結果
| 問題 | No.5007 Steiner Space Travel |
| ユーザー |
 yupiteru_kun
|
| 提出日時 | 2022-07-30 17:52:07 |
| 言語 | C# (.NET 8.0.203) |
| 結果 |
AC
|
| 実行時間 | 954 ms / 1,000 ms |
| コード長 | 39,641 bytes |
| コンパイル時間 | 8,144 ms |
| 実行使用メモリ | 178,456 KB |
| スコア | 7,934,965 |
| 最終ジャッジ日時 | 2022-07-30 17:52:49 |
| 合計ジャッジ時間 | 39,102 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge10 |
| 純コード判定しない問題か言語 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 945 ms
42,200 KB |
| testcase_01 | AC | 922 ms
43,020 KB |
| testcase_02 | AC | 915 ms
42,336 KB |
| testcase_03 | AC | 950 ms
42,944 KB |
| testcase_04 | AC | 923 ms
42,668 KB |
| testcase_05 | AC | 943 ms
44,484 KB |
| testcase_06 | AC | 917 ms
42,864 KB |
| testcase_07 | AC | 922 ms
43,232 KB |
| testcase_08 | AC | 954 ms
42,952 KB |
| testcase_09 | AC | 919 ms
42,432 KB |
| testcase_10 | AC | 932 ms
42,832 KB |
| testcase_11 | AC | 923 ms
44,808 KB |
| testcase_12 | AC | 919 ms
43,036 KB |
| testcase_13 | AC | 941 ms
43,012 KB |
| testcase_14 | AC | 916 ms
43,792 KB |
| testcase_15 | AC | 946 ms
42,120 KB |
| testcase_16 | AC | 920 ms
42,904 KB |
| testcase_17 | AC | 936 ms
43,012 KB |
| testcase_18 | AC | 941 ms
42,756 KB |
| testcase_19 | AC | 921 ms
42,468 KB |
| testcase_20 | AC | 932 ms
42,248 KB |
| testcase_21 | AC | 933 ms
42,700 KB |
| testcase_22 | AC | 922 ms
44,200 KB |
| testcase_23 | AC | 931 ms
42,924 KB |
| testcase_24 | AC | 918 ms
42,672 KB |
| testcase_25 | AC | 936 ms
43,268 KB |
| testcase_26 | AC | 921 ms
42,284 KB |
| testcase_27 | AC | 928 ms
42,824 KB |
| testcase_28 | AC | 925 ms
42,840 KB |
| testcase_29 | AC | 915 ms
178,456 KB |
コンパイルメッセージ
Determining projects to restore... Restored /home/judge/data/code/main.csproj (in 129 ms). .NET 向け Microsoft (R) Build Engine バージョン 17.0.0-preview-21470-01+cb055d28f Copyright (C) Microsoft Corporation.All rights reserved. プレビュー版の .NET を使用しています。https://aka.ms/dotnet-core-preview をご覧ください main -> /home/judge/data/code/bin/Release/net6.0/main.dll main -> /home/judge/data/code/bin/Release/net6.0/publish/
ソースコード
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
using System.Globalization;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using Library;
namespace Program
{
public static class ProblemA
{
static bool SAIKI = false;
static public int numberOfRandomCases = 0;
static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
{
}
static int A = 5;
static int N = 5;
static int M = 5;
static int TAYOU = 4;
static public long Func1((int x, int y)[] ab, List<(int from, int to, int keiyu)> pathList)
{
var startTime = DateTime.Now;
Func<int, int, long> calcDist = (f, t) =>
{
var fromX = 0;
var fromY = 0;
var toX = 0;
var toY = 0;
var fromCoef = 1L;
var toCoef = 1L;
fromX = ab[f - 1].x;
fromY = ab[f - 1].y;
if (f <= N)
{
fromCoef = A;
}
toX = ab[t - 1].x;
toY = ab[t - 1].y;
if (t <= N)
{
toCoef = A;
}
return fromCoef * toCoef * ((fromX - toX) * (fromX - toX) + (fromY - toY) * (fromY - toY));
};
var score = 0L;
{
var done = new bool[N + 1];
var from = 1;
done[from] = true;
for (var i = 1; i < N; ++i)
{
var kouho = new LIB_PriorityQueue();
for (var j = 1; j <= N; ++j)
{
if (done[j]) continue;
kouho.Push(-calcDist(from, j), j);
if (kouho.Count > TAYOU) kouho.Pop();
}
var kouhoList = new List<int>();
