結果
問題 | No.1479 Matrix Eraser |
ユーザー |
![]() |
提出日時 | 2021-04-16 20:54:55 |
言語 | C#(csc) (csc 3.9.0) |
結果 |
AC
|
実行時間 | 466 ms / 3,000 ms |
コード長 | 33,369 bytes |
コンパイル時間 | 3,039 ms |
コンパイル使用メモリ | 129,188 KB |
実行使用メモリ | 73,280 KB |
最終ジャッジ日時 | 2024-07-02 23:37:20 |
合計ジャッジ時間 | 14,455 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 39 |
コンパイルメッセージ
Microsoft (R) Visual C# Compiler version 3.9.0-6.21124.20 (db94f4cc) Copyright (C) Microsoft Corporation. All rights reserved.
ソースコード
using System;using System.Collections;using System.Collections.Generic;using System.Diagnostics;using System.Globalization;using System.IO;using System.Linq;using System.Numerics;using System.Runtime.CompilerServices;using System.Runtime.InteropServices;using System.Text;namespace YukiCoder{class Program{static void Main(){using var cin = new Scanner();var (h, w) = cin.Int2();var map = new HashMap<int, List<(int i, int j)>>(x => new List<(int i, int h)>());for (int i = 0; i < h; i++) {for (int j = 0; j < w; j++) {int a = cin.Int();map[a].Add((i, j));}}var keys = map.Keys.ToArray();Array.Sort(keys);Array.Reverse(keys);var ss = new HashSet<int>();var tt = new HashSet<int>();long ans = 0;foreach (var k in keys) {if (k == 0) {continue;}if (map[k].Count == 1) {ans++;continue;}ss.Clear();tt.Clear();foreach (var p in map[k]) {ss.Add(p.i);tt.Add(p.j);}var compH = new Compression<int>(ss.ToArray());var compW = new Compression<int>(tt.ToArray());compH.Compress();compW.Compress();int hh = compH.Count;int m = compH.Count + compW.Count;int s = m;int t = m + 1;var flow = new MaxFlow(m + 2);foreach (var p in map[k]) {flow.AddEdge(compH.Zip(p.i), compW.Zip(p.j) + hh, 1);}foreach (var sss in ss) {flow.AddEdge(s, compH.Zip(sss), 1);}foreach (var ttt in tt) {flow.AddEdge(compW.Zip(ttt) + hh, t, 1);}flow.Build();var ret = flow.Dinic(s, t);ans += ret;}Console.WriteLine(ans);}}public class Compression<T>where T : IComparable<T>{public static int Compress(Span<T> raws,Func<int, T> cast){int n = raws.Length;var comp = new Compression<T>(raws);comp.Compress();for (int i = 0; i < n; i++) {raws[i] = cast.Invoke(comp.Zip(raws[i]));}return comp.Count;}private readonly HashSet<T> raws_ = new HashSet<T>();private T[] values_;private Dictionary<T, int> map_;public int Count => values_.Length;public Compression() { }public Compression(ReadOnlySpan<T> values){Add(values);}[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Add(T value) => raws_.Add(value);[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Add(ReadOnlySpan<T> values){foreach (var value in values) {raws_.Add(value);}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Compress(int offset = 0){values_ = raws_.ToArray();Array.Sort(values_);map_ = new Dictionary<T, int>(values_.Length);int number = offset;for (int i = 0; i < values_.Length; ++i, ++number) {map_[values_[i]] = number;}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public int Zip(T value) => map_[value];[MethodImpl(MethodImplOptions.AggressiveInlining)]public T UnZip(int index) => values_[index];[MethodImpl(MethodImplOptions.AggressiveInlining)]public int LowerBound(T value){int ng = -1;int ok = values_.Length - 1;while (ok - ng > 1) {int mid = (ok + ng) / 2;if (values_[mid].CompareTo(value) >= 0) {ok = mid;} else {ng = mid;}}return ok;}}public class MaxFlow{private const long INF = long.MaxValue;private readonly int n_;private readonly List<(int v, int index)> edgeInfos_;private readonly JagList2<EdgeInternal> edges_;private JagList2<EdgeInternal> flowedEdges_;public MaxFlow(int n){n_ = n;edgeInfos_ = new List<(int v, int index)>();edges_ = new