結果
問題 | No.2337 Equidistant |
ユーザー |
![]() |
提出日時 | 2023-06-03 12:23:42 |
言語 | C# (.NET 8.0.404) |
結果 |
AC
|
実行時間 | 891 ms / 4,000 ms |
コード長 | 34,253 bytes |
コンパイル時間 | 12,361 ms |
コンパイル使用メモリ | 166,112 KB |
実行使用メモリ | 293,684 KB |
最終ジャッジ日時 | 2024-12-29 02:43:24 |
合計ジャッジ時間 | 29,309 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 1 |
other | AC * 28 |
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 (96 ms)。 MSBuild のバージョン 17.9.6+a4ecab324 (.NET) 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;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{[MethodImpl(MethodImplOptions.AggressiveOptimization)]static void Main(){using var cin = new Scanner();var (n, q) = cin.Int2();var la = new LevelAncestor(n);var edges = new JagList2<int>(n);var ab = new (int a, int b)[n - 1];for (int i = 0; i < n - 1; i++) {var (a, b) = cin.Int2(-1);ab[i] = (a, b);}for (int i = 0; i < n - 1; i++) {var (a, b) = ab[i];la.AddEdge2W(a, b);edges.Add(a, b);edges.Add(b, a);}la.Build();edges.Build();var counts = new int[n];int Dfs(int v, int p){int ret = 1;foreach (var next in edges[v]) {if (next == p) {continue;}ret += Dfs(next, v);}counts[v] = ret;return ret;}Dfs(0, -1);var st = new (int s, int t)[q];for (int i = 0; i < q; i++) {st[i] = cin.Int2(-1);}for (int i = 0; i < q; i++) {var (s, t) = st[i];int lca = la.Lca(s, t);int ds = la.Depth(s);int dt = la.Depth(t);int dc = la.Depth(lca);int ans = 0;int dist = la.Distance(s, t);if (ds == dt) {ans += n - counts[lca];int ss = la.Next(lca, s);int tt = la.Next(lca, t);int temp = counts[lca] - counts[ss] - counts[tt];ans += temp;} else if (dist % 2 == 0) {int v = s;if (dt > ds) {v = t;}int dd = dist / 2;int p = la.Up(v, dd);int w = la.Next(p, v);int temp = counts[p] - counts[w];ans += temp;}Console.WriteLine(ans);}}}public class LevelAncestor{private readonly List<int>[] _edges;private readonly int[,] _parents;private readonly List<List<int>> _lad;private readonly int[] _depth;private readonly int[] _next;private readonly int[] _length;private readonly int[] _path;private readonly int[] _order;private readonly int[] _hs;public LevelAncestor(int n){_edges = new List<int>[n];for (int i = 0; i < n; ++i) {_edges[i] = new List<int>();}_lad = new List<List<int>>();_depth = new int[n];_next = new int[n];_next.AsSpan().Fill(-1);_length = new int[n];_path = new int[n];_order = new int[n];_hs = new int[n + 1];int h = 1;while ((1 << h) <= n) {++h;}_parents = new int[h, n];MemoryMarshal.CreateSpan<int>(ref _parents[0, 0], _parents.Length).Fill(-1);for (int i = 2; i <= n; ++i) {_hs[i] = _hs[i >> 1] + 1;}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public void AddEdge2W(int u, int v){_edges[u].Add(v);_edges[v].Add(u);}[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Dfs(int v, int p, int d, bool isFirst){if (_next[v] < 0) {_next[v] = v;_parents[0, v] = p;_length[v] = d;_depth[v] = d;foreach (int u in _edges[v]) {if (u == p) {continue;}Dfs(u, v, d + 1, false);if (_length[v] < _length[u]) {_next[v] = u;_length[v] = _length[u];}}}if (isFirst == false) {return;}_path[v] = _lad.Count;_lad.Add(new List<int>());for (int k = v; ; k = _next[k]) {_lad[^1].Add(k);_path[k] = _path[v];if (k == _next[k]) {break;}}for (; ; p = v, v = _next[v]) {foreach (var u in _edges[v]) {if (u != p && u != _next[v]) {Dfs(u, v, d + 1, true);}}if (v == _next[v]) {break;}}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Build(int root = 0){int n = _edges.Length;Dfs(root, -1, 0, true);for (int k = 0; k + 1 < _parents.GetLength(0); ++k) {for (int v = 0; v < n; ++v) {if (_parents[k, v] < 0) {_parents[k + 1, v] = -1;} else {_parents[k + 1, v] = _parents[k, _parents[k, v]];}}}for (int i = 0; i < _lad.Count; ++i) {int v = _lad[i][0];int p = _parents[0, v];if (~p != 0) {int k = _path[p];int l = Math.Min(_order[p] + 1, _lad[i].Count);_lad[i].AddRange(Enumerable.Repeat(0, l));for (int j = 0, m = _lad[i].Count; j + l < m; ++j) {_lad[i][m - (j + 1)] = _lad[i][m - (j + l + 1)];}for (int j = 0; j < l; ++j) {_lad[i][j] = _lad[k][_order[p] - l + j + 1];}}for (int j = 0; j < _lad[i].Count; ++j) {if (_path[_lad[i][j]] == i) {_order[_lad[i][j]] = j;}}}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public int Depth(int v) => _depth[v];[MethodImpl(MethodImplOptions.AggressiveInlining)]public int Lca(int u, int v){int h = _parents.GetLength(0);if (_depth[u] > _depth[v]) {(u, v) = (v, u);}for (int k = 0; k < h; ++k) {if (((_depth[v] - _depth[u]) >> k & 1) != 0) {v = _parents[k, v];}}if (u == v) {return u;}for (int k = h - 1; k >= 0; --k) {if (_parents[k, u] == _parents[k, v]) {continue;}u = _parents[k, u];v = _parents[k, v];}return _parents[0, u];}[MethodImpl(MethodImplOptions.AggressiveInlining)]public int Distance(int u, int v) => Distance(u, v, Lca(u, v));[MethodImpl(MethodImplOptions.AggressiveInlining)]private int Distance(int u, int v, int lca){return _depth[u] + _depth[v] - _depth[lca] * 2;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public int Up(int v, int d){if (d == 0) {return v;}v = _parents[_hs[d], v];d -= 1 << _hs[d];return _lad[_path[v]][_order[v] - d];}[MethodImpl(MethodImplOptions.AggressiveInlining)]public int Next(int u, int v){// from u to vif (_depth[u] >= _depth[v]) {return _parents[0, u];}int l = Up(v, _depth[v] - _depth[u] - 1);return _parents[0, l] == u ? l : _parents[0, u];}[MethodImpl(MethodImplOptions.AggressiveInlining)]public int Next(int u, int v, int d){int lca = Lca(u, v);if (Distance(u, v, lca) < d) {return -1;}int du = _depth[u] - _depth[lca];if (du >= d) {return Up(u, d);}d -= du;int dv = _depth[v] - _depth[lca];return Up(v, dv - d);}}public struct BitFlag{public static BitFlag Begin() => 0;public static BitFlag End(int bitCount) => 1 << bitCount;public static BitFlag FromBit(int bitNumber) => 1 << bitNumber;public static BitFlag Fill(int count) => (1 << count) - 1;public static IEnumerable<BitFlag> All(int n){for (var f = Begin(); f < End(n); ++f) {yield return f;}}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 int PopCount() => BitOperations.PopCount((uint)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 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 bit, int shift) => bit.flags_ << shift;public static BitFlag operator >>(BitFlag bit, int shift) => bit.flags_ >> shift;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_})";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 + 1;}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>{public static HashMap<TKey, TValue> Merge(HashMap<TKey, TValue> src1,HashMap<TKey, TValue> src2,Func<TValue, TValue, TValue> mergeValues){if (src1.Count < src2.Count) {(src1, src2) = (src2, src1);}foreach (var key in src2.Keys) {src1[key] = mergeValues(src1[key], src2[key]);}return src1;}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 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 class DijkstraQ{private int count_ = 0;private long[] distanceHeap_;private int[] vertexHeap_;public int Count => count_;public DijkstraQ(){distanceHeap_ = new long[8];vertexHeap_ = new int[8];}[MethodImpl(MethodImplOptions.AggressiveInlining)]public void Enqueue(long distance, int v){if (distanceHeap_.Length == count_) {var newDistanceHeap = new long[distanceHeap_.Length << 1];var newVertexHeap = new int[vertexHeap_.Length << 1];Unsafe.CopyBlock(ref Unsafe.As<long, byte>(ref newDistanceHeap[0]),ref Unsafe.As<long, byte>(ref distanceHeap_[0]),(uint)(8 * count_));Unsafe.CopyBlock(ref Unsafe.As<int, byte>(ref newVertexHeap[0]),ref