結果
問題 | No.3041 非対称じゃんけん |
ユーザー |
![]() |
提出日時 | 2025-01-06 00:50:05 |
言語 | C# (.NET 8.0.404) |
結果 |
WA
|
実行時間 | - |
コード長 | 57,352 bytes |
コンパイル時間 | 9,403 ms |
コンパイル使用メモリ | 174,456 KB |
実行使用メモリ | 66,848 KB |
最終ジャッジ日時 | 2025-01-06 00:50:41 |
合計ジャッジ時間 | 36,052 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 1 |
other | AC * 2 WA * 8 TLE * 8 |
コンパイルメッセージ
復元対象のプロジェクトを決定しています... /home/judge/data/code/main.csproj を復元しました (118 ミリ秒)。 main -> /home/judge/data/code/bin/Release/net8.0/main.dll main -> /home/judge/data/code/bin/Release/net8.0/publish/
ソースコード
using System.ComponentModel;using System.Diagnostics.CodeAnalysis;using System.Numerics;using System.Runtime.CompilerServices;using System.Runtime.InteropServices;using System.Collections;using System.Text;using System.Text.RegularExpressions;using static Tmpl;using static CPDebug;using System.Collections.Specialized;using System.Globalization;using System.Diagnostics;StreamWriter writer = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };//using StreamWriter writer = new StreamWriter(File.Open("turn.txt", FileMode.Create, FileAccess.ReadWrite));Console.SetOut(writer);//using StreamReader reader = new StreamReader(File.Open("in.txt", FileMode.Open));//Console.SetIn(reader);Solver.Solve();Console.Out.Flush();public static class Solver{private static readonly AtCoderIO cin = new AtCoderIO();public static unsafe void Solve(){int N = cin.Int();int F = cin.Int();int[] A = cin.IntArray(N);int[] B = cin.IntArray(N);int[] C = cin.IntArray(N);int max = F * N;bool[] dp = new bool[max + 1];bool[] nextdp = new bool[max + 1];dp[A[0]] = true;dp[B[0]] = true;dp[C[0]] = true;int one = 0;for (int i = 0; i < max; i++){if (dp[i]) one++;}print(one);for (int i = 2; i <= N; i++){int ans = 0;for (int j = 0; j <= max; j++){if (j >= A[i - 1]){nextdp[j] |= dp[j - A[i - 1]];}if (j >= B[i - 1]){nextdp[j] |= dp[j - B[i - 1]];}if (j >= C[i - 1]){nextdp[j] |= dp[j - C[i - 1]];}if (nextdp[j]) ans++;}print(ans);(dp, nextdp) = (nextdp, dp);}}}public struct Vector<T> where T : struct, INumber<T>{private T[] _data;private int _size;public T this[int index]{get => _data[index];set => _data[index] = value;}public int Size => _size;public T[] Data => _data;public Vector(int size){_data = new T[size];_size = size;}}public struct Matrix<T> where T : struct, INumber<T>{private T[,] _data;private int _size;public T this[int r, int c]{get{return _data[r, c];}set{_data[r, c] = value;}}public T[,] Data => _data;public int Size => _size;public Matrix(int size){_size = size;_data = new T[size, size];}public static Matrix<T> operator +(Matrix<T> left, Matrix<T> right){if (left.Size != right.Size){throw new InvalidOperationException();}Matrix<T> dest = new(left.Size);for (int r = 0; r < left.Size; r++){for (int c = 0; c < left.Size; c++){dest[r, c] = left[r, c] + right[r, c];}}return dest;}public static Matrix<T> operator -(Matrix<T> left, Matrix<T> right){if (left.Size != right.Size){throw new InvalidOperationException();}Matrix<T> dest = new(left.Size);for (int r = 0; r < left.Size; r++){for (int c = 0; c < left.Size; c++){dest[r, c] = left[r, c] - right[r, c];}}return dest;}public static Matrix<T> operator *(Matrix<T> left, Matrix<T> right){if (left.Size != right.Size){throw new InvalidOperationException();}Matrix<T> dest = new(left.Size);for (int r = 0; r < dest.Size; r++){for (int c = 0; c < dest.Size; c++){for (int i = 0; i < dest.Size; i++){dest[r, c] += right[i, c] * left[r, i];}}}return dest;}public override string ToString(){StringBuilder sb = new();for (int r = 0; r < _size; r++){sb.Append('|');for (int c = 0; c < _size; c++){sb.Append(_data[r, c]);if (c != _size - 1){sb.Append(',');sb.Append('\t');}}sb.Append('|');sb.Append(Environment.NewLine);}return sb.ToString();}}static class Constants{public const long Mod = 998244353L;//public const long Mod = 10007L;//public const long Mod = 1000000007L;}public readonly struct Point{public readonly int X;public readonly int Y;public Point(int x, int y){X = x;Y = y;}public override int GetHashCode() => (X, Y).GetHashCode();public override string ToString(){return $"({X}, {Y})";}}public sealed class ReverseComparer<T> : IComparer<T>{public static readonly ReverseComparer<T> Default = new ReverseComparer<T>(Comparer<T>.Default);public static ReverseComparer<T> Reverse(IComparer<T> comparer){return new ReverseComparer<T>(comparer);}private readonly IComparer<T> comparer = Default;private ReverseComparer(IComparer<T> comparer){this.comparer = comparer;}public int Compare(T x, T y){return comparer.Compare(y, x);}}public sealed class AtCoderIO{Queue<string> _readQueue = new Queue<string>();private void LoadQueue(){if (_readQueue.Count > 0) return;string line = Console.ReadLine();string[] split = line.Split(' ', StringSplitOptions.RemoveEmptyEntries);for (int i = 0; i < split.Length; i++) _readQueue.Enqueue(split[i]);}private void Guard(){if (_readQueue.Count == 0){throw new Exception("NO DATA TO READ");}}public int Int(){LoadQueue();Guard();return int.Parse(_readQueue.Dequeue());}public long Long(){LoadQueue();Guard();return long.Parse(_readQueue.Dequeue());}public