JagList2<EdgeInternal>(n);}[MethodImpl(MethodImplOptions.AggressiveInlining)]public void AddEdge(int from, int to, long capacity){edgeInfos_.Add((from, edges_.Raw[from].Count));edges_.Add(from, new EdgeInternal(to, capacity, edges_.Raw[to].Count));edges_.Add(to, new EdgeInternal(from, 0, edges_.Raw[from].Count - 1));}[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Build(){edges_.Build();}[MethodImpl(MethodImplOptions.AggressiveInlining)]private Edge GetFlowedEdge(int i){var to = flowedEdges_[edgeInfos_[i].v][edgeInfos_[i].index];var from = flowedEdges_[to.To][to.ReverseEdgeIndex];return new Edge(edgeInfos_[i].v, to.To, (to.Capacity + from.Capacity), from.Capacity);}[MethodImpl(MethodImplOptions.AggressiveInlining)]public ReadOnlySpan<Edge> GetFlowedEdges(){if (flowedEdges_ is null) {flowedEdges_ = edges_;}var result = new Edge[edgeInfos_.Count];for (int i = 0; i < result.Length; ++i) {result[i] = GetFlowedEdge(i);}return result;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public long Fulkerson(int s, int t, bool keepsEdges = false){if (keepsEdges) {CopyEdges();} else {flowedEdges_ = edges_;}long Dfs(int s, int t, long f, bool[] done){if (s == t) {return f;}done[s] = true;var edges = flowedEdges_[s];for (int i = 0; i < edges.Length; ++i) {ref var edge = ref edges[i];if (done[edge.To] == false && edge.Capacity > 0) {long d = Dfs(edge.To, t, Math.Min(f, edge.Capacity), done);if (d > 0) {edge.Capacity -= d;flowedEdges_[edge.To][edge.ReverseEdgeIndex].Capacity += d;return d;}}}return 0;}long flow = 0;while (true) {var done = new bool[n_];long f = Dfs(s, t, INF, done);if (f == 0 || f == INF) {break;}flow += f;}return flow;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public long Dinic(int s, int t, bool keepsEdges = false){if (keepsEdges) {CopyEdges();} else {flowedEdges_ = edges_;}long[] Bfs(int s){var d = new long[n_];d.AsSpan().Fill(-1);d[s] = 0;var q = new Queue<int>();q.Enqueue(s);while (q.Count > 0) {int v = q.Dequeue();var edges = flowedEdges_[v];foreach (var edge in edges) {if (edge.Capacity > 0 && d[edge.To] < 0) {d[edge.To] = d[v] + 1;q.Enqueue(edge.To);}}}return d;}long Dfs(int s, int t, long f, int[] done, long[] distance){if (s == t) {return f;}var edges = flowedEdges_[s];for (; done[s] < edges.Length; done[s]++) {ref var edge = ref edges[done[s]];if (edge.Capacity > 0 && distance[s] < distance[edge.To]) {long d = Dfs(edge.To, t, Math.Min(f, edge.Capacity), done, distance);if (d > 0) {edge.Capacity -= d;flowedEdges_[edge.To][edge.ReverseEdgeIndex].Capacity += d;return d;}}}return 0;}long flow = 0;while (true) {var distance = Bfs(s);if (distance[t] < 0) {break;}var done = new int[n_];while (true) {long f = Dfs(s, t, INF, done, distance);if (f == 0 || f == INF) {break;}flow += f;}}return flow;}[MethodImpl(MethodImplOptions.AggressiveInlining)]private void CopyEdges(){flowedEdges_ = new JagList2<EdgeInternal>(n_);for (int i = 0; i < n_; ++i) {var edges = edges_[i];foreach (var edge in edges) {flowedEdges_.Add(i, edge);}}flowedEdges_.Build();}private struct EdgeInternal{public int To { get; set; }public int ReverseEdgeIndex { get; set; }public long Capacity { get; set; }public EdgeInternal(int to, long capacity, int reverse){To = to;Capacity = capacity;ReverseEdgeIndex = reverse;}}public struct Edge{public int From { get; set; }public int To { get; set; }public long Capacity { get; set; }public long Flow { get; set; }public Edge(int from, int to, long capacity, long flow){From = from;To = to;Capacity = capacity;Flow = flow;}};}public class JagList2<T> where T : struct{private readonly int n_;private