Unsafe.As<int, byte>(ref vertexHeap_[0]),(uint)(4 * count_));distanceHeap_ = newDistanceHeap;vertexHeap_ = newVertexHeap;}ref var dRef = ref distanceHeap_[0];ref var vRef = ref vertexHeap_[0];Unsafe.Add(ref dRef, count_) = distance;Unsafe.Add(ref vRef, count_) = v;++count_;int c = count_ - 1;while (c > 0) {int p = (c - 1) >> 1;var tempD = Unsafe.Add(ref dRef, p);if (tempD <= distance) {break;} else {Unsafe.Add(ref dRef, c) = tempD;Unsafe.Add(ref vRef, c) = Unsafe.Add(ref vRef, p);c = p;}}Unsafe.Add(ref dRef, c) = distance;Unsafe.Add(ref vRef, c) = v;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public (long distance, int v) Dequeue(){ref var dRef = ref distanceHeap_[0];ref var vRef = ref vertexHeap_[0];(long distance, int v) ret = (dRef, vRef);int n = count_ - 1;var distance = Unsafe.Add(ref dRef, n);var vertex = Unsafe.Add(ref vRef, n);int p = 0;int c = (p << 1) + 1;while (c < n) {if (c != n - 1 && Unsafe.Add(ref dRef, c + 1) < Unsafe.Add(ref dRef, c)) {++c;}var tempD = Unsafe.Add(ref dRef, c);if (distance > tempD) {Unsafe.Add(ref dRef, p) = tempD;Unsafe.Add(ref vRef, p) = Unsafe.Add(ref vRef, c);p = c;c = (p << 1) + 1;} else {break;}}Unsafe.Add(ref dRef, p) = distance;Unsafe.Add(ref vRef, p) = vertex;--count_;return ret;}}public struct ModInt{public const long P = 1000000007;//public const long P = 998244353;//public const long P = 2;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)=> lhs * Inverse(rhs);public static implicit operator ModInt(long n) => new ModInt(n, true);[MethodImpl(MethodImplOptions.AggressiveInlining)]public static ModInt Inverse(ModInt value) => Pow(value, P - 2);[MethodImpl(MethodImplOptions.AggressiveInlining)]public static ModInt Pow(ModInt value, long k) => Pow(value.value_, k);[MethodImpl(MethodImplOptions.AggressiveInlining)]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);}[MethodImpl(MethodImplOptions.AggressiveInlining)]public long ToLong() => value_;public override string ToString() => value_.ToString();}public static class Helper{public static long INF => 1L << 50;[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T Clamp<T>(this T value, T min, T max) where T : struct, IComparable<T>{if (value.CompareTo(min) <= 0) {return min;}if (value.CompareTo(max) >= 0) {return max;}return value;}[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 long BinarySearchOKNG(long ok, long ng, Func<long, bool> satisfies){while (ng - ok > 1) {long mid = (ok + ng) / 2;if (satisfies(mid)) {ok = mid;} else {ng = mid;}}return ok;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static long BinarySearchNGOK(long ng, long ok, Func<long, bool> satisfies){while (ok - ng > 1) {long mid = (ok + ng) / 2;if (satisfies(mid)) {ok = mid;} else {ng = mid;}}return ok;}[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));[MethodImpl(MethodImplOptions.AggressiveInlining)]public static T[] Merge<T>(ReadOnlySpan<T> first, ReadOnlySpan<T> second) where T : IComparable<T>{var ret = new T[first.Length + second.Length];int p = 0;int q = 0;while (p < first.Length || q < second.Length) {if (p == first.Length) {ret[p + q] = second[q];q++;continue;}if (q == second.Length) {ret[p + q] = first[p];p++;continue;}if (first[p].CompareTo(second[q]) < 0) {ret[p + q] = first[p];p++;} else {ret[p + q] = second[q];q++;}}return ret;}private static readonly int[] delta4_ = { 1, 0, -1, 0, 1 };[MethodImpl(MethodImplOptions.AggressiveInlining)]public static IEnumerable<(int i, int j)> Adjacence4(int i, int j, int imax, int jmax){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) {yield return (d4i, d4j);}}}private static readonly int[] delta8_ = { 1, 0, -1, 0, 1, 1, -1, -1, 1 };[MethodImpl(MethodImplOptions.AggressiveInlining)]public static