // problem6.5test2.txt: 4715\n"
  },
  {
    "path": "rselect/main.kt",
    "content": "import java.io.File\nimport kotlin.random.Random\n\nfun partition(A: MutableList<Int>, L: Int, R: Int): Int {\n    var i = L + 1\n    var j = L + 1\n    var k = Random.nextInt(L, R + 1)          // +1 for L..R inclusive\n    A[L] = A[k].also { A[k] = A[L] }          // swap pivot A[k] with first element of subarray A[L]\n    while (j <= R) {\n        if (A[j] < A[L]) {                    // maintain loop invariant A[i] < pivot < A[j]\n            A[i] = A[j].also { A[j] = A[i] }\n            ++i\n        }\n        ++j\n    }\n    A[L] = A[i - 1].also { A[i - 1] = A[L] }  // swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n}\n\nfun rselect(A: MutableList<Int>, i: Int, L_: Int, R_: Int): Int {\n    var L = L_\n    var R = R_\n    var k = partition(A, L, R)\n    if (i == k)\n        return A[k]  // 🎯 lucky guess\n    if (i < k)\n        R = k - 1\n    else\n        L = k + 1\n    return rselect(A, i, L, R)\n}\n\nfun run(filename: String, i: Int): Int {\n    var A = mutableListOf<Int>()\n    File(filename).forEachLine { A.add(it.toInt()) }\n    var N = A.size\n    return rselect(A, i - 1, 0 , N - 1)  // -1 for 0-based indexing\n}\n\nfun main() {\n    println(\"problem6.5test1.txt: \" + run(\"problem6.5test1.txt\", 5))   // problem6.5test1.txt: 5469\n    println(\"problem6.5test2.txt: \" + run(\"problem6.5test2.txt\", 50))  // problem6.5test2.txt: 4715\n}\n"
  },
  {
    "path": "rselect/main.py",
    "content": "from random import uniform\nfrom math import floor\n\ndef partition(A, L, R):\n    i = L + 1\n    j = L + 1\n    k = floor(uniform(L, R))\n    A[L], A[k] = A[k], A[L]          # swap pivot A[k] with first element of subarray A[L]\n    while j <= R:\n        if A[j] < A[L]:              # maintain loop invariant A[i] < pivot < A[j]\n            A[i], A[j] = A[j], A[i]\n            i += 1\n        j += 1\n    A[L], A[i - 1] = A[i - 1], A[L]  # swap pivot A[L] with last value less-than pivot A[i - 1]\n    return i - 1\n\ndef rselect(A, i, L, R):\n    k = partition(A, L, R)\n    if i == k:\n        return A[k]  # 🎯 lucky guess\n    if i < k:\n        R = k - 1\n    else:\n        L = k + 1\n    return rselect(A, i, L, R)\n\ndef run(filename, i):\n    A = []\n    with open(filename) as fin:\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            A.append(int(line))\n    N = len(A)\n    return rselect(A, i - 1, 0, N - 1)  # -1 for 0-based indexing\n\nprint('problem6.5test1.txt:', run('problem6.5test1.txt', 5))   # problem6.5test1.txt: 5469\nprint('problem6.5test2.txt:', run('problem6.5test2.txt', 50))  # problem6.5test2.txt: 4715\n"
  },
  {
    "path": "rselect/package.json",
    "content": "{\n  \"name\": \"rselect\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"Clayton Wong\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "rselect/problem6.5test1.txt",
    "content": "2148\r\n9058\r\n7742\r\n3153\r\n6324\r\n609\r\n7628\r\n5469\r\n7017\r\n504\r\n"
  },
  {
    "path": "rselect/problem6.5test2.txt",
    "content": "2148\r\n9058\r\n7742\r\n3153\r\n6324\r\n609\r\n7628\r\n5469\r\n7017\r\n504\r\n4092\r\n1582\r\n9572\r\n1542\r\n5697\r\n2081\r\n4218\r\n3130\r\n7923\r\n9595\r\n6558\r\n3859\r\n9832\r\n3062\r\n6788\r\n7578\r\n7432\r\n479\r\n8439\r\n9079\r\n7173\r\n2667\r\n2770\r\n2655\r\n972\r\n4264\r\n2014\r\n3171\r\n4715\r\n345\r\n4388\r\n3816\r\n8887\r\n3915\r\n3490\r\n2327\r\n123\r\n4596\r\n4307\r\n8737\r\n4007\r\n6798\r\n6551\r\n1627\r\n1190\r\n4984\r\n2480\r\n3404\r\n2027\r\n4778\r\n2951\r\n2795\r\n5002\r\n8121\r\n8910\r\n9593\r\n5254\r\n448\r\n6237\r\n5565\r\n1816\r\n392\r\n8143\r\n9310\r\n9293\r\n3138\r\n4869\r\n6756\r\n872\r\n6183\r\n3517\r\n3513\r\n1676\r\n5498\r\n9172\r\n5739\r\n6108\r\n7538\r\n7671\r\n5780\r\n8666\r\n540\r\n9771\r\n6837\r\n9341\r\n1590\r\n5689\r\n1605\r\n1103\r\n5859\r\n"
  },
  {
    "path": "strassen/main.py",
    "content": "#\n# Strassen's Recursive Matrix Multiplication\n#\n# Input: n x n integer matrices X and Y\n# Output: Z = X * Y\n# Assumption: n is a power of 2\n# Complexity: O(n^log2(7))\n#\nimport numpy as np\n\ndef go(X, Y):\n    n = X.shape[0]\n\n    # Base case: 1x1 matrix\n    if n == 1:\n        return X * Y\n\n    # Divide: Partition A and B into n/2 x n/2 submatrices\n    k = n // 2\n\n    A, B = X[:k, :k], X[:k, k:]\n    C, D = X[k:, :k], X[k:, k:]\n\n    E, F = Y[:k, :k], Y[:k, k:]\n    G, H = Y[k:, :k], Y[k:, k:]\n\n    # Combine: Reconstruct the full matrix from quadrants\n    Z = np.zeros((n, n), dtype=X.dtype)\n    P1 = go(A, F - H)\n    P2 = go(A + B, H)\n    P3 = go(C + D, E)\n    P4 = go(D, G - E)\n    P5 = go(A + D, E + H)\n    P6 = go(B - D, G + H)\n    P7 = go(A - C, E + F)\n    Z[:k, :k], Z[:k, k:] = (P5 + P4 - P2 + P6), (P1 + P2)\n    Z[k:, :k], Z[k:, k:] = (P3 + P4), (P1 + P5 - P3 - P7)\n    return Z\n\ndef pretty_print(A, label=''):\n    col_width = max(len(str(x)) for x in A.flat)\n    if len(label):\n        print(label)\n        n = A.shape[0]\n        spaces = n - 1\n        print('-' * (n * col_width + spaces))\n\n    fmt = f'{{:>{col_width}d}}'\n    for row in A:\n        print(' '.join(fmt.format(x) for x in row))\n    print()\n\ndef main():\n    n = 4 # n must be a power of 2 for this simple implementation\n    A = np.random.randint(0, 10, (n, n))\n    B = np.random.randint(0, 10, (n, n))\n\n    expect = A @ B\n    actual = go(A, B)\n    pretty_print(A, 'A')\n    pretty_print(B, 'B')\n    pretty_print(expect, 'A * B (expect)')\n    pretty_print(actual, 'A * B (actual)')\n    assert(np.array_equal(expect, actual))\n\nif __name__ == \"__main__\":\n    main()\n\n# ➜  strassen git:(main) ✗ uv run ./main.py\n# A\n# -------\n# 3 8 3 3\n# 9 2 9 6\n# 1 8 4 8\n# 1 2 8 4\n\n# B\n# -------\n# 7 3 1 9\n# 1 7 9 2\n# 6 7 7 8\n# 0 1 5 8\n\n# A * B (expect)\n# ---------------\n#  47  89 111  91\n# 119 110 120 205\n#  39  95 141 121\n#  57  77  95 109\n\n# A * B (actual)\n# ---------------\n#  47  89 111  91\n# 119 110 120 205\n#  39  95 141 121\n#  57  77  95 109\n"