while (kouho.Count > 0) kouhoList.Add(kouho.Pop().Value);
var minNum = kouhoList[(int)(xorshift % kouhoList.Count)];
score += calcDist(from, minNum);
pathList.Add((from, minNum, -1));
from = minNum;
done[from] = true;
}
score += calcDist(from, 1);
pathList.Add((from, 1, -1));
}
var hasEdge = ab.Select(_ =>
{
var ret = new int[2];
ret[0] = ret[1] = -1;
return ret;
}).ToArray();
for (var i = 0; i < pathList.Count; ++i)
{
if (hasEdge[pathList[i].from - 1][0] == -1) hasEdge[pathList[i].from - 1][0] = i;
else hasEdge[pathList[i].from - 1][1] = i;
if (hasEdge[pathList[i].to - 1][0] == -1) hasEdge[pathList[i].to - 1][0] = i;
else hasEdge[pathList[i].to - 1][1] = i;
}
while ((DateTime.Now - startTime).TotalMilliseconds < 170)
{
var p1 = (int)(xorshift % pathList.Count);
var p2 = (int)(xorshift % (pathList.Count - 1));
if (p2 >= p1) ++p2;
if (pathList[p1].from == pathList[p2].from || pathList[p1].from == pathList[p2].to ||
pathList[p1].to == pathList[p2].from || pathList[p1].to == pathList[p2].to)
{
continue;
}
var goal = 0;
{
var from = pathList[p1].from;
goal = pathList[p1].to;
while (true)
{
if (goal == pathList[p2].from || goal == pathList[p2].to) break;
var to = 0;
var pos1 = pathList[hasEdge[goal - 1][0]];
var pos2 = pathList[hasEdge[goal - 1][1]];
if (pos1.from == from || pos1.to == from)
{
if (pos2.from == goal) to = pos2.to;
else to = pos2.from;
}
else
{
if (pos1.from == goal) to = pos1.to;
else to = pos1.from;
}
from = goal;
goal = to;
}
}
var newScore = score;
newScore -= calcDist(pathList[p1].from, pathList[p1].to);
newScore -= calcDist(pathList[p2].from, pathList[p2].to);
if (goal == pathList[p2].from)
{
newScore += calcDist(pathList[p1].from, pathList[p2].from);
newScore += calcDist(pathList[p2].to, pathList[p1].to);
if (newScore < score)
{
score = newScore;
if (hasEdge[pathList[p1].to - 1][0] == p1)
{
hasEdge[pathList[p1].to - 1][0] = p2;
}
else
{
hasEdge[pathList[p1].to - 1][1] = p2;
}
if (hasEdge[pathList[p2].from - 1][0] == p2)
{
hasEdge[pathList[p2].from - 1][0] = p1;
}
else
{
hasEdge[pathList[p2].from - 1][1] = p1;
}
var newp1 = (pathList[p1].from, pathList[p2].from, -1);
var newp2 = (pathList[p2].to, pathList[p1].to, -1);
pathList[p1] = newp1;
pathList[p2] = newp2;
}
}
else
{
newScore += calcDist(pathList[p1].from, pathList[p2].to);
newScore += calcDist(pathList[p2].from, pathList[p1].to);
if (newScore < score)
{
score = newScore;
if (hasEdge[pathList[p1].to - 1][0] == p1)
{
hasEdge[pathList[p1].to - 1][0] = p2;
}
else
{
hasEdge[pathList[p1].to - 1][1] = p2;
}
if (hasEdge[pathList[p2].to - 1][0] == p2)
{
hasEdge[pathList[p2].to - 1][0] = p1;
}
else
{
hasEdge[pathList[p2].to - 1][1] = p1;
}
var newp1 = (pathList[p1].from, pathList[p2].to, -1);
var newp2 = (pathList[p2].from, pathList[p1].to, -1);
pathList[p1] = newp1;
pathList[p2] = newp2;
}
}
}
var addedNum = 0;
{
var maxKaizen = 0L;
var maxNum = 0;
for (var i = 0; i < pathList.Count; ++i)
{
var thisKaizen = calcDist(pathList[i].from, pathList[i].to) - calcDist(pathList[i].from, pathList[i].to) / 25;
ab[N] = ab[pathList[i].from - 1];
ab[N + 1] = ab[pathList[i].to - 1];
for (var j = 0; j < pathList.Count; ++j)
{
if (i == j) continue;
var item = pathList[j];
var kijunDist = calcDist(item.from, item.to);