string String(){LoadQueue();Guard();return _readQueue.Dequeue();}public short Short(){LoadQueue();Guard();return short.Parse(_readQueue.Dequeue());}public byte Byte(){LoadQueue();Guard();return byte.Parse(_readQueue.Dequeue());}public char Char(){LoadQueue();Guard();return char.Parse(_readQueue.Dequeue());}public double Double(){LoadQueue();Guard();return double.Parse(_readQueue.Dequeue());}public float Float(){LoadQueue();Guard();return float.Parse(_readQueue.Dequeue());}public ModInt ModInt(){return new ModInt(Long());}public T Read<T>(){Type type = typeof(T);if (type == typeof(int)) return (T)(object)Int();else if (type == typeof(long)) return (T)(object)Long();else if (type == typeof(float)) return (T)(object)Float();else if (type == typeof(double)) return (T)(object)Double();else if (type == typeof(short)) return (T)(object)Short();else if (type == typeof(byte)) return (T)(object)Byte();else if (type == typeof(char)) return (T)(object)Char();else if (type == typeof(string)) return (T)(object)String();else if (type == typeof(ModInt)) return (T)(object)ModInt();else return default(T);}public int[] IntArray(int n){if (n == 0) return Array.Empty<int>();int[] arr = new int[n];for (int i = 0; i < n; i++){arr[i] = Int();}return arr;}public int[] ZeroIndexedPermutation(int n){if (n == 0) return Array.Empty<int>();int[] arr = new int[n];for (int i = 0; i < n; i++){arr[i] = Int() - 1;}return arr;}public long[] LongArray(int n){if (n == 0) return Array.Empty<long>();long[] arr = new long[n];for (int i = 0; i < n; i++){arr[i] = Long();}return arr;}public double[] DoubleArray(int n){if (n == 0) return Array.Empty<double>();double[] arr = new double[n];for (int i = 0; i < n; i++){arr[i] = Double();}return arr;}public ModInt[] ModIntArray(int n){if (n == 0) return Array.Empty<ModInt>();ModInt[] arr = new ModInt[n];for (int i = 0; i < n; i++){arr[i] = (ModInt)Long();}return arr;}public T[] ReadArray<T>(int n){if (n == 0) return Array.Empty<T>();T[] arr = new T[n];for (int i = 0; i < n; i++){arr[i] = Read<T>();}return arr;}}public static class CPDebug{public static void check<T>(T value, [CallerArgumentExpression(nameof(value))] string name = "value"){#if DEBUGConsole.WriteLine($"[DEBUG] {name}={value.ToString()}");#endif}public static void check<T>(IEnumerable<T> value, [CallerArgumentExpression(nameof(value))] string name = "value"){#if DEBUGConsole.WriteLine($"[DEBUG] {name}=({string.Join(' ', value)})");#endif}}public static class Tmpl{public static int combination(int n, int r){int c = 1;for (int i = 1; i <= r; i++){c = c * (n - i + 1) / i;}return c;}public static long combination(long n, long r){long c = 1;for (long i = 1; i <= r; i++){c = c * (n - i + 1) / i;}return c;}public static long pow(long b, long exp){if (exp == 0) return 1;if (exp == 1) return b;long m = pow(b, exp / 2L);m *= m;if (exp % 2L == 1) m *= b;return m;}public static long modpow(long b, long exp, long mod){if (exp == 0) return 1;if (exp == 1) return b % mod;long m = modpow(b, exp / 2L, mod);m *= m;m %= mod;if (exp % 2L == 1) m *= b % mod;m %= mod;return m;}static long modinv( long a, long mod ){long b = mod, u = 1, v = 0;while ( b > 0 ){long t = a / b;a -= t * b; swap( ref a, ref b );u -= t * v; swap( ref u, ref v );}u %= mod;if (u < 0) u += mod;return u;}public static long calcLcm(long a, long b){return a * b / calcGcd(a, b);}public static long calcGcd(long a, long b){if (a % b == 0) return b;return calcGcd(b, a % b);}// ax ≡ b (mod m)なる最小のxを求めるpublic static bool solveModLinear(long a, long b, long m, out long minSolution){long gcd = calcGcd(calcGcd(a, b), m);a /= gcd;b /= gcd;m /= gcd;if (calcGcd(a, m) == 1){long inv = modinv(a, m);minSolution = (b * inv) % m;return true;}minSolution = 0;return false;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void YesNo(bool t){Console.WriteLine(t ? "Yes" : "No");}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void YESNO(bool t){Console.WriteLine(t ? "YES" : "NO");}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void yesno(bool t){Console.WriteLine(t ? "yes" : "no");}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static bool checkBit(int bit, int n){return ((1 << n) & bit) != 0;}public static bool nextCombination(int n, int r, int[] array){int i = array.Length - 1;while (i >= 0 && array[i] == i + n - r){i--;}if (i < 0) return false;array[i]++;for (int j = i + 1; j < r; j++){array[j] = array[j - 1] + 1;}return true;}public static bool nextPermutation<T>(T[] array, int start, int length) where T : IComparable<T>{int end = start + length - 1;if (end <= start) return false;int last = end;while (true){int pos = last--;if (array[last].CompareTo(array[pos]) < 0){int i;for (i = end + 1; array[last].CompareTo(array[--i]) >= 0; ) { }T tmp = array[last]; array[last] = array[i]; array[i] = tmp;Array.Reverse(array, pos, end - pos + 1);return true;}if (last == start){Array.Reverse(array, start, end - start);return false;}}throw new Exception("NextPermutation: Fatal error");}public static unsafe Dictionary<char, int> cntCharOcc(string s){Dictionary<char, int> dict = new