IEnumerable<(int i, int j)> Adjacence8(int i, int j, int imax, int jmax){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) {yield return (d8i, d8j);}}}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static IEnumerable<int> SubBitsOf(int bit){for (int sub = bit; sub > 0; sub = --sub & bit) {yield return 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 Exchange(string src, char a, char b){var chars = src.ToCharArray();for (int i = 0; i < chars.Length; i++) {if (chars[i] == a) {chars[i] = b;} else if (chars[i] == b) {chars[i] = a;}}return new string(chars);}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static void Swap(this string str, int i, int j){var span = str.AsWriteableSpan();(span[i], span[j]) = (span[j], span[i]);}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static char Replace(this string str, int index, char c){var span = str.AsWriteableSpan();char old = span[index];span[index] = c;return old;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public static Span<char> AsWriteableSpan(this string str){var span = str.AsSpan();return MemoryMarshal.CreateSpan(ref MemoryMarshal.GetReference(span), span.Length);}[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{[MethodImpl(MethodImplOptions.AggressiveInlining)]public static Span<T> AsSpan<T>(this List<T> list){return Unsafe.As<FakeList<T>>(list).Array.AsSpan(0, list.Count);}private class FakeList<T>{public T[] Array = null;}}public class Scanner : IDisposable{private const int BUFFER_SIZE = 1024;private const int ASCII_SPACE = 32;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 string NextLine(){var sb = new StringBuilder();for (var b = Char(); b >= ASCII_SPACE && b <= ASCII_CHAR_END; b = (char)Read()) {sb.Append(b);}return sb.ToString();}[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 String(){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] = String();}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, int, int, int, int) Int5(int offset = 0)=> (Int(offset), 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, long, long, long, long) Long5(long offset = 0)=> (Long(offset), 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, BigInteger, BigInteger, BigInteger, BigInteger) Big5(long offset = 0)=> (Big(offset), 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(String(), 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, double, double, double, double) Double5(double offset = 0)=> (Double(offset), 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;}[MethodImpl(MethodImplOptions.AggressiveInlining)]public decimal Decimal() => decimal.Parse(String(), CultureInfo.InvariantCulture);[MethodImpl(MethodImplOptions.AggressiveInlining)]public decimal Decimal(decimal offset) => Decimal() + offset;[MethodImpl(MethodImplOptions.AggressiveInlining)]public (decimal, decimal) Decimal2(decimal offset = 0)=> (Decimal(offset), Decimal(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public (decimal, decimal, decimal) Decimal3(decimal offset = 0)=> (Decimal(offset), Decimal(offset), Decimal(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public (decimal, decimal, decimal, decimal) Decimal4(decimal offset = 0)=> (Decimal(offset), Decimal(offset), Decimal(offset), Decimal(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public (decimal, decimal, decimal, decimal, decimal) Decimal5(decimal offset = 0)=> (Decimal(offset), Decimal(offset), Decimal(offset), Decimal(offset), Decimal(offset));[MethodImpl(MethodImplOptions.AggressiveInlining)]public decimal[] ArrayDecimal(int length, decimal offset = 0){var array = new decimal[length];for (int i = 0; i < length; ++i) {array[i] = Decimal(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);}}}