var newDist1 = calcDist(item.from, N + 1) + calcDist(N + 1, item.to);
var newDist2 = calcDist(item.from, N + 2) + calcDist(N + 2, item.to);
thisKaizen += Max(0, kijunDist - Min(newDist1, newDist2));
}
if (maxKaizen.Chmax(thisKaizen)) maxNum = i;
}
ab[N] = ab[pathList[maxNum].from - 1];
ab[N + 1] = ab[pathList[maxNum].to - 1];
score -= calcDist(pathList[maxNum].from, pathList[maxNum].to);
score += calcDist(N + 1, N + 2);
var newForFrom = pathList.Count;
pathList.Add((pathList[maxNum].from, N + 1, -1));
var newForTo = pathList.Count;
pathList.Add((pathList[maxNum].to, N + 2, -1));
if (hasEdge[pathList[maxNum].from - 1][0] == maxNum) hasEdge[pathList[maxNum].from - 1][0] = newForFrom;
else hasEdge[pathList[maxNum].from - 1][1] = newForFrom;
if (hasEdge[pathList[maxNum].to - 1][0] == maxNum) hasEdge[pathList[maxNum].to - 1][0] = newForTo;
else hasEdge[pathList[maxNum].to - 1][1] = newForTo;
hasEdge[N + 0][0] = newForFrom;
hasEdge[N + 1][0] = newForTo;
hasEdge[N + 0][1] = maxNum;
hasEdge[N + 1][1] = maxNum;
pathList[maxNum] = (N + 1, N + 2, -1);
addedNum += 2;
}
{
var kouho = new List<(long kaizen, int x, int y)>();
for (var i = 0; i <= 1000; i += 20)
{
for (var j = 0; j <= 1000; j += 20)
{
ab[N + addedNum] = (i, j);
var sum = 0L;
foreach (var item in pathList)
{
var kijunDist = calcDist(item.from, item.to);
var newDist = calcDist(item.from, N + addedNum + 1) + calcDist(N + addedNum + 1, item.to);
sum += Max(0, kijunDist - newDist);
}
if (sum > 0) kouho.Add((sum, i, j));
}
}
{
var sum = 0L;
foreach (var item in pathList)
{
var kijunDist = calcDist(item.from, item.to);
var newDist = calcDist(item.from, N + 1) + calcDist(N + 1, item.to);
sum += Max(0, kijunDist - newDist);
}
if (sum > 0) kouho.Add((sum, -1, -1));
}
{
var sum = 0L;
foreach (var item in pathList)
{
var kijunDist = calcDist(item.from, item.to);
var newDist = calcDist(item.from, N + 2) + calcDist(N + 2, item.to);
sum += Max(0, kijunDist - newDist);
}
if (sum > 0) kouho.Add((sum, -2, -2));
}
kouho = kouho.OrderByDescending(e => e.kaizen).ToList();
foreach (var item2 in kouho)
{
var staNum = addedNum + N + 1;
if (item2.x < 0)
{
staNum = -item2.x + N;
}
else
{
staNum = addedNum + N + 1;
ab[staNum - 1] = (item2.x, item2.y);
}
var sum = 0L;
foreach (var item in pathList)
{
if (item.keiyu != -1) continue;
var kijunDist = calcDist(item.from, item.to);
var newDist = calcDist(item.from, staNum) + calcDist(staNum, item.to);
sum += Max(0, kijunDist - newDist);
}
if (sum >= item2.kaizen * 9 / 10 && sum > 0)
{
for (var i = 0; i < pathList.Count; ++i)
{
var item = pathList[i];
if (item.keiyu != -1) continue;
var kijunDist = calcDist(item.from, item.to);
var newDist = calcDist(item.from, staNum) + calcDist(staNum, item.to);
var thisKaizen = kijunDist - newDist;
if (thisKaizen > 0)
{
score -= thisKaizen;
pathList[i] = (item.from, item.to, staNum);
}
}
if (item2.x >= 0) ++addedNum;
}
if (addedNum == M) break;
}
}
return score;
}
static public long Func2((int x, int y)[] ab, List<(int from, int to, int keiyu)> pathList)
{
var startTime = DateTime.Now;
Func<int, int, long> calcDist = (f, t) =>
{
var fromX = 0;
var fromY = 0;
var toX = 0;
var toY = 0;
var fromCoef = 1L;
var toCoef = 1L;
fromX = ab[f - 1].x;
fromY = ab[f - 1].y;
if (f <= N)
{
fromCoef = A;