Dictionary<char, int>();fixed (char* ptr = s){for (int i = 0; i < s.Length; i++){if (dict.ContainsKey(ptr[i])){dict[ptr[i]] += 1;}else{dict[ptr[i]] = 1;}}}return dict;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void chmax<T> (ref T target, T value) where T : struct, IComparisonOperators<T, T, bool>{if (value > target){target = value;}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void chmin<T>(ref T target, T value) where T : struct, IComparisonOperators<T, T, bool>{if (value < target){target = value;}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void arrMod<T>(T[] array, T b) where T : IModulusOperators<T, T, T>{for (int i = 0; i < array.Length; i++){array[i] %= b;}}public static ReadOnlySpan<T> spanOf<T>(List<T> list){return CollectionsMarshal.AsSpan(list);}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void swap<T>(T[] array, int i, int j) where T : struct{(array[i], array[j]) = (array[j], array[i]);}public static void shuffle<T>(T[] array) where T : struct{Random random = new Random();for (int i = array.Length - 1; i > 0; i--){int index = random.Next(0, i + 1);swap(array, index, i);}}public static int lowerBound<T>(T[] array, int start, int end, T value) where T : struct, IComparisonOperators<T, T, bool>{int low = start;int high = end;int mid;while (low < high){mid = ((high - low) >> 1) + low;if (array[mid] < value)low = mid + 1;elsehigh = mid;}if (low == array.Length - 1 && array[low] < value){return array.Length;}return low;}public static int lowerBound<T>(List<T> array, int start, int end, T value) where T : struct, IComparisonOperators<T, T, bool>{int low = start;int high = end;int mid;while (low < high){mid = ((high - low) >> 1) + low;if (array[mid] < value)low = mid + 1;elsehigh = mid;}if (low == array.Count - 1 && array[low] < value){return array.Count;}return low;}public static int upperBound<T>(T[] array, T value) where T : struct, IComparisonOperators<T, T, bool>{var l = 0;var r = array.Length - 1;while (l <= r){var mid = l + (r - l) / 2;if (array[mid] <= value) l = mid + 1;else r = mid - 1;}return l;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void swap<T>(ref T a, ref T b) where T : struct{T temp = a;a = b;b = temp;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static bool dbleq(double a, double b){return Math.Abs(a - b) < double.Epsilon;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static int dblAsInt(double d){return (int)Math.Round(d, 0);}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static long dblAsLong(double d){return (long)Math.Round(d, 0);}public static int[] compressCoords<T>(T[] a) where T : struct, IComparisonOperators<T, T, bool>{T[] b = a.OrderBy(x => x).Distinct().ToArray();int[] result = new int[a.Length];for (int i = 0; i < a.Length; i++){result[i] = lowerBound(b, 0, b.Length - 1, a[i]);}return result;}public static List<RunLengthElement<T>> compressRunLength<T>(T[] array) where T : struct, IEquatable<T>{List<RunLengthElement<T>> list = new List<RunLengthElement<T>>();int count = 1;int start = 0;T prev = array[0];for (int i = 1; i < array.Length; i++){if (prev.Equals(array[i])){count++;}else{list.Add(new RunLengthElement<T>(start, count, prev));start = i;count = 1;}prev = array[i];}list.Add(new RunLengthElement<T>(start, count, prev));return list;}public static char[] alphabetsLower(){return new[] { 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y','z' };}public static char[] alphebetsUpper(){return new[]{ 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y','Z'};}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void print<T>(IEnumerable<T> array, char delimiter = ' '){Console.WriteLine(string.Join(delimiter, array));}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void fprint<T>(IEnumerable<T> array, char delimiter = ' '){print(array);Console.Out.Flush();}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void print(string msg){Console.WriteLine(msg);}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void fprint(string msg){Console.WriteLine(msg);Console.Out.Flush();}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void print(int val){print(val.ToString());}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void print(long val){print(val.ToString());}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void print(ModInt val){print(val.ToString());}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void fprint(int val){print(val.ToString());Console.Out.Flush();}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void fprint(long val){print(val.ToString());Console.Out.Flush();}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void fprint(ModInt val){fprint(val.ToString());Console.Out.Flush();}public static void print<T>(T[,] grid){for (int y = 0; y < grid.GetLength(0); y++){for (int x = 0; x < grid.GetLength(1); x++){Console.Write(grid[y, x] + "\t");}Console.WriteLine();}}public static void print01(bool t){Console.WriteLine(t ? "1" : "0");}public static TSrc lowerBoundKth<TSrc, TCnt>(TSrc min, TSrc max, Func<TSrc, TCnt> f, TCnt bound)where TSrc: struct, INumber<TSrc> where