  },
  {
    "path": "strassen/pyproject.toml",
    "content": "[project]\nname = \"strassen\"\nversion = \"0.1.0\"\ndescription = \"Add your description here\"\nreadme = \"README.md\"\nrequires-python = \">=3.14\"\ndependencies = [\n    \"numpy>=2.4.1\",\n]\n"
  },
  {
    "path": "strassen/variants.py",
    "content": "#\n# Strassen-family Recursive Matrix Multiplication (2x2 block form)\n#\n# Methods:\n#   - \"strassen\"  : classical Strassen scheme (7 recursive multiplies)\n#   - \"winograd\"  : Winograd rearrangement of Strassen (7 multiplies, fewer additions)\n#   - \"basis2017\" : alternative-basis 7-multiply scheme (basis change + recombination)\n#\n# All methods:\n#   - Recursively split X and Y into 2x2 blocks\n#   - Perform 7 recursive multiplications\n#   - Recombine into result blocks\n#\n# Assumption: n is a power of 2\n#\nimport numpy as np\n\n\ndef go(X: np.ndarray, Y: np.ndarray, method: str = \"strassen\") -> np.ndarray:\n    n = X.shape[0]\n\n    # Base case: 1x1 matrix multiply\n    if n == 1:\n        return X * Y\n\n    k = n // 2\n\n    # Partition X into 2x2 block matrix\n    # X = [[A11 A12]\n    #      [A21 A22]]\n    A11, A12 = X[:k, :k], X[:k, k:]\n    A21, A22 = X[k:, :k], X[k:, k:]\n\n    # Partition Y into 2x2 block matrix\n    # Y = [[B11 B12]\n    #      [B21 B22]]\n    B11, B12 = Y[:k, :k], Y[:k, k:]\n    B21, B22 = Y[k:, :k], Y[k:, k:]\n\n    # Allocate result matrix\n    Z = np.zeros((n, n), dtype=X.dtype)\n\n    # ============================================================\n    # Classical Strassen scheme\n    # ============================================================\n    if method == \"strassen\":\n\n        # 7 recursive multiplications\n        M1 = go(A11 + A22, B11 + B22, method)\n        M2 = go(A21 + A22, B11, method)\n        M3 = go(A11, B12 - B22, method)\n        M4 = go(A22, B21 - B11, method)\n        M5 = go(A11 + A12, B22, method)\n        M6 = go(A21 - A11, B11 + B12, method)\n        M7 = go(A12 - A22, B21 + B22, method)\n\n        # Recombine into C blocks\n        C11 = M1 + M4 - M5 + M7\n        C12 = M3 + M5\n        C21 = M2 + M4\n        C22 = M1 - M2 + M3 + M6\n\n        Z[:k, :k] = C11\n        Z[:k, k:] = C12\n        Z[k:, :k] = C21\n        Z[k:, k:] = C22\n        return Z\n\n    # ============================================================\n    # Winograd rearrangement of Strassen\n    # Same 7 multiplies, different additive structure\n    # ============================================================\n    if method == \"winograd\":\n\n        # Core recursive products\n        t = go(A11, B11, method)\n        u = go(A21 - A11, B12 - B22, method)\n        v = go(A21 + A22, B12 - B11, method)\n\n        # w reuses t to reduce total additions\n        w = t + go(A21 + A22 - A11, B11 + B22 - B12, method)\n\n        # Recombine result blocks\n        C11 = t + go(A12, B21, method)\n        C12 = w + v + go(A11 + A12 - A21 - A22, B22, method)\n        C21 = w + u + go(A22, B21 + B12 - B11 - B22, method)\n        C22 = w + u + v\n\n        Z[:k, :k] = C11\n        Z[:k, k:] = C12\n        Z[k:, :k] = C21\n        Z[k:, k:] = C22\n        return Z\n\n    # ============================================================\n    # 2017 alternative-basis 7-multiply scheme\n    # Performs a basis change on A22 and B22 blocks\n    # ============================================================\n    if method == \"basis2017\":\n\n        # Basis transformation of lower-right blocks\n        A22p = A12 - A21 + A22\n        B22p = B12 - B21 + B22\n\n        # Linear combinations used by recursive multiplies\n        t1 = A21 + A22p\n        t2 = A22p - A12\n        t3 = A22p - A11\n        t4 = B22p - B11\n        t5 = B21 + B22p\n        t6 = B22p - B12\n\n        # 7 recursive multiplications\n        M1 = go(A11, B11, method)\n        M2 = go(A12, B21, method)\n        M3 = go(A21, t4, method)\n        M4 = go(A22p, B22p, method)\n        M5 = go(t1, t5, method)\n        M6 = go(t2, t6, method)\n        M7 = go(t3, B12, method)\n\n        # Initial recombination\n        C11 = M1 + M2\n        C12 = M5 - M7\n        C21 = M3 + M6\n        C22 = M5 + M6 - M2 - M4\n\n        # Final correction step required by basis change\n        C12 = C12 - C22\n        C21 = C22 - C21\n\n        Z[:k, :k] = C11\n        Z[:k, k:] = C12\n        Z[k:, :k] = C21\n        Z[k:, k:] = C22\n        return Z\n\n    raise ValueError(\n        f\"Unknown method: {method!r}. Use 'strassen', 'winograd', or 'basis2017'.