}
toX = ab[t - 1].x;
toY = ab[t - 1].y;
if (t <= N)
{
toCoef = A;
}
return fromCoef * toCoef * ((fromX - toX) * (fromX - toX) + (fromY - toY) * (fromY - toY));
};
var score = 0L;
{
var done = new bool[N + 1];
var from = 1;
done[from] = true;
for (var i = 1; i < N; ++i)
{
var kouho = new LIB_PriorityQueue();
for (var j = 1; j <= N; ++j)
{
if (done[j]) continue;
kouho.Push(-calcDist(from, j), j);
if (kouho.Count > TAYOU) kouho.Pop();
}
var kouhoList = new List<int>();
while (kouho.Count > 0) kouhoList.Add(kouho.Pop().Value);
var minNum = kouhoList[(int)(xorshift % kouhoList.Count)];
score += calcDist(from, minNum);
pathList.Add((from, minNum, -1));
from = minNum;
done[from] = true;
}
score += calcDist(from, 1);
pathList.Add((from, 1, -1));
}
var hasEdge = ab.Select(_ =>
{
var ret = new int[2];
ret[0] = ret[1] = -1;
return ret;
}).ToArray();
for (var i = 0; i < pathList.Count; ++i)
{
if (hasEdge[pathList[i].from - 1][0] == -1) hasEdge[pathList[i].from - 1][0] = i;
else hasEdge[pathList[i].from - 1][1] = i;
if (hasEdge[pathList[i].to - 1][0] == -1) hasEdge[pathList[i].to - 1][0] = i;
else hasEdge[pathList[i].to - 1][1] = i;
}
while ((DateTime.Now - startTime).TotalMilliseconds < 170)
{
var p1 = (int)(xorshift % pathList.Count);
var p2 = (int)(xorshift % (pathList.Count - 1));
if (p2 >= p1) ++p2;
if (pathList[p1].from == pathList[p2].from || pathList[p1].from == pathList[p2].to ||
pathList[p1].to == pathList[p2].from || pathList[p1].to == pathList[p2].to)
{
continue;
}
var goal = 0;
{
var from = pathList[p1].from;
goal = pathList[p1].to;
while (true)
{
if (goal == pathList[p2].from || goal == pathList[p2].to) break;
var to = 0;
var pos1 = pathList[hasEdge[goal - 1][0]];
var pos2 = pathList[hasEdge[goal - 1][1]];
if (pos1.from == from || pos1.to == from)
{
if (pos2.from == goal) to = pos2.to;
else to = pos2.from;
}
else
{
if (pos1.from == goal) to = pos1.to;
else to = pos1.from;
}
from = goal;
goal = to;
}
}
var newScore = score;
newScore -= calcDist(pathList[p1].from, pathList[p1].to);
newScore -= calcDist(pathList[p2].from, pathList[p2].to);
if (goal == pathList[p2].from)
{
newScore += calcDist(pathList[p1].from, pathList[p2].from);
newScore += calcDist(pathList[p2].to, pathList[p1].to);
if (newScore < score)
{
score = newScore;
if (hasEdge[pathList[p1].to - 1][0] == p1)
{
hasEdge[pathList[p1].to - 1][0] = p2;
}
else
{
hasEdge[pathList[p1].to - 1][1] = p2;
}
if (hasEdge[pathList[p2].from - 1][0] == p2)
{
hasEdge[pathList[p2].from - 1][0] = p1;
}
else
{
hasEdge[pathList[p2].from - 1][1] = p1;
}
var newp1 = (pathList[p1].from, pathList[p2].from, -1);
var newp2 = (pathList[p2].to, pathList[p1].to, -1);
pathList[p1] = newp1;
pathList[p2] = newp2;
}
}
else
{
newScore += calcDist(pathList[p1].from, pathList[p2].to);
newScore += calcDist(pathList[p2].from, pathList[p1].to);
if (newScore < score)
{
score = newScore;
if (hasEdge[pathList[p1].to - 1][0] == p1)
{
hasEdge[pathList[p1].to - 1][0] = p2;
}
else
{
hasEdge[pathList[p1].to - 1][1] = p2;
}
if (hasEdge[pathList[p2].to - 1][0] == p2)
{
hasEdge[pathList[p2].to - 1][0] = p1;
}
else
{
hasEdge[pathList[p2].to - 1][1] = p1;
}
var newp1 = (pathList[p1].from, pathList[p2].to, -1);
var newp2 = (pathList[p2].from, pathList[p1].to, -1);
pathList[p1] = newp1;