readonly List<T>[] tempValues_;private T[][] values_;public int Count => n_;public List<T>[] Raw => tempValues_;public T[][] Values => values_;public T[] this[int index] => values_[index];public JagList2(int n){n_ = n;tempValues_ = new List<T>[n];for (int i = 0; i < n; ++i) {tempValues_[i] = new List<T>();}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Add(int i, T value) => tempValues_[i].Add(value);[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Build(){values_ = new T[n_][];for (int i = 0; i < values_.Length; ++i) {values_[i] = tempValues_[i].ToArray();}}}public struct BitFlag{public static BitFlag Begin() => 0;public static BitFlag End(int bitCount) => 1 << bitCount;public static BitFlag FromBit(int bitNumber) => 1 << bitNumber;private readonly int flags_;public int Flag => flags_;public bool this[int bitNumber] => (flags_ & (1 << bitNumber)) != 0;public BitFlag(int flags) { flags_ = flags; }public bool Has(BitFlag target) => (flags_ & target.flags_) == target.flags_;public bool Has(int target) => (flags_ & target) == target;public bool HasBit(int bitNumber) => (flags_ & (1 << bitNumber)) != 0;public BitFlag OrBit(int bitNumber) => (flags_ | (1 << bitNumber));public BitFlag AndBit(int bitNumber) => (flags_ & (1 << bitNumber));public BitFlag XorBit(int bitNumber) => (flags_ ^ (1 << bitNumber));public BitFlag ComplementOf(BitFlag sub) => flags_ & (~sub.flags_);public static BitFlag operator ++(BitFlag src) => new BitFlag(src.flags_ + 1);public static BitFlag operator --(BitFlag src) => new BitFlag(src.flags_ - 1);public static BitFlag operator |(BitFlag lhs, BitFlag rhs)=> new BitFlag(lhs.flags_ | rhs.flags_);public static BitFlag operator |(BitFlag lhs, int rhs)=> new BitFlag(lhs.flags_ | rhs);public static BitFlag operator |(int lhs, BitFlag rhs)=> new BitFlag(lhs | rhs.flags_);public static BitFlag operator &(BitFlag lhs, BitFlag rhs)=> new BitFlag(lhs.flags_ & rhs.flags_);public static BitFlag operator &(BitFlag lhs, int rhs)=> new BitFlag(lhs.flags_ & rhs);public static BitFlag operator &(int lhs, BitFlag rhs)=> new BitFlag(lhs & rhs.flags_);public static bool operator <(BitFlag lhs, BitFlag rhs) => lhs.flags_ < rhs.flags_;public static bool operator <(BitFlag lhs, int rhs) => lhs.flags_ < rhs;public static bool operator <(int lhs, BitFlag rhs) => lhs < rhs.flags_;public static bool operator >(BitFlag lhs, BitFlag rhs) => lhs.flags_ > rhs.flags_;public static bool operator >(BitFlag lhs, int rhs) => lhs.flags_ > rhs;public static bool operator >(int lhs, BitFlag rhs) => lhs > rhs.flags_;public static bool operator <=(BitFlag lhs, BitFlag rhs) => lhs.flags_ <= rhs.flags_;public static bool operator <=(BitFlag lhs, int rhs) => lhs.flags_ <= rhs;public static bool operator <=(int lhs, BitFlag rhs) => lhs <= rhs.flags_;public static bool operator >=(BitFlag lhs, BitFlag rhs) => lhs.flags_ >= rhs.flags_;public static bool operator >=(BitFlag lhs, int rhs) => lhs.flags_ >= rhs;public static bool operator >=(int lhs, BitFlag rhs) => lhs >= rhs.flags_;public static implicit operator BitFlag(int t) => new BitFlag(t);public static implicit operator int(BitFlag t) => t.flags_;public override string ToString() => $"{Convert.ToString(flags_, 2).PadLeft(32, '0')} ({flags_})";[MethodImpl(MethodImplOptions.AggressiveInlining)]public void ForEachSubBits(Action<BitFlag> action){for (BitFlag sub = (flags_ - 1) & flags_; sub > 0; sub = --sub & flags_) {action(sub);}}public SubBitsEnumerator SubBits => new SubBitsEnumerator(flags_);public struct SubBitsEnumerator : IEnumerable<BitFlag>{private readonly int flags_;public