\"\n    )\n\ndef pretty_print(A, label=''):\n    col_width = max(len(str(int(x))) for x in A.flat)\n    if label:\n        print(label)\n        n = A.shape[0]\n        print('-' * (n * col_width + (n - 1)))\n    fmt = f'{{:>{col_width}d}}'\n    for row in A:\n        print(' '.join(fmt.format(int(x)) for x in row))\n    print()\n\ndef main():\n    n = 4  # power of 2\n    X = np.random.randint(0, 10, (n, n), dtype=int)\n    Y = np.random.randint(0, 10, (n, n), dtype=int)\n\n    expect = X @ Y\n\n    for method in [\"strassen\", \"winograd\", \"basis2017\"]:\n        actual = go(X, Y, method=method)\n        print(f\"=== {method} ===\")\n        assert np.array_equal(expect, actual), f\"Mismatch for {method}\"\n\n    pretty_print(X, \"X\")\n    pretty_print(Y, \"Y\")\n    pretty_print(expect, \"X * Y (expect)\")\n    pretty_print(go(X, Y, \"strassen\"), \"X * Y (strassen)\")\n    pretty_print(go(X, Y, \"winograd\"), \"X * Y (winograd)\")\n    pretty_print(go(X, Y, \"basis2017\"), \"X * Y (basis2017)\")\n\nif __name__ == \"__main__\":\n    main()\n\n# ➜  strassen git:(main) ✗ uv run strassen.py\n# === strassen ===\n# === winograd ===\n# === basis2017 ===\n# X\n# -------\n# 0 1 6 6\n# 4 9 0 4\n# 8 2 4 0\n# 1 9 7 7\n\n# Y\n# -------\n# 5 3 4 0\n# 7 2 8 0\n# 5 9 3 2\n# 0 1 3 8\n\n# X * Y (expect)\n# ---------------\n#  37  62  44  60\n#  83  34 100  32\n#  74  64  60   8\n# 103  91 118  70\n\n# X * Y (strassen)\n# ---------------\n#  37  62  44  60\n#  83  34 100  32\n#  74  64  60   8\n# 103  91 118  70\n\n# X * Y (winograd)\n# ---------------\n#  37  62  44  60\n#  83  34 100  32\n#  74  64  60   8\n# 103  91 118  70\n\n# X * Y (basis2017)\n# ---------------\n#  37  62  44  60\n#  83  34 100  32\n#  74  64  60   8\n# 103  91 118  70\n"
  },
  {
    "path": "topo_sort/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(topo_sort)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(topo_sort main.cpp)"
  },
  {
    "path": "topo_sort/main.cpp",
    "content": "#include <iostream>\n#include <sstream>\n#include <vector>\n#include <unordered_map>\n#include <unordered_set>\n#include <queue>\n\nusing namespace std;\n\nusing VI = vector<int>;\nusing AdjList = unordered_map<char, VI>;\nusing Set = unordered_set<char>;\nusing Map = unordered_map<char, int>;\nusing Queue = queue<char>;\nusing fun = function<void(char)>;\n\nclass Solution {\nprivate:\n    AdjList adj;\n    const int N;\n    Map m;\n    Set seen;\n    int color;\npublic:\n    Solution(AdjList& adj) : adj{ adj }, N{ int(adj.size()) } {\n    }\n    void init(int start) {\n        m.clear();\n        seen.clear();\n        color = start;\n    }\n    string topo_sort_bfs() {\n        init(1);  // 👉 color forward from 1..N\n        bfs();\n        return to_string();\n    }\n    string topo_sort_dfs() {\n        init(N);  // 👈 color reverse from N..1 (as the recursive stack unwinds)\n        for (auto [u, _]: adj)\n            dfs(u);\n        return to_string();\n    }\n    void bfs() {\n        Map degree;\n        for (auto [_, neighbors]: adj)\n            for (auto v: neighbors)\n                ++degree[v];\n        Queue q;\n        for (auto [u, _]: adj)\n            if (!degree[u] && seen.insert(u).second)\n                q.push(u);\n        while (q.size()) {\n            auto u = q.front(); q.pop();\n            m[u] = color++;\n            for (auto v: adj[u])\n                if (!--degree[v] && seen.insert(v).second)\n                    q.push(v);\n        }\n    }\n    void dfs(char start) {\n        fun go = [&](auto u) {\n            if (!seen.insert(u).second)\n                return;\n            for (auto v: adj[u])\n                go(v);\n            m[u] = color--;\n        };\n        go(start);\n    }\n    string to_string() {\n        ostringstream os;\n        for (auto [u, color]: m)\n            os << u << \": \" << color << endl;\n        return os.str();\n    }\n};\n\nint main() {\n    //\n    // graph from Quiz 8.3 on page 45 of Algorithms Illuminated: Part 2\n    //\n    AdjList adj{\n        { 's', { 'v', 'w' } },\n        { 'v', { 't' } },\n        { 'w', { 't' } },\n        { 't', {} }\n    };\n    Solution solution{ adj };\n\n    cout << \"BFS:\" << endl << solution.topo_sort_bfs() << endl\n         << \"DFS:\" << endl << solution.topo_sort_dfs() << endl;\n\n//    BFS:\n//    t: 4\n//    w: 3\n//    v: 2\n//    s: 1\n//\n//    DFS:\n//    s: 1\n//    w: 2\n//    v: 3\n//    t: 4\n\n    return 0;\n}\n"
  },
  {
    "path": "topo_sort/main.js",
    "content": "class Solution {\n    constructor(adj) {\n        this.adj = adj;\n        this.N = this.adj.size;\n    }\n    init(start) {\n        this.color = start;\n        this.seen = new Set();\n        this.m = new Map();\n    }\n    topo_sort_bfs() {\n        this.init(1);       // 👉 color forward from 1..N\n        this.bfs();\n        return this.to_string();\n    }\n    topo_sort_dfs() {\n        this.init(this.N);  // 👈 color reverse from N..1 (as the recursive stack unwinds)\n        for (let [u, _] of [...this.adj])\n            this.dfs(u);\n        return this.to_string();\n    }\n    bfs() {\n        let degree = new Map();\n        for (let [u, _] of [...this.adj]) {\n            degree.set(u, (degree.get(u) || 0));\n            for (let v of this.adj.get(u))\n                degree.set(v, 1 + (degree.get(v) || 0));\n        }\n        let q = [...this.adj].map(([u, _]) => u).filter(u => !degree.get(u));\n        let seen = new Set(q);\n        while (q.length) {\n            let u = q.shift();\n            this.m.set(u, this.color++);\n            for (let v of this.adj.get(u)) {\n                degree.set(v, -1 + degree.get(v));\n                if (!degree.get(v) && !seen.has(v))\n                    q.push(v), seen.add(v);\n            }\n        }\n    }\n    dfs(u) {\n        if (this.seen.has(u))\n            return;\n        this.seen.add(u);\n        for (let v of this.adj.get(u))\n            if (!this.seen.has(v))\n                this.dfs(v);\n        this.m.set(u, this.color--);\n    }\n    to_string() {\n        let s = [];\n        for (let [u, color] of [...this.m])\n            s.push(`${u}: ${color}`);\n        return s.join('\\n');\n    }\n}\n\nlet adj = new Map();\nadj.set('s', ['v', 'w']);\nadj.set('v', ['t']);\nadj.set('w', ['t']);\nadj.set('t', []);\nlet solution = new Solution(adj);\nconsole.log(`BFS:\\n${solution.topo_sort_bfs()}\\n\\nDFS:\\n${solution.topo_sort_dfs()}`);\n\n//    BFS:\n//    s: 1\n//    v: 2\n//    w: 3\n//    t: 4\n\n//    DFS:\n//    t: 4\n//    v: 3\n//    w: 2\n//    s: 1\n"