TCnt: struct, INumber<TCnt>{TSrc left = min;TSrc right = max;TSrc two = TSrc.CreateChecked(2);TSrc one = TSrc.CreateChecked(1);while (right > left){TSrc mid = left + (right - left) / two;TCnt c = f(mid);if (c < bound){left = mid + one;}else{right = mid;}}return left;}public static bool isSquareNumber(long n){long q = (long)Math.Floor(Math.Sqrt(n));return q * q == n;}}public readonly struct RunLengthElement<T> where T : struct{public readonly int Count;public readonly int StartIndex;public readonly T Value;public RunLengthElement(int startIndex, int count, T value){this.StartIndex = startIndex;this.Count = count;this.Value = value;}}public readonly struct Edge<T> : IEquatable<Edge<T>>, IComparable<Edge<T>> where T : struct, INumber<T>{public readonly int To;public readonly int From;public readonly T Weight;public Edge(int to, T weight){this.To = to;this.Weight = weight;}public Edge(int from, int to, T weight){this.To = to;this.From = from;this.Weight = weight;}public override bool Equals(object obj){if (obj is Edge<T> edge){return this.Equals(edge);}else{return false;}}public int CompareTo(Edge<T> other){return Weight.CompareTo(other.Weight);}public bool Equals(Edge<T> edge){return To == edge.To && From == edge.From && Weight == edge.Weight;}public override int GetHashCode(){return (To, From, Weight).GetHashCode();}public static bool operator ==(Edge<T> left, Edge<T> right){return left.Equals(right);}public static bool operator !=(Edge<T> left, Edge<T> right){return !left.Equals(right);}}public readonly struct ModInt : IEquatable<ModInt>{private readonly long Value;public static ModInt One => (ModInt)1L;public static ModInt Zero => (ModInt)0L;public ModInt(long value){Value = SafeMod(value);}[MethodImpl(MethodImplOptions.AggressiveInlining)]private static long SafeMod(long a){a %= Constants.Mod;if (a < 0) a += Constants.Mod;return a;}public ModInt Power(long exp){if (exp <= -1) return this;if (exp == 0) return 1;if (exp == 1) return this;ModInt m = Power(exp / 2);m *= m;if (exp % 2 == 1) m *= this;return m;}public ModInt Inv(){return this.Power(Constants.Mod - 2L);}public static ModInt operator +(ModInt left, ModInt right){return new ModInt(SafeMod(left.Value + right.Value));}public static ModInt operator -(ModInt left, ModInt right){return new ModInt(SafeMod(left.Value - right.Value));}public static ModInt operator *(ModInt left, ModInt right){return new ModInt(SafeMod(left.Value * right.Value));}public static ModInt operator /(ModInt left, ModInt right){if (right.Value == 0L){return Zero;}ModInt inv = right.Inv();return SafeMod(left * inv);}public static ModInt operator %(ModInt left, ModInt right){if (right.Value == 0L){return Zero;}return new ModInt(SafeMod(left.Value % right.Value));}public static bool operator ==(ModInt left, ModInt right){return left.Value == right.Value;}public static bool operator != (ModInt left, ModInt right){return !(left == right);}public bool Equals(ModInt other){return Value == other.Value;}public override bool Equals(object other){if (other is ModInt m){return this == m;}else return false;}public override int GetHashCode(){return Value.GetHashCode();}public static implicit operator ModInt(long v){return new ModInt(v);}public static implicit operator ModInt(int v){return new ModInt(v);}public static implicit operator long(ModInt m){return m.Value;}public static implicit operator int(ModInt m){return (int)m.Value;}public long Raw() => Value;public override string ToString(){return Value.ToString();}}public delegate T Monoid<T>(T a, T b);public delegate T Apply<T, M>(T x, M m, int len);// 一点に対する操作と区間に対するクエリを処理する.// 空間計算量: O(2N)// 時間計算量:// - 構築: O(N)// - 操作: O(logN)// - クエリ: O(logN)public sealed class SegmentTree<T> where T : struct{private int _treeSize;private int _dataSize;private int _originalDataSize;private T[] _data;private Monoid<T> _operator;private Monoid<T> _apply;private T _identity;public int OriginalDataSize => _originalDataSize;public int TreeSize => _treeSize;public T Identity => _identity;public T this[int index]{get{return _data[_dataSize - 1 + index];}}public SegmentTree(int n, Monoid<T> op, Monoid<T> apply, T identity){_originalDataSize = n;int size = 1;while (n > size){size <<= 1;}_dataSize = size;_treeSize = 2 * size - 1;_data = new T[_treeSize];_identity = identity;_operator = op;_apply = apply;}public void Build(T[] array){for (int i = 0; i < array.Length; i++){_data[i + _dataSize - 1] = array[i];}for (int i = _dataSize - 2; i >= 0; i--){_data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]);}}public void Apply(int index, T value){index += _dataSize - 1;_data[index] = _apply(_data[index], value);while (index > 0){index = (index - 1) >> 1;_data[index] = _operator(_data[(index << 1) + 1], _data[(index << 1) + 2]);}}public T Query(int left, int right){return QueryRec(left, right, 0, 0, _dataSize);}private T QueryRec(int left, int right, int index, int nodeLeft, int nodeRight){if (left >= nodeRight || right <= nodeLeft){return _identity;}if (left <= nodeLeft && nodeRight <= right){return _data[index];}T leftChild = QueryRec(left, right, (index << 1) + 1, nodeLeft, (nodeLeft + nodeRight) >> 1);T rightChild = QueryRec(left, right, (index << 1) + 2, (nodeLeft + nodeRight) >> 1, nodeRight);return _operator(leftChild, rightChild);}// 返されたArraySegment<T>は変更してはいけない.public ArraySegment<T> GetData(){return new ArraySegment<T>(_data, _dataSize - 1, _originalDataSize);}}// 区間に対する操作と区間に対するクエリを処理する.