SubBitsEnumerator(int flags){flags_ = flags;}IEnumerator<BitFlag> IEnumerable<BitFlag>.GetEnumerator() => new Enumerator(flags_);IEnumerator IEnumerable.GetEnumerator() => new Enumerator(flags_);public Enumerator GetEnumerator() => new Enumerator(flags_);public struct Enumerator : IEnumerator<BitFlag>{private readonly int src_;public BitFlag Current { get; private set; }object IEnumerator.Current => Current;public Enumerator(int flags){src_ = flags;Current = flags;}public void Dispose() { }[MethodImpl(MethodImplOptions.AggressiveInlining)]public bool MoveNext() => (Current = --Current & src_) > 0;[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Reset() => Current = src_;}}}public class HashMap<TKey, TValue> : Dictionary<TKey, TValue>{private readonly Func<TKey, TValue> initialzier_;public HashMap(Func<TKey, TValue> initialzier): base(){initialzier_ = initialzier;}public HashMap(Func<TKey, TValue> initialzier, int capacity): base(capacity){initialzier_ = initialzier;}new public TValue this[TKey key]{get{if (TryGetValue(key, out TValue value)) {return value;} else {var init = initialzier_(key);base[key] = init;return init;}}set { base[key] = value; }}public HashMap<TKey, TValue> Merge(HashMap<TKey, TValue> src,Func<TValue, TValue, TValue> mergeValues){foreach (var key in src.Keys) {this[key] = mergeValues(this[key], src[key]);}return this;}}public struct ModInt{//public const long P = 1000000007;public const long P = 998244353;public const long ROOT = 3;// (924844033, 5)// (998244353, 3)// (1012924417, 5)// (167772161, 3)// (469762049, 3)// (1224736769, 3)private long value_;public static ModInt New(long value, bool mods) => new ModInt(value, mods);public ModInt(long value) => value_ = value;public ModInt(long value, bool mods){if (mods) {value %= P;if (value < 0) {value += P;}}value_ = value;}public static ModInt operator +(ModInt lhs, ModInt rhs){lhs.value_ = (lhs.value_ + rhs.value_) % P;return lhs;}public static ModInt operator +(long lhs, ModInt rhs){rhs.value_ = (lhs + rhs.value_) % P;return rhs;}public static ModInt operator +(ModInt lhs, long rhs){lhs.value_ = (lhs.value_ + rhs) % P;return lhs;}public static ModInt operator -(ModInt lhs, ModInt rhs){lhs.value_ = (P + lhs.value_ - rhs.value_) % P;return lhs;}public static ModInt operator -(long lhs, ModInt rhs){rhs.value_ = (P + lhs - rhs.value_) % P;return rhs;}public static ModInt operator -(ModInt lhs, long rhs){lhs.value_ = (P + lhs.value_ - rhs) % P;return lhs;}public static ModInt operator *(ModInt lhs, ModInt rhs){lhs.value_ = lhs.value_ * rhs.value_ % P;return lhs;}public static ModInt operator *(long lhs, ModInt rhs){rhs.value_ = lhs * rhs.value_ % P;return rhs;}public static ModInt operator *(ModInt lhs, long rhs){lhs.value_ = lhs.value_ * rhs % P;return lhs;}public static ModInt operator /(ModInt lhs, ModInt rhs){long exp = P - 2;while (exp > 0) {if (exp % 2 > 0) {lhs *= rhs;}rhs *= rhs;exp /= 2;}return lhs;}public static implicit operator ModInt(long n) => new ModInt(n, true);public static ModInt Inverse(ModInt value) => Pow(value, P - 2);public static ModInt Pow(ModInt value, long k) => Pow(value.value_, k);public static ModInt Pow(long value, long k){long ret = 1;while (k > 0) {if ((k & 1) != 0) {ret = ret * value % P;}value = value * value % P;k >>= 1;}return new ModInt(ret);}public static Span<ModInt> NTT(Span<int> values, bool inverses = false)=> NumberTheoreticTransform(values, inverses);public static Span<ModInt> NumberTheoreticTransform(Span<int> values, bool inverses = false){var mods = new ModInt[values.Length];for (int i = 0; i < mods.Length; i++) {mods[i] = new ModInt(values[i]);}return NumberTheoreticTransform(mods, inverses);}public static Span<ModInt> NTT(Span<long> values, bool inverses = false)=> NumberTheoreticTransform(values, inverses);public static Span<ModInt> NumberTheoreticTransform(Span<long> values, bool inverses = false){var mods = new ModInt[values.Length];for (int i = 0; i < mods.Length; i++) {mods[i] = new ModInt(values[i]);}return NumberTheoreticTransform(mods, inverses);}public static Span<ModInt> NTT(Span<ModInt> values, bool inverses = false)=> NumberTheoreticTransform(values, inverses);public static Span<ModInt> NumberTheoreticTransform(Span<ModInt> a, bool inverses = false){int n = a.Length;if (n == 1) {return a;}var b = new ModInt[n].AsSpan();int r = inverses? (int)(P - 1 - (P - 1) / n): (int)((P - 1) / n);ModInt s = Pow(ROOT, r);var kp = new ModInt[n / 2 + 1];kp.AsSpan().Fill(1);for (int i = 0; i < n / 2; ++i) {kp[i + 1] = kp[i] * s;}int l = n / 2;for (int i = 1; i < n; i <<= 1, l >>= 1) {r = 0;for (int j = 0; j < l; ++j, r += i) {s = kp[i * j];for (int k = 0; k < i; ++k) {var p = a[k + r];var q = a[k + r + n / 2];b[k + 2 * r] = p + q;b[k + 2 * r + i] = (p - q) * s;}}var temp = a;a = b;b = temp;}if (inverses) {s = Inverse(n);for (int i = 0; i < n; i++) {a[i] = a[i] * s;}}return a;}public static ModInt[,] Ntt2D(ModInt[,] a, bool inverses = false)=> NumberTheoreticTransform2D(a, inverses);public static ModInt[,] NumberTheoreticTransform2D(ModInt[,] a, bool inverses = false){int h = a.GetLength(0);int w = a.GetLength(1);if (h == 1 && w == 1) {return a;}var b = new ModInt[h, w];{int n = w;int r = inverses? (int)(P - 1 - (P - 1) / n): (int)((P - 1) / n);ModInt s = Pow(ROOT, r);var kp = new ModInt[n / 2 + 1];kp.AsSpan().Fill(1);for (int i = 0; i < n / 2; ++i) {kp[i + 1] = kp[i] * s;}for (int y = 0; y < h; y++) {int l = n / 2;for (int i = 1; i < n; i <<= 1, l >>= 1) {r = 0;for (int j = 0; j < l; ++j, r += i) {s = kp[i * j];for (int k = 0; k < i; ++k) {var p = a[y, k + r];var q = a[y, k + r + n / 2];b[y, k + 2 * r] = p + q;b[y, k + 2 * r + i] = (p - q) * s;}}var temp = a;a = b;b = temp;}if (inverses) {s = Inverse(n);for (int i = 0; i < n; i++) {a[y, i] = a[y, i] * s;}}}}for (int i = 0; i < h; i++) {for (int j = 0; j < w; j++) {b[h, w] = 0;}}{int n = h;int r = inverses? (int)(P - 1 - (P - 1) / n): (int)((P - 1) / n);ModInt s = Pow(ROOT, r);var kp = new ModInt[n / 2 + 1];kp.AsSpan().Fill(1);for (int i = 0; i < n / 2; ++i) {kp[i + 1] = kp[i] * s;}for (int x = 0; x < w; x++) {int l = n / 2;for (int i = 1; i < n; i <<= 1, l >>= 1) {r = 0;for (int j = 0; j < l; ++j, r += i) {s = kp[i * j];for (int k = 0; k < i; ++k) {var p = a[k + r, x];var q = a[k + r + n / 2, x];b[k + 2 * r, x] = p + q;b[k + 2 * r + i, x] = (p - q) * s;}}var temp = a;a = b;b = temp;}if (inverses) {s = Inverse(n);for (int i = 0; i < n; i++) {a[i, x] = a[i, x] * s;}}}}return a;}public static Span<ModInt> Convolve(ReadOnlySpan<ModInt> a, ReadOnlySpan<ModInt> b){int resultLength = a.Length + b.Length - 1;int nttLenght = 1;while (nttLenght < resultLength) {nttLenght <<= 1;}var aa = new ModInt[nttLenght];a.CopyTo(aa);var bb = new ModInt[nttLenght];b.CopyTo(bb);var fa = NumberTheoreticTransform(aa);var fb = NumberTheoreticTransform(bb);for (int i = 0; i < nttLenght; i++) {fa[i] *= fb[i];}var convolved = NumberTheoreticTransform(fa, true);return convolved.Slice(0, resultLength);}public long ToLong() => value_;public override string ToString() => value_.ToString();}public static class Helper{[MethodImpl(MethodImplOptions.AggressiveInlining)]public static int Pow(int n, int