  },
  {
    "path": "topo_sort/main.kt",
    "content": "import java.util.Queue\nimport java.util.LinkedList\n\nclass Solution(val adj: MutableMap<Char, List<Char>>) {\n\n    var N: Int\n    var color: Int\n    var m = mutableMapOf<Char, Int>()\n    var seen = mutableSetOf<Char>()\n\n    init {\n        N = adj.size\n        color = 0\n    }\n\n    fun init(start: Int) {\n        color = start\n        m.clear()\n        seen.clear()\n    }\n\n    fun topoSortBFS(): String {\n        init(1)  // 👉 color forward from 1..N\n        bfs()\n        return toString()\n    }\n\n    fun topoSortDFS(): String {\n        init(N)  // 👈 color reverse from N..1 (as the recursive stack unwinds)\n        adj.forEach{ (u, _) -> dfs(u) }\n        return toString()\n    }\n\n    fun bfs() {\n        var degree = mutableMapOf<Char, Int>()\n        adj.forEach{ (_, neighbors) ->\n            neighbors.forEach{ v ->\n                degree[v] = 1 + degree.getOrDefault(v, 0)\n            }\n        }\n        var q: Queue<Char> = LinkedList(adj.map{ (u, _) -> u }.filter{ !degree.contains(it) })\n        while (0 < q.size) {\n            var u = q.poll()\n            m[u] = color++\n            adj[u]!!.forEach{ v ->\n                degree[v] = degree[v]!!.minus(1)\n                if (degree[v] == 0 && !seen.contains(v)) {\n                    q.add(v); seen.add(v)\n                }\n            }\n        }\n    }\n\n    fun dfs(u: Char) {\n        if (seen.contains(u))\n            return\n        seen.add(u)\n        adj[u]!!.forEach{ v ->\n            dfs(v)\n        }\n        m[u] = color--\n    }\n\n    override fun toString(): String {\n        var s = mutableListOf<String>()\n        adj.forEach{ (u, _) ->\n            s.add(\"$u: ${m[u]}\")\n        }\n        return s.joinToString(\"\\n\")\n    }\n}\n\nfun main() {\n    var adj = mutableMapOf<Char, List<Char>>(\n        's' to listOf<Char>('v', 'w'),\n        'v' to listOf<Char>('t'),\n        'w' to listOf<Char>('t'),\n        't' to listOf<Char>()\n    )\n    var solution = Solution(adj)\n    println(\"BFS:\\n${solution.topoSortBFS()}\\n\\nDFS:\\n${solution.topoSortDFS()}\")\n\n//    BFS:\n//    s: 1\n//    v: 2\n//    w: 3\n//    t: 4\n\n//    DFS:\n//    s: 1\n//    v: 3\n//    w: 2\n//    t: 4\n\n}\n"
  },
  {
    "path": "topo_sort/main.py",
    "content": "from collections import deque\n\nclass Solution:\n    def __init__(self, adj):\n        self.adj = adj\n        self.N = len(adj)\n        self.seen = set()\n        self.m = {}\n\n    def init(self, start):\n        self.color = start\n        self.seen.clear()\n        self.m.clear()\n\n    def topo_sort_bfs(self):\n        self.init(1)         # 👉 color forward from 1..N\n        self.bfs()\n        return self.to_string()\n\n    def topo_sort_dfs(self):\n        self.init(self.N)  # 👈 color reverse from N..1 (as the recursive stack unwinds)\n        for u, _ in self.adj.items():\n            self.dfs(u)\n        return self.to_string()\n\n    def bfs(self):\n        degree = {}\n        for _, neighbors in self.adj.items():\n            for v in neighbors:\n                degree[v] = 1 + (degree[v] if v in degree else 0)\n        q = deque(u for u, _ in self.adj.items() if u not in degree)\n        self.seen.update(*q)\n        while q:\n            u = q.popleft()\n            self.m[u] = self.color; self.color += 1\n            for v in adj[u]:\n                degree[v] -= 1\n                if not degree[v] and v not in self.seen:\n                    q.append(v); self.seen.add(v)\n\n    def dfs(self, u):\n        if u in self.seen:\n            return\n        self.seen.add(u)\n        for v in adj[u]:\n            self.dfs(v)\n        self.m[u] = self.color; self.color -= 1\n\n    def to_string(self):\n        s = []\n        for u, color in self.m.items():\n            s.append(f'{u}: {color}')\n        return '\\n'.join(s)\n\n#\n# graph from Quiz 8.3 on page 45 of Algorithms Illuminated: Part 2\n#\nadj = {\n    's': ['v', 'w'],\n    'v': ['t'],\n    'w': ['t'],\n    't': []\n}\nsolution = Solution(adj)\n\nprint(f'BFS:\\n{solution.topo_sort_bfs()}\\n\\nDFS:\\n{solution.topo_sort_dfs()}')\n\n#    BFS:\n#    s: 1\n#    v: 2\n#    w: 3\n#    t: 4\n\n#    DFS:\n#    t: 4\n#    v: 3\n#    w: 2\n#    s: 1\n"
  },
  {
    "path": "traveling_salesman/README.md",
    "content": "Quiz 19.2 and 20.7 input file format:\n\n```\n[number_of_vertices] [number_of_edges]\n[one_endpoint_of_edge_1] [other_endpoint_of_edge_1] [edge_1_cost]\n[one_endpoint_of_edge_2] [other_endpoint_of_edge_2] [edge_2_cost]\n```"
  },
  {
    "path": "traveling_salesman/main.cpp",
    "content": "#include <fstream>\n#include <iostream>\n#include <iterator>\n#include <sstream>\n#include <unordered_map>\n#include <unordered_set>\n#include <vector>\n\nusing namespace std;\nusing VI = vector<int>;\nusing Pair = pair<int, VI>;\nusing Set = unordered_set<int>;\nusing Adj = unordered_map<int, Set>;\nusing Cost = unordered_map<string, int>;\n\nclass Solution {\n    int best, start, M, N;\n    VI best_path;\n    Adj adj;\n    Cost cost;\n    string key(int u, int v) {\n        stringstream ss;\n        ss << u << \",\" << v;\n        return ss.str();\n    }\n    void init(const string& input_file, string line = {}) {\n        best = 1e9 + 7; start = M = N = 0;\n        best_path.clear();\n        adj.clear();\n        cost.clear();\n        auto i = 0;\n        fstream fin{ input_file };\n        while (getline(fin, line)) {\n            VI A;\n            istringstream is{ line };\n            