pathList[p2] = newp2;
}
}
}
var addedNum = 0;
{
var kouho = new List<(long kaizen, int x, int y)>();
for (var i = 0; i <= 1000; i += 20)
{
for (var j = 0; j <= 1000; j += 20)
{
ab[N + addedNum] = (i, j);
var sum = 0L;
foreach (var item in pathList)
{
var kijunDist = calcDist(item.from, item.to);
var newDist = calcDist(item.from, N + addedNum + 1) + calcDist(N + addedNum + 1, item.to);
sum += Max(0, kijunDist - newDist);
}
if (sum > 0) kouho.Add((sum, i, j));
}
}
kouho = kouho.OrderByDescending(e => e.kaizen).ToList();
foreach (var item2 in kouho)
{
var staNum = addedNum + N + 1;
ab[staNum - 1] = (item2.x, item2.y);
var sum = 0L;
foreach (var item in pathList)
{
if (item.keiyu != -1) continue;
var kijunDist = calcDist(item.from, item.to);
var newDist = calcDist(item.from, staNum) + calcDist(staNum, item.to);
sum += Max(0, kijunDist - newDist);
}
if (sum >= item2.kaizen * 9 / 10 && sum > 0)
{
for (var i = 0; i < pathList.Count; ++i)
{
var item = pathList[i];
if (item.keiyu != -1) continue;
var kijunDist = calcDist(item.from, item.to);
var newDist = calcDist(item.from, staNum) + calcDist(staNum, item.to);
var thisKaizen = kijunDist - newDist;
if (thisKaizen > 0)
{
score -= thisKaizen;
pathList[i] = (item.from, item.to, staNum);
}
}
++addedNum;
}
if (addedNum == M) break;
}
}
return score;
}
static public void Solve()
{
N = (int)NN;
M = (int)NN;
(int x, int y)[] ab = Repeat(0, N).Select(_ => ((int)NN, (int)NN)).Concat(Repeat(0, M).Select(_ => (0, 0))).ToArray();
var pathList = new List<(int from, int to, int keiyu)>();
var ab1 = ab.ToArray();
var pathList1 = new List<(int from, int to, int keiyu)>();
var ab2 = ab.ToArray();
var pathList2 = new List<(int from, int to, int keiyu)>();
var ab3 = ab.ToArray();
var pathList3 = new List<(int from, int to, int keiyu)>();
var score1 = Func1(ab1, pathList1);
var score2 = Func2(ab2, pathList2);
var score3 = Func2(ab3, pathList3);
var max = Min(score1, Min(score2, score3));
if (max == score1)
{
ab = ab1;
pathList = pathList1;
}
else if (max == score2)
{
ab = ab2;
pathList = pathList2;
}
else
{
ab = ab3;
pathList = pathList3;
}
{
var hasEdge = ab.Select(_ =>
{
var ret = new int[2];
ret[0] = ret[1] = -1;
return ret;
}).ToArray();
for (var i = 0; i < pathList.Count; ++i)
{
if (hasEdge[pathList[i].from - 1][0] == -1) hasEdge[pathList[i].from - 1][0] = i;
else hasEdge[pathList[i].from - 1][1] = i;
if (hasEdge[pathList[i].to - 1][0] == -1) hasEdge[pathList[i].to - 1][0] = i;
else hasEdge[pathList[i].to - 1][1] = i;
}
for (var i = 0; i < M; ++i)
{
Console.WriteLine($"{ab[i + N].x} {ab[i + N].y}");
}
var ansList = new List<string>();
var from = -1;
var now = 1;
ansList.Add($"1 1");
for (var i = 0; i < pathList.Count; ++i)
{
var to = 0;
var p1 = pathList[hasEdge[now - 1][0]];
var p2 = pathList[hasEdge[now - 1][1]];
var keiyu = -1;
if (p1.from == from || p1.to == from)
{
if (p2.from == now) to = p2.to;
else to = p2.from;
keiyu = p2.keiyu;
}
else
{
if (p1.from == now) to = p1.to;
else to = p1.from;
keiyu = p1.keiyu;
}
from = now;
now = to;
if (keiyu != -1) ansList.Add($"2 {keiyu - N}");
if (now > N) ansList.Add($"2 {now - N}");
else ansList.Add($"1 {now}");
}
Console.WriteLine(ansList.Count);
foreach (var item in ansList)
{
Console.WriteLine(item);