// 空間計算量: O(4N)// 時間計算量:// - 構築: O(N)// - 操作: O(logN)// - クエリ: O(logN)// - 一点参照: O(logN)// operator: クエリに対応する二項演算をする// mapping: 作用素を作用させる// composition: 作用素を合成するpublic sealed class LazySegmentTree<T, M> where T : struct, IEquatable<T> where M : struct, IEquatable<M>{private int _treeSize;private int _dataSize;private int _originalDataSize;private T[] _data;private M?[] _lazy;private Monoid<T> _operator;private Apply<T, M> _mapping;private Monoid<M> _composition;private T _identity;public T this[int index]{get{return GetByIndex(index);}}public LazySegmentTree(int n, Monoid<T> op, Apply<T, M> mapping, Monoid<M> composition, T identity){_originalDataSize = n;int size = 1;while (n > size){size <<= 1;}_dataSize = size;_treeSize = 2 * size - 1;_data = new T[_treeSize];_data.AsSpan().Fill(_identity);_lazy = new M?[_treeSize];_identity = identity;_operator = op;_mapping = mapping;_composition = composition;}public void Build(T[] array){for (int i = 0; i < array.Length; i++){_data[i + _dataSize - 1] = array[i];}for (int i = _dataSize - 2; i >= 0; i--){_data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]);}}private void Evaluate(int index, int l, int r){if (_lazy[index] is null){return;}if (index < _dataSize - 1){_lazy[(index << 1) + 1] = GuardComposition(_lazy[(index << 1) + 1], _lazy[index]);_lazy[(index << 1) + 2] = GuardComposition(_lazy[(index << 1) + 2], _lazy[index]);}_data[index] = _mapping(_data[index], (M)_lazy[index], r - l);_lazy[index] = null;}private M GuardComposition(M? a, M? b){if (a is null){return (M)b;}else{return _composition((M)a, (M)b);}}private void ApplyRec(int a, int b, M m, int index, int l, int r){Evaluate(index, l, r);if (a <= l && r <= b){_lazy[index] = GuardComposition(_lazy[index], m);Evaluate(index, l, r);}else if (a < r && l < b){ApplyRec(a, b, m, (index << 1) + 1, l, (l + r) / 2);ApplyRec(a, b, m, (index << 1) + 2, (l + r) / 2, r);_data[index] = _operator(_data[(index << 1) + 1], _data[(index << 1) + 2]);}}public void Apply(int left, int right, M m){ApplyRec(left, right, m, 0, 0, _dataSize);}public T Query(int left, int right){return QueryRec(left, right, 0, 0, _dataSize);}private T QueryRec(int left, int right, int index, int nodeLeft, int nodeRight){Evaluate(index, nodeLeft, nodeRight);if (left >= nodeRight || right <= nodeLeft){return _identity;}if (left <= nodeLeft && nodeRight <= right){return _data[index];}T leftChild = QueryRec(left, right, (index << 1) + 1, nodeLeft, (nodeLeft + nodeRight) >> 1);T rightChild = QueryRec(left, right, (index << 1) + 2, (nodeLeft + nodeRight) >> 1, nodeRight);return _operator(leftChild, rightChild);}public T GetByIndex(int target){if (target < 0 || target >= _originalDataSize){throw new Exception("Index is out of range.");}return AccessRec(target, 0, 0, _dataSize);}private T AccessRec(int target, int index, int l, int r){Evaluate(index, l, r);if (index >= _dataSize - 1){return _data[index];}int mid = (l + r) / 2;if (target < mid){return AccessRec(target, (index << 1) + 1, l, mid);}else{return AccessRec(target, (index << 1) + 2, mid, r);}}// index以下のノードをすべて即時に評価する.private void EvaluateAll(int index, int l, int r){if (_lazy[index] is null){if (index < _dataSize - 1){EvaluateAll((index << 1) + 1, l, (l + r) / 2);EvaluateAll((index << 1) + 2, (l + r) / 2, r);}return;}if (index < _dataSize - 1){_lazy[(index << 1) + 1] = GuardComposition(_lazy[(index << 1) + 1], _lazy[index]);_lazy[(index << 1) + 2] = GuardComposition(_lazy[(index << 1) + 2], _lazy[index]);EvaluateAll((index << 1) + 1, l, (l + r) / 2);EvaluateAll((index << 1) + 2, (l + r) / 2, r);}_data[index] = _mapping(_data[index], (M)_lazy[index], r - l);_lazy[index] = null;}// 返されたArraySegment<T>は変更してはいけない.public ArraySegment<T> GetData(){EvaluateAll(0, 0, _dataSize);return new ArraySegment<T>(_data, _dataSize - 1, _originalDataSize);}}public struct BeatsNode<T> where T : struct, IEquatable<T>{public T Value;public bool Failed;public BeatsNode(T value){Failed = false;Value = value;}}// 区間に対する操作と区間に対するクエリを処理する.// 空間計算量: O(4N)// 時間計算量:// - 構築: O(N)// - 操作: (操作に依存した計算量)// - クエリ: O(logN)// operator: クエリに対応する二項演算をする. 必ず計算ができる必要がある.// mapping: 作用素を作用させる. 計算が出来なければFailed←trueとして返す. この際, 子ノードに対する評価が実行される.// composition: 作用素を合成するpublic sealed class SegmentTreeBeats<T, M> where T : struct, IEquatable<T> where M : struct, IEquatable<M>{private int _treeSize;private int _dataSize;private int _originalDataSize;private BeatsNode<T>[] _data;private M?[] _lazy;private Monoid<BeatsNode<T>> _operator;private Apply<BeatsNode<T>, M> _mapping;private Monoid<M> _composition;private T _identity;private BeatsNode<T> _identityNode;public T this[int index]{get{return GetByIndex(index);}}public SegmentTreeBeats(int n, Monoid<BeatsNode<T>> op, Apply<BeatsNode<T>, M> mapping, Monoid<M> composition, T identity){_originalDataSize = n;int size = 1;while (n > size){size <<= 1;}_dataSize = size;_treeSize = 2 * size - 1;_data = new BeatsNode<T>[_treeSize];_identityNode = new BeatsNode<T>(_identity);_data.AsSpan().Fill(_identityNode);_lazy = new M?