copy(istream_iterator<int>(is), istream_iterator<int>(), back_inserter(A));\n            if (0 < i++) {\n                auto [u, v, w] = tie(A[0], A[1], A[2]);\n                adj[u].insert(v); cost[key(u, v)] = w;\n                adj[v].insert(u); cost[key(v, u)] = w;\n            } else {\n                N = A[0];\n                M = A[1];\n            }\n        }\n    }\n    void go(int u, VI&& path, Set&& seen, int t = 0) {\n        if (seen.size() == N) {\n            t += cost[key(u, start)]; // connect ultimate edge of tour\n            if (adj[u].find(start) != adj[u].end() && t < best)\n                best = t, best_path = path;\n            return;\n        }\n        for (auto v: adj[u]) {\n            if (seen.find(v) != seen.end())\n                continue;\n            path.push_back(v), seen.insert(v);\n            go(v, move(path), move(seen), t + cost[key(u, v)]);\n            path.pop_back(), seen.erase(v);\n        }\n    }\npublic:\n    Pair run(const string& input_file) {\n        init(input_file);\n        start = 1;\n        go(start, {start}, {start});\n        return {best, best_path};\n    }\n};\n\nint main() {\n    auto s = Solution();\n    for (auto& input_file: {\"quiz19.2.txt\", \"quiz20.7.txt\"}) {\n        auto [best, path] = s.run(input_file);\n        cout << input_file << \"  best: \" << best << \"  path: \";\n        copy(path.begin(), path.end(), ostream_iterator<int>(cout, \" \"));\n        cout << endl;\n    }\n    // quiz19.2.txt  best: 13  path: 1 3 4 2\n    // quiz20.7.txt  best: 23  path: 1 4 5 2 3\n    return 0;\n}\n"
  },
  {
    "path": "traveling_salesman/main.js",
    "content": "let LineByLine = require('n-readlines');\n\nclass Solution {\n    key = (u, v) => `${u},${v}`;\n    init(input_file) {\n        this.best = Number(1e9 + 7);\n        this.best_path = [];\n        this.M = 0;\n        this.N = 0;\n        this.adj = new Map();\n        this.cost = new Map();\n        let [A, line, i] = [[], '', 0];\n        let input = new LineByLine(input_file);\n        while (line = input.next()) {\n            let A = String.fromCharCode(...line).trim().split(' ').map(Number);\n            if (0 < i++) {\n                let [u, v, w] = A;\n                if (!this.adj.has(u)) this.adj.set(u, new Set());\n                if (!this.adj.has(v)) this.adj.set(v, new Set());\n                this.adj.get(u).add(v), this.cost.set(this.key(u, v), w);\n                this.adj.get(v).add(u), this.cost.set(this.key(v, u), w);\n            } else {\n                [this.N, this.M] = A;\n            }\n        }\n    }\n    run(input_file) {\n        this.init(input_file);\n        this.start = 1;\n        this.go(this.start, [this.start], new Set([this.start]));\n        return [this.best, this.best_path];\n    }\n    go(u, path, seen, t = 0) {\n        if (seen.size == this.N) {\n            t += this.cost.get(this.key(u, this.start)) || 0;\n            if (this.adj.get(u).has(this.start) && t < this.best)\n                this.best = t, this.best_path = [...path];\n            return;\n        }\n        for (let v of this.adj.get(u)) {\n            if (seen.has(v))\n                continue;\n            path.push(v), seen.add(v);\n            this.go(v, path, seen, t + this.cost.get(this.key(u, v)));\n            path.pop(), seen.delete(v);\n        }\n    }\n}\n\nlet s = new Solution();\nfor (let input_file of ['quiz19.2.txt', 'quiz20.7.txt']) {\n    let [best, path] = s.run(input_file);\n    console.log(`${input_file}  best: ${best}  path: ${path}`);\n}\n// quiz19.2.txt  best: 13  path: 1,2,4,3\n// quiz20.7.txt  best: 23  path: 1,3,2,5,4"
  },
  {
    "path": "traveling_salesman/main.kt",
    "content": "import java.io.File\n\nclass Solution() {\n    private var best = (1e9 + 7).toInt()\n    private var best_path = listOf<Int>()\n    private var start = 0\n    private var M = 0\n    private var N = 0\n    private var adj = mutableMapOf<Int, MutableSet<Int>>()\n    private var cost = mutableMapOf<String, Int>()\n    private var key = { u: Int, v: Int -> \"$u,$v\" }\n    private fun init(input_file: String) {\n        best = (1e9 + 7).toInt()\n        best_path = mutableListOf<Int>()\n        adj = mutableMapOf<Int, MutableSet<Int>>()\n        cost = mutableMapOf<String, Int>()\n        var i = 0\n        File(input_file).forEachLine { line ->\n            var A = line.trim().split(\" \").map{ it.toInt() }\n            if (0 < i++) {\n                var (u, v, w) = A\n                if (!adj.contains(u)) adj[u] = mutableSetOf<Int>()\n                if (!adj.contains(v)) adj[v] = mutableSetOf<Int>()\n                adj[u]!!.add(v); cost[key(u, v)] = w\n                adj[v]!!.add(u); cost[key(v, u)] = w\n            } else {\n                N = A[0]\n                M = A[1]\n            }\n        }\n    }\n    fun run(input_file: String): Pair<Int, List<Int>> {\n        init(input_file)\n        start = 1\n        go(start, mutableListOf<Int>(start), mutableSetOf<Int>(start))\n        return Pair<Int, List<Int>>(best, best_path)\n    }\n    fun go(u: Int, path: MutableList<Int>, seen: MutableSet<Int>, t_: Int = 0) {\n        if (seen.size == N) {\n            var t = t_ + (cost[key(u, start)] ?: 0)\n            if (adj[u]!!.contains(start) && t < best) {\n                best = t; best_path = path.toList()\n            }\n            return\n        }\n        for (v in adj[u]!!) {\n            if (seen.contains(v))\n                continue\n            path.add(v); seen.add(v)\n            go(v, path, seen, t_ + cost[key(u, v)]!!)\n            path.removeLast(); seen.remove(v)\n        }\n    }\n}\n\nfun main() {\n    var s = Solution()\n    for (input_file in listOf(\"quiz19.2.txt\", \"quiz20.7.txt\")) {\n        var (best, path) = s.run(input_file)\n        println(\"$input_file  best: $best  path: ${path.joinToString()}\")\n    }\n}\n// quiz19.2.txt  best: 13  path: 1, 2, 4, 3\n// quiz20.7.txt  best: 23  path: 1, 3, 2, 5, 4"