}
}
}
class Printer : StreamWriter
{
public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }
public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }
}
static LIB_FastIO fastio = new LIB_FastIODebug();
static public void Main(string[] args) { if (args.Length == 0) { fastio = new LIB_FastIO(); Console.SetOut(new Printer(Console.OpenStandardOutput())); } if (SAIKI) { var t = new Thread(Solve, 134217728); t.Start(); t.Join(); } else Solve(); Console.Out.Flush(); }
static long NN => fastio.Long();
static double ND => fastio.Double();
static string NS => fastio.Scan();
static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
static IOrderedEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x, _ => xorshift);
static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x.OrderByRand(), e => e);
static IOrderedEnumerable<T1> OrderBy<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderBy(x.OrderByRand(), selector);
static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x) => Enumerable.OrderByDescending(x.OrderByRand(), e => e);
static IOrderedEnumerable<T1> OrderByDescending<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderByDescending(x.OrderByRand(), selector);
static IOrderedEnumerable<string> OrderBy(this IEnumerable<string> x) => x.OrderByRand().OrderBy(e => e, StringComparer.OrdinalIgnoreCase);
static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderBy(selector, StringComparer.OrdinalIgnoreCase);
static IOrderedEnumerable<string> OrderByDescending(this IEnumerable<string> x) => x.OrderByRand().OrderByDescending(e => e, StringComparer.OrdinalIgnoreCase);
static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderByDescending(selector, StringComparer.OrdinalIgnoreCase);
static string Join<T>(this IEnumerable<T> x, string separator = "") => string.Join(separator, x);
static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
static IEnumerator<uint> _xsi = _xsc();
static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
static bool Chmax<T>(this ref T lhs, T rhs) where T : struct, IComparable<T> { if (lhs.CompareTo(rhs) < 0) { lhs = rhs; return true; } return false; }
static bool Chmin<T>(this ref T lhs, T rhs) where T : struct, IComparable<T> { if (lhs.CompareTo(rhs) > 0) { lhs = rhs; return true; } return false; }
static void Fill<T>(this T[] array, T value) => array.AsSpan().Fill(value);
static void Fill<T>(this T[,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0], array.Length).Fill(value);
static void Fill<T>(this T[,,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0, 0], array.Length).Fill(value);
static void Fill<T>(this T[,,,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0, 0, 0], array.Length).Fill(value);
}
}
namespace Library {
class LIB_FastIO
{
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public LIB_FastIO() { str = Console.OpenStandardInput(); }
readonly Stream str;
readonly byte[] buf = new byte[2048];
int len, ptr;
[MethodImpl(MethodImplOptions.AggressiveInlining)]
byte read()
{
if (ptr >= len)
{
ptr = 0;
if ((len = str.Read(buf, 0, 2048)) <= 0)
{
return 0;
}
}
return buf[ptr++];
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
char Char()
{
byte b = 0;
do b = read();
while (b < 33 || 126 < b);