k)=> (int)Pow((long)n, (long)k);[MethodImpl(MethodImplOptions.AggressiveInlining)]public static long Pow(long n, long k){long ret = 1;long mul = n;while (k > 0) {if ((k & 1) != 0) {ret *= mul;}k >>= 1;mul *= mul;}return ret;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void UpdateMin<T>(this ref T target, T value) where T : struct, IComparable<T>=> target = target.CompareTo(value) > 0 ? value : target;[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void UpdateMin<T>(this ref T target, T value, Action<T> onUpdated)where T : struct, IComparable<T>{if (target.CompareTo(value) > 0) {target = value;onUpdated(value);}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void UpdateMax<T>(this ref T target, T value) where T : struct, IComparable<T>=> target = target.CompareTo(value) < 0 ? value : target;[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void UpdateMax<T>(this ref T target, T value, Action<T> onUpdated)where T : struct, IComparable<T>{if (target.CompareTo(value) < 0) {target = value;onUpdated(value);}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T[] Array1<T>(int n, T initialValue) where T : struct=> new T[n].Fill(initialValue);[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T[] Array1<T>(int n, Func<int, T> initializer)=> Enumerable.Range(0, n).Select(x => initializer(x)).ToArray();[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T[] Fill<T>(this T[] array, T value)where T : struct{array.AsSpan().Fill(value);return array;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T[,] Array2<T>(int n, int m, T initialValule) where T : struct=> new T[n, m].Fill(initialValule);[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T[,] Array2<T>(int n, int m, Func<int, int, T> initializer){var array = new T[n, m];for (int i = 0; i < n; ++i) {for (int j = 0; j < m; ++j) {array[i, j] = initializer(i, j);}}return array;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T[,] Fill<T>(this T[,] array, T initialValue)where T : struct{MemoryMarshal.CreateSpan<T>(ref array[0, 0], array.Length).Fill(initialValue);return array;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static Span<T> AsSpan<T>(this T[,] array, int i)=> MemoryMarshal.CreateSpan<T>(ref array[i, 0], array.GetLength(1));[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T[,,] Array3<T>(int n1, int n2, int n3, T initialValue)where T : struct=> new T[n1, n2, n3].Fill(initialValue);[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T[,,] Fill<T>(this T[,,] array, T initialValue)where T : struct{MemoryMarshal.CreateSpan<T>(ref array[0, 0, 0], array.Length).Fill(initialValue);return array;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static Span<T> AsSpan<T>(this T[,,] array, int i, int j)=> MemoryMarshal.CreateSpan<T>(ref array[i, j, 0], array.GetLength(2));[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T[,,,] Array4<T>(int n1, int n2, int n3, int n4, T initialValue)where T : struct=> new T[n1, n2, n3, n4].Fill(initialValue);[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T[,,,] Fill<T>(this T[,,,] array, T initialValue)where T : struct{MemoryMarshal.CreateSpan<T>(ref array[0, 0, 0, 0], array.Length).Fill(initialValue);return array;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static Span<T> AsSpan<T>(this T[,,,] array, int i, int j, int k)=> MemoryMarshal.CreateSpan<T>(ref array[i, j, k, 0], array.GetLength(3));private static readonly int[] delta4_ = { 1, 0, -1, 0, 1 };[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void DoIn4(int i, int j, int imax, int jmax, Action<int, int> action){for (int dn = 0; dn < 