  },
  {
    "path": "traveling_salesman/main.py",
    "content": "from random import randint\nfrom collections import defaultdict\n\nclass Solution():\n    def init(self, input_file):\n        self.best = int(1e9 + 7)\n        self.best_path = []\n        self.M = 0\n        self.N = 0\n        self.adj = defaultdict(set)\n        self.cost = defaultdict(int)\n        with open(input_file) as input:\n            for i, line in enumerate(input):\n                A = [int(x) for x in line.strip().split(' ')]\n                if 0 < i:\n                    u, v, w = A\n                    self.adj[u].add(v); self.cost[(u, v)] = w\n                    self.adj[v].add(u); self.cost[(v, u)] = w\n                else:\n                    self.N, self.M = A\n    def run(self, input_file):\n        self.init(input_file)\n        self.start = 1\n        self.go(self.start, [self.start], set([self.start]))\n        return self.best, self.best_path\n\n    def go(self, u, path, seen, t = 0):\n        if len(seen) == self.N:\n            t += self.cost[(u, self.start)] # connect ultimate edge of tour\n            if self.start in self.adj[u] and t < self.best:\n                self.best = t\n                self.best_path = path[:]\n            return\n        for v in self.adj[u]:\n            if v not in seen:\n                path.append(v); seen.add(v)\n                self.go(v, path, seen, t + self.cost[(u, v)])\n                path.pop(); seen.remove(v)\n\ns = Solution()\nfor input_file in ['quiz19.2.txt', 'quiz20.7.txt']:\n    best, path = s.run(input_file)\n    print(f'{input_file}  best: {best}  path: {path}')\n# quiz19.2.txt  best: 13  path: [1, 2, 4, 3]\n# quiz20.7.txt  best: 23  path: [1, 3, 2, 5, 4]"
  },
  {
    "path": "traveling_salesman/package.json",
    "content": "{\n  \"name\": \"traveling_salesman\",\n  \"version\": \"1.0.0\",\n  \"description\": \"Quiz 19.2 and 20.7 input file format:\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "traveling_salesman/quiz19.2.txt",
    "content": "4 6\n1 2 1\n1 3 4\n1 4 3\n2 3 5\n2 4 2\n3 4 6"
  },
  {
    "path": "traveling_salesman/quiz20.7.txt",
    "content": "5 10\n1 2 1\n1 3 4\n1 4 5\n1 5 10\n2 3 2\n2 4 6\n2 5 3\n3 4 7\n3 5 8\n4 5 9"
  },
  {
    "path": "traveling_salesman_nearest_neighbor/README.md",
    "content": "Quiz 20.7 input file format:\n\n```\n[number_of_vertices] [number_of_edges]\n[one_endpoint_of_edge_1] [other_endpoint_of_edge_1] [edge_1_cost]\n[one_endpoint_of_edge_2] [other_endpoint_of_edge_2] [edge_2_cost]\n```\n\nThe nearest neighbor heuristic algorithm greedily consume the minimum weight edge\nof each unvisited vertex:\n\n1. Begin a tour at an arbitrary vertex\n2. Repeat until all vertices have been visited:\n    a. If the current vertex is u, proceed to the closet unvisited vertex v\n3. Return to the starting vertex"
  },
  {
    "path": "traveling_salesman_nearest_neighbor/input.txt",
    "content": "5 10\n1 2 1\n1 3 4\n1 4 5\n1 5 10\n2 3 2\n2 4 6\n2 5 3\n3 4 7\n3 5 8\n4 5 9"
  },
  {
    "path": "traveling_salesman_nearest_neighbor/main.py",
    "content": "from collections import defaultdict\n\nN, M = -1, -1\nadj = defaultdict(list)\ncost, key = {}, lambda u, v: f'{u},{v}'\nwith open('input.txt') as input:\n    for line in input:\n        A = [int(x) for x in line.strip().split(' ')]\n        if len(A) == 3:\n            u, v, w = A\n            adj[u].append(v); cost[key(u, v)] = w\n            adj[v].append(u); cost[key(v, u)] = w\n        elif len(A) == 2:\n            N, M = A\n\nstart = 1\nu, seen, path = start, set([start]), [start]\nwhile len(seen) < N:\n    best, best_v = float('inf'), -1\n    for v in adj[u]:\n        if v not in seen:\n            cand = cost[key(u, v)]\n            if best > cand:\n                best = cand; best_v = v\n    u = best_v; seen.add(best_v); path.append(best_v)\npath.append(start) # add last edge to complete the tour\nt = sum(cost[key(path[i - 1], path[i])] for i in range(1, len(path)))\nprint(f'total: {t}  path: {path}')\n# total: 29  path: [1, 2, 3, 4, 5, 1]"
  },
  {
    "path": "weighted_independent_set/CMakeLists.txt",
    "content": "cmake_minimum_required(VERSION 3.16)\nproject(weighted_independent_set)\n\nset(CMAKE_CXX_STANDARD 17)\n\nadd_executable(weighted_independent_set main.cpp)"
  },
  {
    "path": "weighted_independent_set/main.cpp",
    "content": "/*\n * In this problem, each file describes the weights of vertices in a path graph and has the format:\n * [number_of_vertices_in_path_graph]\n * [weight of first vertex]\n * [weight of second vertex]\n * ...\n * Test case: (contributed by Logan Travis) What is the value of a maximum-weight independent set of the 10-vertex path graph described in this file, and which vertices belong to the MWIS? (Answer: 2617, and the vertices 2, 4, 7, and 10).\n * Challenge data set: Repeat the previous problem for the 1000-vertex path graph described in this file.