[_treeSize];_identity = identity;_operator = op;_mapping = mapping;_composition = composition;}public void Build(T[] array){for (int i = 0; i < array.Length; i++){_data[i + _dataSize - 1] = new BeatsNode<T>(array[i]);}for (int i = _dataSize - 2; i >= 0; i--){_data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]);}}private void Evaluate(int index, int l, int r){if (_lazy[index] is null){return;}if (index < _dataSize - 1){//_lazy[(index << 1) + 1] = GuardComposition(_lazy[(index << 1) + 1], _lazy[index]);//_lazy[(index << 1) + 2] = GuardComposition(_lazy[(index << 1) + 2], _lazy[index]);if (_lazy[(index << 1) + 1] is not null){Evaluate((index << 1) + 1, l, (l + r) / 2);}_lazy[(index << 1) + 1] = _lazy[index];if (_lazy[(index << 1) + 2] is not null){Evaluate((index << 1) + 2, (l + r) / 2, r);}_lazy[(index << 1) + 2] = _lazy[index];}//_data[index] = _mapping(_data[index], (M)_lazy[index], r - l);// 計算してみるBeatsNode<T> val = _mapping(_data[index], (M)_lazy[index], r - l);// 計算出来なければif (val.Failed){if (index >= _dataSize - 1){throw new Exception("葉ノードに対するmappingは失敗してはいけません");}// 子ノードを即評価Evaluate((index << 1) + 1, l, (l + r) / 2);Evaluate((index << 1) + 2, (l + r) / 2, r);// 子ノードの結果から親を更新_data[index] = _operator(_data[(index << 1) + 1], _data[(index << 1) + 2]);}else{// 計算できればそのまま更新_data[index] = val;}_lazy[index] = null;}private M GuardComposition(M? a, M? b){if (a is null){return (M)b;}else{return _composition((M)a, (M)b);}}private void ApplyRec(int a, int b, M m, int index, int l, int r){Evaluate(index, l, r);if (a <= l && r <= b){_lazy[index] = GuardComposition(_lazy[index], m);Evaluate(index, l, r);}else if (a < r && l < b){ApplyRec(a, b, m, (index << 1) + 1, l, (l + r) / 2);ApplyRec(a, b, m, (index << 1) + 2, (l + r) / 2, r);_data[index] = _operator(_data[(index << 1) + 1], _data[(index << 1) + 2]);}}public void Apply(int left, int right, M m){ApplyRec(left, right, m, 0, 0, _dataSize);}public T Query(int left, int right){return QueryRec(left, right, 0, 0, _dataSize).Value;}private BeatsNode<T> QueryRec(int left, int right, int index, int nodeLeft, int nodeRight){Evaluate(index, nodeLeft, nodeRight);if (left >= nodeRight || right <= nodeLeft){return _identityNode;}if (left <= nodeLeft && nodeRight <= right){return _data[index];}BeatsNode<T> leftChild = QueryRec(left, right, (index << 1) + 1, nodeLeft, (nodeLeft + nodeRight) >> 1);BeatsNode<T> rightChild = QueryRec(left, right, (index << 1) + 2, (nodeLeft + nodeRight) >> 1, nodeRight);return _operator(leftChild, rightChild);}public T GetByIndex(int target){if (target < 0 || target >= _originalDataSize){throw new Exception("Index is out of range.");}return AccessRec(target, 0, 0, _dataSize);}private T AccessRec(int target, int index, int l, int r){Evaluate(index, l, r);if (index >= _dataSize - 1){return _data[index].Value;}int mid = (l + r) / 2;if (target < mid){return AccessRec(target, (index << 1) + 1, l, mid);}else{return AccessRec(target, (index << 1) + 2, mid, r);}}// index以下のノードをすべて即時に評価する.private void EvaluateAll(int index, int l, int r){if (_lazy[index] is null){if (index < _dataSize - 1){EvaluateAll((index << 1) + 1, l, (l + r) / 2);EvaluateAll((index << 1) + 2, (l + r) / 2, r);}return;}if (index < _dataSize - 1){//_lazy[(index << 1) + 1] = GuardComposition(_lazy[(index << 1) + 1], _lazy[index]);//_lazy[(index << 1) + 2] = GuardComposition(_lazy[(index << 1) + 2], _lazy[index]);if (_lazy[(index << 1) + 1] is not null){Evaluate((index << 1) + 1, l, (l + r) / 2);}_lazy[(index << 1) + 1] = _lazy[index];if (_lazy[(index << 1) + 2] is not null){Evaluate((index << 1) + 2, (l + r) / 2, r);}_lazy[(index << 1) + 2] = _lazy[index];EvaluateAll((index << 1) + 1, l, (l + r) / 2);EvaluateAll((index << 1) + 2, (l + r) / 2, r);}_data[index] = _mapping(_data[index], (M)_lazy[index], r - l);_lazy[index] = null;}// 返されたArraySegment<T>は変更してはいけない.public void GetData(T[] destination){if (destination.Length < _originalDataSize){throw new Exception("書き込み先配列の大きさが足りない");}EvaluateAll(0, 0, _dataSize);//return new ArraySegment<T>(_data, _dataSize - 1, _originalDataSize);for (int i = 0; i < _originalDataSize; i++){destination[i] = _data[_dataSize - 1 + i].Value;}}}public struct ChangeNode<T> : IEquatable<ChangeNode<T>> where T : struct, INumber<T>, IMinMaxValue<T>{public T Max;public int MaxCount;public T SecondMax;public T Min;public int MinCount;public T SecondMin;public T Sum;public bool Equals(ChangeNode<T> other){return this.Equals(other);}public static ChangeNode<R> MakeLeaf<R>(R value) where R : struct, INumber<R>, IMinMaxValue<R>{return new ChangeNode<R>(){Max = value,MaxCount = 1,SecondMax = R.MinValue,Min = value,MinCount = 1,SecondMin = R.MaxValue,Sum = value};}}public static class SegmentTreeBuilder{public static LazySegmentTree<T, T> RangeAddMax<T>(int n, T identity) where T : struct, INumber<T>{return new LazySegmentTree<T, T>(n, T.Max,(x, m, l) =>{return x + m;},(a, b) => { return a + b; },identity);}public static LazySegmentTree<T, T> RangeUpdateMax<T>(int n, T identity) where T : struct, INumber<T>{return new LazySegmentTree<T, T>(n, T.Max,(x, m, l) =>{return m;},(x, y) => { return y; },identity);}public static LazySegmentTree<T, T> RangeAddMin<T>(int n, T identity) where T : struct, INumber<T>{return new LazySegmentTree<T, T>(n, T.Min,(x, m, l) =>{return x + m;},(a, b) => { return a + b; },identity);}public static LazySegmentTree<T, T> RangeUpdateMin<T>(int n, T identity) where T : struct, INumber<T>{return new LazySegmentTree<T, T>(n, T.Min,(x, m, l) =>{return m;},(x, y) => { return y; },identity);}public static LazySegmentTree<T, T> RangeAddSum<T>(int n, T identity) where T : struct, INumber<T>{return new LazySegmentTree<T, T>(n, (x, y) => x + y,(x, m, l) =>{return x + m * T.CreateChecked(l);},(a, b) => { return a + b; },identity);}public static LazySegmentTree<T, T> RangeUpdateSum<T>(int n, T identity) where T : struct, INumber<T>{return new LazySegmentTree<T, T>(n, (x, y) => x + y,(x, m, l) =>{return m * T.CreateChecked(l);},(a, b) => { return b; },identity);}public static SegmentTree<T> PointUpdateMax<T>(int n, T identity) where T : struct, INumber<T>{return new SegmentTree<T>(n, T.Max, (a, b) => b, identity);}public static SegmentTree<T> PointAddMax<T>(int n, T identity) where T : struct, INumber<T>{return new SegmentTree<T>(n, T.Max, (a, b) => a + b, identity);}public static SegmentTree<T> PointUpdateMin<T>(int n, T identity) where T : struct, INumber<T>{return new SegmentTree<T>(n, T.Min, (a, b) => b, identity);}public static SegmentTree<T> PointAddMin<T>(int n, T identity) where T : struct, INumber<T>{return new SegmentTree<T>(n, T.Min, (a, b) => a + b, identity);}public static SegmentTree<T> PointUpdateSum<T>(int n, T identity) where T : struct, INumber<T>{return new SegmentTree<T>(n, (x, y) => x + y, (a, b) => b, identity);}public static SegmentTree<T> PointAddSum<T>(int n, T identity) where T : struct, INumber<T>{return new SegmentTree<T>(n, (x, y) => x + y, (a, b) => a + b, identity);}}public sealed class PrefixSum2D<T> where T : struct, IAdditionOperators<T, T, T>, ISubtractionOperators<T, T, T>{private T[,] _sums;public PrefixSum2D(T[,] sequence){int height = sequence.GetLength(0);int width = sequence.GetLength(1);_sums = new T[height + 1, width + 1];// build prefix sumfor (int y = 0; y < height; y++){for (int x = 0; x < width; x++){_sums[y + 1, x + 1] = _sums[y + 1, x] + _sums[y, x + 1] - _sums[y, x] + sequence[y, x];}}}public T Sum(int startInclX, int startInclY, int endExclX, int endExclY){return _sums[endExclY, endExclX] + _sums[startInclY, startInclX] - _sums[startInclY, endExclX] - _sums[endExclY, startInclX];}public T AllSum(){return _sums[_sums.GetLength(0) - 1, _sums.GetLength(1) - 1];}}public sealed class PrefixSum<T> where T : struct, IAdditionOperators<T, T, T>, ISubtractionOperators<T, T, T>, IAdditiveIdentity<T, T>{private T[] _sums;public PrefixSum(T[] sequence){_sums = new T[sequence.Length + 1];_sums[0] = T.AdditiveIdentity;for (int i = 0; i < sequence.Length; i++){_sums[i + 1] = _sums[i] + sequence[i];}}// [a, b)public T Sum(int aIncl, int bExcl){return _sums[bExcl] - _sums[aIncl];}public T AllSum(){return _sums[^1];}public T[] GetArray(){return _sums;}}public sealed class UnionFind{private int[] _parents;private int[] _size;private int _vertexCount;public int VertexCount => _vertexCount;public UnionFind(int n){_vertexCount = n;_parents = new int[n];_size = new int[n];for (int i = 0; i < n; i++){_parents[i] = i;_size[i] = 1;}}public int Root(int x){if (_parents[x] == x)return x;return _parents[x] = Root(_parents[x]);}public void Unite(int x, int y){int rootX = Root(x);int rootY = Root(y);if (rootX == rootY)return;int from = rootX;int to = rootY;// merge from to toif (_size[from] > _size[to]){(from, to) = (to, from);}_size[to] += _size[from];_parents[from] = to;}public List<int> Find(int x){int rootX = Root(x);List<int> set = new List<int>();for (int i = 0; i < _vertexCount; i++){if (Root(i) == rootX)set.Add(i);}return set;}public Dictionary<int, List<int>> FindAll(){Dictionary<int, List<int>> sets = new Dictionary<int, List<int>>();for (int i = 0; i < _vertexCount; i++){int root = Root(i);if (sets.ContainsKey(root))sets[root].Add(i);elsesets[root] = new List<int>() { i };}return sets;}public bool Same(int x, int y){int rootX = Root(x);int rootY = Root(y);return rootX == rootY;}public int Size(int v){return _size[Root(v)];}public void Clear(){for (int i = 0; i < _vertexCount; i++){_parents[i] = i;}}}public sealed class RollbackUnionFind{private int[] _data;private Stack<(int, int)> _history;int _innerSnap;public RollbackUnionFind(int n){_innerSnap = 0;_data = new int[n];Array.Fill(_data, -1);_history = new Stack<(int, int)>();}public bool Unite(int x, int y){x = Find(x);y = Find(y);_history.Push((x, _data[x]));_history.Push((y, _data[y]));if (x == y)return false;if (_data[x] > _data[y]){swap(ref x, ref y);}_data[x] += _data[y];_data[y] = x;return