return (char)b;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
virtual public string Scan()
{
var sb = new StringBuilder();
for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
sb.Append(b);
return sb.ToString();
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
virtual public long Long()
{
long ret = 0; byte b = 0; var 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 << 3) + (ret << 1) + b - '0';
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
virtual public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
}
class LIB_FastIODebug : LIB_FastIO
{
Queue<string> param = new Queue<string>();
[MethodImpl(MethodImplOptions.AggressiveInlining)]
string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public LIB_FastIODebug() { }
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public override string Scan() => NextString();
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public override long Long() => long.Parse(NextString());
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public override double Double() => double.Parse(NextString());
}
class LIB_PriorityQueue
{
long[] heap;
int[] dat;
public (long Key, int Value) Peek => (heap[0], dat[0]);
public long Count
{
get;
private set;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public LIB_PriorityQueue()
{
heap = new long[8];
dat = new int[8];
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Push(long key) => Push(key, 0);
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Push(long key, int val)
{
if (Count == heap.Length) Expand();
var i = (int)Count++;
ref long heapref = ref heap[0];
ref int datref = ref dat[0];
Unsafe.Add<long>(ref heapref, i) = key;
Unsafe.Add<int>(ref datref, i) = val;
while (i > 0)
{
var ni = (i - 1) / 2;
var heapni = Unsafe.Add<long>(ref heapref, ni);
if (key >= heapni) break;
Unsafe.Add<long>(ref heapref, i) = heapni;
Unsafe.Add<int>(ref datref, i) = Unsafe.Add<int>(ref datref, ni);
i = ni;
}
Unsafe.Add<long>(ref heapref, i) = key;
Unsafe.Add<int>(ref datref, i) = val;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public (long Key, int Value) Pop()
{
ref long heapref = ref heap[0];
ref int datref = ref dat[0];
var ret = (heapref, datref);
var cnt = (int)(--Count);
var key = Unsafe.Add<long>(ref heapref, cnt);
var val = Unsafe.Add<int>(ref datref, cnt);
if (cnt == 0) return ret;
var i = 0; while ((i << 1) + 1 < cnt)
{
var i1 = (i << 1) + 1;
var i2 = (i << 1) + 2;
if (i2 < cnt && Unsafe.Add<long>(ref heapref, i1) > Unsafe.Add<long>(ref heapref, i2)) i1 = i2;
var heapi1 = Unsafe.Add<long>(ref heapref, i1);
if (key <= heapi1) break;
Unsafe.Add<long>(ref heapref, i) = heapi1;
Unsafe.Add<int>(ref datref, i) = Unsafe.Add<int>(ref datref, i1);
i = i1;
}
Unsafe.Add<long>(ref heapref, i) = key;
Unsafe.Add<int>(ref datref, i) = val;
return ret;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
void Expand()
{
var len = heap.Length;
var tmp = new long[len << 1];
var tmp2 = new int[len << 1];
Unsafe.CopyBlock(ref Unsafe.As<long, byte>(ref tmp[0]), ref Unsafe.As<long, byte>(ref heap[0]), (uint)(8 * len));
Unsafe.CopyBlock(ref Unsafe.As<int, byte>(ref tmp2[0]), ref Unsafe.As<int, byte>(ref dat[0]), (uint)(4 * len));
heap = tmp;