\n */\n\n#include <cassert>\n#include <iostream>\n#include <fstream>\n#include <vector>\n#include <unordered_map>\n\nusing namespace std;\nusing LL = long long;\nusing List = vector<LL>;\nusing Map = unordered_map<int, LL>;\n\nnamespace TopDown {\n    LL best(List& A, Map m = {}) {\n        int N = A.size();\n        using fun = function<LL(int)>;\n        fun go = [&](auto i) {\n            if (m[i]) return m[i];                // 🤔 memo\n            if (i < 0) return m[i] = 0LL;         // 🛑 empty set\n            if (!i) return m[i] = A[0];           // 🛑 single set\n            auto include = go(i - 2) + A[i],      // ✅ include A[i]\n                 exclude = go(i - 1);             // 🚫 exclude A[i]\n            return m[i] = max(include, exclude);  // 🎯 best\n        };\n        return go(N - 1);\n    }\n}\nnamespace BottomUp {\n    LL best(List& A, Map m = {}) {\n        int N = A.size();\n        List dp(N + 1);                           // 🤔 memo\n        dp[0] = 0LL;                              // 🛑 empty set\n        dp[1] = A[0];                             // 🛑 single set\n        for (auto i{ 2 }; i <= N; ++i) {\n            auto include = dp[i - 2] + A[i - 1],  // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n                 exclude = dp[i - 1];             // 🚫 exclude A[i]\n            dp[i] = max(include, exclude);        // 🎯 best\n        }\n        return dp[N];\n    }\n}\n\nnamespace BottomUpMemOpt {\n    LL best(List& A) {\n        int N = A.size();\n        LL a = 0LL,                       // 🤔 memo + 🛑 empty set\n           b = A[0],                      // 🤔 memo + 🛑 single set\n           c = -1;\n        for (auto i{ 2 }; i <= N; ++i) {\n            auto include = a + A[i - 1],  // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n                 exclude = b;             // 🚫 exclude A[i]\n            c = max(include, exclude);    // 🎯 best\n            a = b, b = c;                 // 👈 slide window\n        }\n        return c;\n    }\n}\n\nvoid run(const string& filename) {\n    List A;\n    fstream fin{ filename };\n    int N; fin >> N;\n    copy_n(istream_iterator<LL>(fin), N, back_inserter(A));\n    auto a = TopDown::best(A),\n         b = BottomUp::best(A),\n         c = BottomUpMemOpt::best(A);\n    assert(a == b && b == c); // 💩 sanity check\n    cout << filename << \": \" << a << endl;\n}\n\nint main() {\n    run(\"problem16.6test.txt\");  // problem16.6test.txt: 2617\n    run(\"problem16.6.txt\");      // problem16.6.txt: 2955353732\n    return 0;\n}\n"
  },
  {
    "path": "weighted_independent_set/main.js",
    "content": "/*\n * In this problem, each file describes the weights of vertices in a path graph and has the format:\n * [number_of_vertices_in_path_graph]\n * [weight of first vertex]\n * [weight of second vertex]\n * ...\n * Test case: (contributed by Logan Travis) What is the value of a maximum-weight independent set of the 10-vertex path graph described in this file, and which vertices belong to the MWIS? (Answer: 2617, and the vertices 2, 4, 7, and 10).\n * Challenge data set: Repeat the previous problem for the 1000-vertex path graph described in this file.\n */\n\nconst assert = require('assert');\nconst LineByLine = require('n-readlines');\n\nlet top_down = (A, m = {}) => {\n    let N = A.length;\n    let go = (i = N - 1) => {\n        if (m[i])                                     // 🤔 memo\n            return m[i];\n        if (i < 0) return m[i] = 0;                   // 🛑 empty set\n        if (!i) return m[i] = A[0];                   // 🛑 single set\n        let include = go(i - 2) + A[i],               // ✅ include A[i]\n            exclude = go(i - 1);                      // 🚫 exclude A[i]\n        return m[i] = Math.max(include, exclude);     // 🎯 best\n    };\n    return go();\n};\n\nlet bottom_up = A => {\n    let N = A.length;\n    let dp = Array(N + 1);                    // 🤔 memo\n    dp[0] = 0;                                // 🛑 empty set\n    dp[1] = A[0];                             // 🛑 single set\n    for (let i = 2; i <= N; ++i) {\n        let include = dp[i - 2] + A[i - 1],   // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n            exclude = dp[i - 1];              // 🚫 exclude A[i]\n        dp[i] = Math.max(include, exclude);   // 🎯 best\n    }\n    return dp[N];\n};\n\nlet bottom_up_memopt = A => {\n    let N = A.length;\n    let a = 0,                           // 🤔 memo + 🛑 empty set\n        b = A[0],                        // 🤔 memo + 🛑 single set\n        c = -1;\n    for (let i = 2; i <= N; ++i) {\n        let include = a + A[i - 1],      // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n            exclude = b;                 // 🚫 exclude A[i]\n        c = Math.max(include, exclude);  // 🎯 best\n        a = b, b = c;                    // 👈 slide window\n    }\n    return c;\n};\n\nlet run = filename => {\n    let A = [];\n    let input = new LineByLine(filename);\n    let line;\n    let first = true;\n    while (line = input.next()) {\n        if (!first) {\n            A.push(Number(line.toString('ascii')));\n        } else {\n            first = false;\n        }\n    }\n    let a = top_down(A),\n        b = bottom_up(A),\n        c = bottom_up_memopt(A);\n    assert(a == b && b == c); // 💩 sanity check\n    console.log(`${filename}: ${a}`);\n};\n\nrun('problem16.6test.txt');  // problem16.6test.txt: 2617\nrun('problem16.6.txt');      // problem16.6.txt: 2955353732\n"
  },
  {
    "path": "weighted_independent_set/main.kt",