4; ++dn) {int d4i = i + delta4_[dn];int d4j = j + delta4_[dn + 1];if ((uint)d4i < (uint)imax && (uint)d4j < (uint)jmax) {action(d4i, d4j);}}}private static readonly int[] delta8_ = { 1, 0, -1, 0, 1, 1, -1, -1, 1 };[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void DoIn8(int i, int j, int imax, int jmax, Action<int, int> action){for (int dn = 0; dn < 8; ++dn) {int d8i = i + delta8_[dn];int d8j = j + delta8_[dn + 1];if ((uint)d8i < (uint)imax && (uint)d8j < (uint)jmax) {action(d8i, d8j);}}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void ForEachSubBits(int bit, Action<int> action){for (int sub = bit; sub >= 0; --sub) {sub &= bit;action(sub);}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static string Reverse(string src){var chars = src.ToCharArray();for (int i = 0, j = chars.Length - 1; i < j; ++i, --j) {var tmp = chars[i];chars[i] = chars[j];chars[j] = tmp;}return new string(chars);}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static string Join<T>(this IEnumerable<T> values, string separator = "")=> string.Join(separator, values);[MethodImpl(MethodImplOptions.AggressiveInlining)]public static string JoinNL<T>(this IEnumerable<T> values)=> string.Join(Environment.NewLine, values);}public static class Extensions{public static uint PopCount(uint bits){bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);return (bits & 0x0000ffff) + (bits >> 16 & 0x0000ffff);}public static int PopCount(ulong bits){bits = ((bits & 0xaaaaaaaaaaaaaaaa) >> 1) + (bits & 0x5555555555555555);bits = ((bits & 0xcccccccccccccccc) >> 2) + (bits & 0x3333333333333333);bits = ((bits & 0xf0f0f0f0f0f0f0f0) >> 4) + (bits & 0x0f0f0f0f0f0f0f0f);bits = ((bits & 0xff00ff00ff00ff00) >> 8) + (bits & 0x00ff00ff00ff00ff);bits = ((bits & 0xffff0000ffff0000) >> 16) + (bits & 0x0000ffff0000ffff);bits = ((bits & 0xffffffff00000000) >> 32) + (bits & 0x00000000ffffffff);return (int)bits;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static int PopCount(this BitFlag bit)=> (int)PopCount((uint)bit.Flag);}public class Scanner : IDisposable{private const int BUFFER_SIZE = 1024;private const int ASCII_CHAR_BEGIN = 33;private const int ASCII_CHAR_END = 126;private readonly string filePath_;private readonly Stream stream_;private readonly byte[] buf_ = new byte[BUFFER_SIZE];private int length_ = 0;private int index_ = 0;private bool isEof_ = false;public Scanner(string file = ""){if (string.IsNullOrWhiteSpace(file)) {stream_ = Console.OpenStandardInput();} else {filePath_ = file;stream_ = new FileStream(file, FileMode.Open);}Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false});}public void Dispose(){Console.Out.Flush();stream_.Dispose();}[MethodImpl(MethodImplOptions.AggressiveInlining)]public char Char(){byte b;do {b = Read();} while (b < ASCII_CHAR_BEGIN || ASCII_CHAR_END < b);return (char)b;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public string Next(){var sb = new StringBuilder();for (var b = Char(); b >= ASCII_CHAR_BEGIN && b <= ASCII_CHAR_END; b = (char)Read()) {sb.Append(b);}return sb.ToString();}[MethodImpl(MethodImplOptions.AggressiveInlining)]public string[] ArrayString(int length){var array = new string[length];for (int i = 0; i < length; ++i) {array[i] = Next();}return array;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public int Int() => (int)Long();[MethodImpl(MethodImplOptions.AggressiveInlining)]public int Int(int offset) => Int() + offset;[MethodImpl(MethodImplOptions.AggressiveInlining)]public (int, int) Int2(int offset = 0)=> (Int(offset), Int(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public (int, int, int) Int3(int offset = 0)=> (Int(offset), Int(offset), Int(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public (int, int, int, int) Int4(int offset = 0)=> (Int(offset), Int(offset), Int(offset), Int(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public int[] ArrayInt(int length, int offset = 0){var array = new int[length];for (int i = 0; i < length; ++i) {array[i] = Int(offset);}return array;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public long Long(){long ret = 0;byte b;bool ng = false;do {b = Read();} while (b != '-' && (b < '0' || '9' < b));if (b == '-') {ng = true;b = Read();}for (; true; b = Read()) {if (b < '0' || '9' < b) {return ng ? -ret : ret;} else {ret = ret * 10 + b - '0';}}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public long Long(long offset) => Long() + offset;[MethodImpl(MethodImplOptions.AggressiveInlining)]public (long, long) Long2(long offset = 0)=> (Long(offset), Long(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public (long, long, long) Long3(long offset = 0)=> (Long(offset), Long(offset), Long(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public (long, long, long, long) Long4(long offset = 0)=> (Long(offset), Long(offset), Long(offset), Long(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public long[] ArrayLong(int length, long offset = 0){var array = new long[length];for (int i = 0; i < length; ++i) {array[i] = Long(offset);}return array;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public BigInteger Big() => new BigInteger(Long());[MethodImpl(MethodImplOptions.AggressiveInlining)]public BigInteger Big(long offset) => Big() + offset;[MethodImpl(MethodImplOptions.AggressiveInlining)]public (BigInteger, BigInteger) Big2(long offset = 0)=> (Big(offset), Big(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public (BigInteger, BigInteger, BigInteger) Big3(long offset = 0)=> (Big(offset), Big(offset), Big(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public (BigInteger, BigInteger, BigInteger, BigInteger) Big4(long offset = 0)=> (Big(offset), Big(offset), Big(offset), Big(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public BigInteger[] ArrayBig(int length, long offset = 0){var array = new BigInteger[length];for (int i = 0; i < length; ++i) {array[i] = Big(offset);}return array;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public double Double() => double.Parse(Next(), CultureInfo.InvariantCulture);[MethodImpl(MethodImplOptions.AggressiveInlining)]public double Double(double offset) => Double() + offset;[MethodImpl(MethodImplOptions.AggressiveInlining)]public (double, double) Double2(double offset = 0)=> (Double(offset), Double(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public (double, double, double) Double3(double offset = 0)=> (Double(offset), Double(offset), Double(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public (double, double, double, double) Double4(double offset = 0)=> (Double(offset), Double(offset), Double(offset), Double(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public double[] ArrayDouble(int length, double offset = 0){var array = new double[length];for (int i = 0; i < length; ++i) {array[i] = Double(offset);}return array;}private byte Read(){if (isEof_) {throw new EndOfStreamException();}if (index_ >= length_) {index_ = 0;if ((length_ = stream_.Read(buf_, 0, BUFFER_SIZE)) <= 0) {isEof_ = true;return 0;}}return buf_[index_++];}public void Save(string text){if (string.IsNullOrWhiteSpace(filePath_)) {return;}File.WriteAllText(filePath_ + "_output.txt", text);}}}