dat = tmp2;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public (long Key, int Value)[] NoSortList()
{
var ret = new (long Key, int Value)[Count];
ref long heapref = ref heap[0];
ref int datref = ref dat[0];
for (var i = 0; i < Count; ++i)
{
ret[i] = (Unsafe.Add<long>(ref heapref, i), Unsafe.Add<int>(ref datref, i));
}
return ret;
}
}
class LIB_PriorityQueue<T>
{
T[] heap;
Comparison<T> comp;
public T Peek => heap[0];
public long Count
{
get;
private set;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public LIB_PriorityQueue(long cap, Comparison<T> cmp, bool asc = true)
{
heap = new T[cap];
comp = asc ? cmp : (x, y) => cmp(y, x);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public LIB_PriorityQueue(Comparison<T> cmp, bool asc = true)
{
heap = new T[8];
comp = asc ? cmp : (x, y) => cmp(y, x);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public LIB_PriorityQueue(long cap, bool asc = true) : this(cap, Comparer<T>.Default.Compare, asc) { }
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public LIB_PriorityQueue(bool asc = true) : this(Comparer<T>.Default.Compare, asc) { }
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Push(T val)
{
if (Count == heap.Length) Expand();
var i = Count++;
heap[i] = val;
while (i > 0)
{
var ni = (i - 1) / 2;
if (comp(val, heap[ni]) >= 0) break;
heap[i] = heap[ni];
i = ni;
}
heap[i] = val;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public T Pop()
{
var ret = heap[0];
var val = heap[--Count];
if (Count == 0) return ret;
var i = 0; while ((i << 1) + 1 < Count)
{
var i1 = (i << 1) + 1;
var i2 = (i << 1) + 2;
if (i2 < Count && comp(heap[i1], heap[i2]) > 0) i1 = i2;
if (comp(val, heap[i1]) <= 0) break;
heap[i] = heap[i1]; i = i1;
}
heap[i] = val;
return ret;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
void Expand()
{
var tmp = new T[Count << 1];
for (var i = 0; i < heap.Length; ++i) tmp[i] = heap[i];
heap = tmp;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public T[] NoSortList()
{
var ret = new List<T>();
for (var i = 0; i < Count; ++i)
{
ret.Add(heap[i]);
}
return ret.ToArray();
}
}
class LIB_PriorityQueue<TK, TV>
{
LIB_PriorityQueue<KeyValuePair<TK, TV>> q;
public KeyValuePair<TK, TV> Peek => q.Peek;
public long Count => q.Count;
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public LIB_PriorityQueue(long cap, Comparison<TK> cmp, bool asc = true)
{
q = new LIB_PriorityQueue<KeyValuePair<TK, TV>>(cap, (x, y) => cmp(x.Key, y.Key), asc);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public LIB_PriorityQueue(Comparison<TK> cmp, bool asc = true)
{
q = new LIB_PriorityQueue<KeyValuePair<TK, TV>>((x, y) => cmp(x.Key, y.Key), asc);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public LIB_PriorityQueue(long cap, bool asc = true) : this(cap, Comparer<TK>.Default.Compare, asc) { }
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public LIB_PriorityQueue(bool asc = true) : this(Comparer<TK>.Default.Compare, asc) { }
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Push(TK k, TV v) => q.Push(new KeyValuePair<TK, TV>(k, v));
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public KeyValuePair<TK, TV> Pop() => q.Pop();
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public KeyValuePair<TK, TV>[] NoSortList() => q.NoSortList();
}
}