    "content": "/*\n * In this problem, each file describes the weights of vertices in a path graph and has the format:\n * [number_of_vertices_in_path_graph]\n * [weight of first vertex]\n * [weight of second vertex]\n * ...\n * Test case: (contributed by Logan Travis) What is the value of a maximum-weight independent set of the 10-vertex path graph described in this file, and which vertices belong to the MWIS? (Answer: 2617, and the vertices 2, 4, 7, and 10).\n * Challenge data set: Repeat the previous problem for the 1000-vertex path graph described in this file.\n */\n\nimport java.io.File\n\nfun topDown(A: MutableList<Long>): Long {\n    var N = A.size\n    var m = mutableMapOf<Int, Long>()\n    fun go(i: Int = N - 1): Long {\n        if (m.contains(i))                    // 🤔 memo\n            return m[i]!!\n        if (i < 0) {                          // 🛑 empty set\n            m[i] = 0\n            return 0\n        }\n        if (i == 0) {                         // 🛑 single set\n            m[i] = A[0]\n            return A[0]\n        }\n        var include = go(i - 2) + A[i]        // ✅ include A[i]\n        var exclude = go(i - 1)               // 🚫 exclude A[i]\n        m[i] = Math.max(include, exclude)     // 🎯 best\n        return m[i]!!\n    }\n    return go()\n}\n\nfun bottomUp(A: MutableList<Long>): Long {\n    var N = A.size\n    var dp = LongArray(N + 1)                 // 🤔 memo\n    dp[0] = 0                                 // 🛑 empty set\n    dp[1] = A[0]                              // 🛑 single set\n    for (i in 2..N) {\n        var include = dp[i - 2] + A[i - 1]    // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        var exclude = dp[i - 1]               // 🚫 exclude A[i]\n        dp[i] = Math.max(include, exclude)    // 🎯 best\n    }\n    return dp[N]\n}\n\nfun bottomUpMemOpt(A: MutableList<Long>): Long {\n    var N = A.size\n    var a: Long = 0                     // 🤔 memo + 🛑 empty set\n    var b: Long = A[0]                  // 🤔 memo + 🛑 single set\n    var c: Long = -1\n    for (i in 2..N) {\n        var include = a + A[i - 1]      // ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        var exclude = b                 // 🚫 exclude A[i]\n        c = Math.max(include, exclude)  // 🎯 best\n        a = b; b = c                    // 👈 slide window\n    }\n    return c\n}\n\nfun run(filename: String) {\n    var A = mutableListOf<Long>()\n    var first = true\n    File(filename).forEachLine { line ->\n        if (!first) {\n            A.add(line.toLong())\n        } else {\n            first = false\n        }\n    }\n    var a = topDown(A)\n    var b = bottomUp(A)\n    var c = bottomUpMemOpt(A)\n    assert(a == b && b == c) // 💩 sanity check\n    println(\"$filename: $a\")\n}\n\nfun main() {\n    run(\"problem16.6test.txt\")  // problem16.6test.txt: 2617\n    run(\"problem16.6.txt\")      // problem16.6.txt: 2955353732\n}\n"
  },
  {
    "path": "weighted_independent_set/main.py",
    "content": "#\n# In this problem, each file describes the weights of vertices in a path graph and has the format:\n# [number_of_vertices_in_path_graph]\n# [weight of first vertex]\n# [weight of second vertex]\n# ...\n# Test case: (contributed by Logan Travis) What is the value of a maximum-weight independent set of the 10-vertex path graph described in this file, and which vertices belong to the MWIS? (Answer: 2617, and the vertices 2, 4, 7, and 10).\n# Challenge data set: Repeat the previous problem for the 1000-vertex path graph described in this file.\n#\n\nfrom functools import lru_cache\n\ndef top_down(A):\n    N = len(A)\n    @lru_cache(maxsize = None)        # 🤔 memo\n    def go(i = N - 1):\n        if i < 0: return 0            # 🛑 empty set\n        if i == 0: return A[0]        # 🛑 single set\n        include = go(i - 2) + A[i]    # ✅ include A[i]\n        exclude = go(i - 1)           # 🚫 exclude A[i]\n        return max(include, exclude)  # 🎯 best\n    return go()\n\ndef bottom_up(A):\n    N = len(A)\n    dp = [0] * (N + 1)                  # 🤔 memo\n    dp[0] = 0                           # 🛑 empty set\n    dp[1] = A[0]                        # 🛑 single set\n    for i in range(2, N + 1):\n        include = dp[i - 2] + A[i - 1]  # ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        exclude = dp[i - 1]             # 🚫 exclude A[i]\n        dp[i] = max(include, exclude)   # 🎯 best\n    return dp[N]\n\ndef bottom_up_memopt(A):\n    N = len(A)\n    a = 0                          # 🤔 memo + 🛑 empty set\n    b = A[0]                       # 🤔 memo + 🛑 single set\n    c = -1\n    for i in range(2, N + 1):\n        include = a + A[i - 1]     # ✅ include A[i] (use A[i - 1] since dp[i] is offset by 1 for explicit 🛑 empty set at index 0, ie. index -1 doesn't exist)\n        exclude = b                # 🚫 exclude A[i]\n        c = max(include, exclude)  # 🎯 best\n        a = b; b = c               # 👈 slide window\n    return c\n\ndef run(filename):\n    A = []\n    with open(filename) as fin:\n        first = True\n        while True:\n            line = fin.readline()\n            if not line:\n                break\n            x = int(line)\n            if not first:\n                A.append(x)\n            else:\n                first = False\n                N = x\n    a = top_down(A)\n    b = bottom_up(A)\n    c = bottom_up_memopt(A)\n    assert(a == b and b == c) # 💩 sanity check\n    print(f'{filename}: {a}')\n\nrun('problem16.6test.txt')     # problem16.6test.txt: 2617\nrun('problem16.6.txt')         # problem16.6.txt: 2955353732\n"
  },
  {
    "path": "weighted_independent_set/package.json",
    "content": "{\n  \"name\": \"weighted_independent_set\",\n  \"version\": \"1.0.0\",\n  \"description\": \"\",\n  \"main\": \"main.js\",\n  \"scripts\": {\n    \"test\": \"echo \\\"Error: no test specified\\\" && exit 1\"\n  },\n  \"author\": \"clayton wong\",\n  \"license\": \"ISC\",\n  \"dependencies\": {\n    \"n-readlines\": \"^1.0.1\"\n  }\n}\n"
  },
  {
    "path": "weighted_independent_set/problem16.6.txt",
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  },
  {
    "path": "weighted_independent_set/problem16.6test.txt",
    "content": "10\n280\n618\n762\n908\n409\n34\n312\n277\n246\n779"
  }
]