true;}public int Find(int k){if (_data[k] < 0) return k;return Find(_data[k]);}public bool Same(int x, int y){return Find(x) == Find(y);}public int Size(int k){return -_data[Find(k)];}public void Undo(){_data[_history.Peek().Item1] = _history.Peek().Item2;_history.Pop();_data[_history.Peek().Item1] = _history.Peek().Item2;_history.Pop();}public void Snapshot(){_innerSnap = _history.Count >> 1;}public int GetState(){return _history.Count >> 1;}public void Rollback(int state = -1){if (state == -1) state = _innerSnap;state <<= 1;while (state < _history.Count) this.Undo();}}public sealed class Imos<T> where T : struct, IAdditionOperators<T, T, T>, ISubtractionOperators<T, T, T>{private T[] _data;public Imos(T[] array){_data = array;}public Imos(int len){_data = new T[len];}public void AddQueryLen(int start, int length, T value){this.AddQuery(start, start + length, value);}public void AddQuery(int start, int end, T value){_data[start] += value;if (end < _data.Length){_data[end] -= value;}}public void Simulate(){for (int i = 1; i < _data.Length; i++){_data[i] += _data[i - 1];}}public T[] GetData(){return _data;}}public sealed class Imos2D<T> where T : struct, IAdditionOperators<T, T, T>, ISubtractionOperators<T, T, T>{private T[,] _data;private int _width;private int _height;public Imos2D(T[,] data){_data = data;_width = data.GetLength(1);_height = data.GetLength(0);}public Imos2D(int h, int w){_data = new T[h, w];_width = w;_height = h;}public void AddQuery(int startX, int startY, int endX, int endY, T value){_data[startY, startX] += value;if (endX < _width){_data[startY, endX] -= value;}if (endY < _height){_data[endY, startX] -= value;}if (endX < _width && endY < _height){_data[endY, endX] += value;}}public void AddQueryLen(int x, int y, int w, int h, T value){this.AddQuery(x, y, x + w, y + h, value);}public void Simulate(){for (int x = 1; x < _width; x++){for (int y = 0; y < _height; y++){_data[y, x] += _data[y, x - 1];}}for (int y = 1; y < _height; y++){for (int x = 0; x < _width; x++){_data[y, x] += _data[y - 1, x];}}}public T[,] GetData(){return _data;}}public static class LIS{// NOTE: 空間計算量O(max), 時間計算量O(nlogn)public static int LengthOfLIS(int[] sequence, int max){if (max >= 1_000_000_00){throw new ArgumentException("Max value is too large.", nameof(max));}var seg = SegmentTreeBuilder.PointUpdateMax<int>(max + 1, 0);for (int i = 1; i <= sequence.Length; i++){int m = seg.Query(0, sequence[i - 1]);seg.Apply(sequence[i - 1], m + 1);}return seg.Query(0, max + 1);}}public static class TestCase{private static Random _random = new Random();public static void Seed(int seed){_random = new Random(seed);}public static string RandomStringLower(int length){Span<char> span = stackalloc char[length];for (int i = 0; i < length; i++){char ch = (char)('a' + _random.Next(0, 26));span[i] = ch;}return new string(span);}public static string RandomStringUpper(int length){return RandomStringLower(length).ToUpperInvariant();}public static int[] RandomPermutation(int length){int[] d = new int[length];for (int i = 0; i < length; i++) d[i] = i + 1;shuffle(d);return d;}public static long[] RandomArrayLong(int length, long min, long max){long[] d = new long[length];for (int i = 0; i < length; i++){d[i] = _random.NextInt64(min, max + 1);}return d;}public static int[] RandomArray(int length, int min, int max){int[] d = new int[length];for (int i = 0; i < length; i++){d[i] = _random.Next(min, max + 1);}return d;}public static int[,] Random2DArray(int height, int width, int min, int max){int[,] d = new int[height, width];for (int y = 0; y < height; y++){for (int x = 0; x < width; x++){d[y, x] = _random.Next(min, max + 1);}}return d;}public static long[,] Random2DArrayLong(int height, int width, int min, int max){long[,] d = new long[height, width];for (int y = 0; y < height; y++){for (int x = 0; x < width; x++){d[y, x] = _random.NextInt64(min, max + 1);}}return d;}public static char[,] RandomCharGrid(int height, int width, params char[] tiles){char[,] d = new char[height, width];for (int y = 0; y < height; y++){for (int x = 0; x < width; x++){d[y, x] = tiles[_random.Next(0, tiles.Length)];}}return d;}}public sealed class NumberUtility{private bool[] _isPrime;private int[] _minFactor;private int[] _mobius;private int _n;public NumberUtility(int max){_n = max;_isPrime = new bool[max + 1];_minFactor = new int[max + 1];_mobius = new int[max + 1];Array.Fill(_isPrime, true);Array.Fill(_minFactor, -1);Array.Fill(_mobius, 1);_isPrime[1] = false;_minFactor[1] = 1;for (int i = 2; i <= _n; i++){if (!_isPrime[i]) continue;_minFactor[i] = i;_mobius[i] = -1;for (int j = i + i; j <= _n; j += i){_isPrime[j] = false;if (_minFactor[j] == -1) _minFactor[j] = i;if (j / i % i == 0) _mobius[j] = 0;else _mobius[j] = -_mobius[j];}}}public int Mu(int n){return _mobius[n];}public int MinFactor(int n){return _minFactor[n];}public bool IsPrime(int n){return _isPrime[n];}}public sealed class Convolution{private readonly long _mod;public Convolution(long mod){_mod = mod;}public List<long> CalcConvolution(List<long> a, List<long> b){return null;}}