結果

問題 No.1483 Many Graph in Namori
ユーザー uwiuwi
提出日時 2021-04-18 15:44:12
言語 Java21
(openjdk 21)
結果
AC  
実行時間 569 ms / 2,000 ms
コード長 22,491 bytes
コンパイル時間 6,345 ms
コンパイル使用メモリ 88,816 KB
実行使用メモリ 81,300 KB
最終ジャッジ日時 2023-09-17 07:47:27
合計ジャッジ時間 28,974 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge13
このコードへのチャレンジ
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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 70 ms
50,208 KB
testcase_01 AC 70 ms
50,452 KB
testcase_02 AC 69 ms
50,248 KB
testcase_03 AC 68 ms
50,380 KB
testcase_04 AC 69 ms
50,492 KB
testcase_05 AC 69 ms
50,468 KB
testcase_06 AC 69 ms
50,504 KB
testcase_07 AC 69 ms
50,292 KB
testcase_08 AC 70 ms
50,452 KB
testcase_09 AC 70 ms
50,692 KB
testcase_10 AC 409 ms
71,392 KB
testcase_11 AC 262 ms
62,936 KB
testcase_12 AC 305 ms
65,772 KB
testcase_13 AC 275 ms
63,164 KB
testcase_14 AC 310 ms
65,876 KB
testcase_15 AC 429 ms
76,320 KB
testcase_16 AC 261 ms
62,864 KB
testcase_17 AC 156 ms
57,468 KB
testcase_18 AC 355 ms
65,044 KB
testcase_19 AC 324 ms
65,616 KB
testcase_20 AC 253 ms
62,916 KB
testcase_21 AC 175 ms
58,012 KB
testcase_22 AC 381 ms
65,320 KB
testcase_23 AC 417 ms
71,760 KB
testcase_24 AC 250 ms
62,696 KB
testcase_25 AC 268 ms
62,816 KB
testcase_26 AC 489 ms
76,340 KB
testcase_27 AC 463 ms
76,108 KB
testcase_28 AC 179 ms
57,900 KB
testcase_29 AC 285 ms
63,196 KB
testcase_30 AC 501 ms
77,312 KB
testcase_31 AC 505 ms
78,184 KB
testcase_32 AC 491 ms
76,780 KB
testcase_33 AC 506 ms
77,556 KB
testcase_34 AC 522 ms
77,492 KB
testcase_35 AC 272 ms
65,476 KB
testcase_36 AC 304 ms
65,896 KB
testcase_37 AC 474 ms
77,808 KB
testcase_38 AC 137 ms
56,796 KB
testcase_39 AC 494 ms
79,156 KB
testcase_40 AC 247 ms
62,944 KB
testcase_41 AC 483 ms
76,368 KB
testcase_42 AC 456 ms
74,796 KB
testcase_43 AC 461 ms
77,480 KB
testcase_44 AC 526 ms
78,120 KB
testcase_45 AC 100 ms
53,984 KB
testcase_46 AC 251 ms
63,200 KB
testcase_47 AC 508 ms
79,244 KB
testcase_48 AC 527 ms
80,456 KB
testcase_49 AC 569 ms
81,300 KB
testcase_50 AC 490 ms
77,764 KB
testcase_51 AC 507 ms
77,960 KB
testcase_52 AC 526 ms
78,648 KB
testcase_53 AC 501 ms
77,552 KB
testcase_54 AC 503 ms
77,832 KB
testcase_55 AC 495 ms
77,560 KB
testcase_56 AC 478 ms
79,844 KB
testcase_57 AC 467 ms
80,608 KB
testcase_58 AC 369 ms
76,176 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

package contest210416;

import java.io.*;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

public class H2 {
	InputStream is;
	FastWriter out;

	String INPUT = "";

	static final int mod = 998244353;
	static long K, L;

	public void solve()
	{
		int n = ni();
		K = ni();
		int[] from = new int[n];
		int[] to = new int[n];
		for (int i = 0; i < n; i++) {
			from[i] = ni() - 1;
			to[i] = ni() - 1;
		}
		int[][] g = packU(n, from, to);
		AnalyzeResult ar = analyze(g);

		L = invl(mod+1-K, mod);

		// cycle[0]-cycle[-1]を切った木についてまず解く
		int[][] h = makeTree(g, ar);
		long ans = solveForTree(h);

		// 残ったケースはかならずcycle[0]-cycle[-1]を含む。
		// - cycleのすべての辺を含む場合 cycleの要素までのDPの結果に、一度にcycleの辺を全部追加する。
		// - それ以外の場合、cycleのどの辺で切るかで値を列挙しておき、両方向をO(|cycle|)でマージする。

		// 足についてDP
		Datum[] dp = solveForSideTrees(ar, g);

		// 全辺追加。cycleの要素はすでに次数2以上の扱いをされている
		Datum base = new Datum(1, 0, 1);
		for(int c : ar.cycle){
			base = merge(base, dp[c]);
		}
		ans += base.f0;

		Datum d11 = new Datum(2L*K*L % mod, K*L % mod, K*L%mod);
		Datum d01 = new Datum(2L*L%mod, L, L);
		Datum[] pref = new Datum[ar.cycle.length];
		Datum[] pre = new Datum[ar.cycle.length];
		for(int i = 0;i < ar.cycle.length;i++){
			int cur = ar.cycle[i];
			pref[i] = i == 0 ? new Datum(dp[cur].f1, dp[cur].f0, dp[cur].fp) : merge(pref[i-1], dp[cur]);
			// curだけは次数1であることを許される。このとき次数2扱いしていたものを除く
			pre[i] = add(pref[i], i == 0 ? sub(d11, d01) : merge(pref[i-1], sub(d11, d01)));
		}

		Datum[] suff = new Datum[ar.cycle.length];
		Datum[] suf = new Datum[ar.cycle.length];
		for(int i = 0;i < ar.cycle.length;i++){
			int cur = ar.cycle[ar.cycle.length-1-i];
			suff[i] = i == 0 ? new Datum(dp[cur].f1, dp[cur].f0, dp[cur].fp) : merge(suff[i-1], dp[cur]);
			// curだけは次数1であることを許される。このとき次数2扱いしていたものを除く
			suf[i] = add(suff[i], i == 0 ? sub(d11, d01) : merge(suff[i-1], sub(d11, d01)));
		}
//		tr(ar.cycle);
//		tr(pre);
//		tr(suf);

		Datum sufcum = new Datum(0, 0, 0);
		for(int i = ar.cycle.length-2;i >= 0;i--){
			sufcum = add(sufcum, suf[ar.cycle.length-2-i]);
			Datum merged = merge(pre[i], sufcum);
			ans += merged.f0;
		}

		ans = ans % mod * pow(mod+1-K, n, mod);
		out.println(ans % mod);
	}

	Datum[] solveForSideTrees(AnalyzeResult ar, int[][] g)
	{
		int n = g.length;
		Datum d01 = new Datum(2L*L%mod, L, L);
//		Datum d00 = new Datum(1L, 0L, 1L);
		Datum d11 = new Datum(2L*K*L % mod, K*L % mod, K*L%mod);
		Datum[] dp = new Datum[n];
		// treeと異なり上に継承するデータのみでよい
		for(int i = n-1;i >= 0;i--){
			int cur = ar.ord[i];
			Datum base = d01;
			for(int e : g[cur]){
				if(ar.par[cur] == e)continue;
				if(ar.next[e] != -1)continue;
				base = merge(base, promote(dp[e]));
			}

			// +点ではじまるやつ(1,1)
			// -無に2ではじまるやつ (0,1)
			// base = base + d11 - d01
			if(ar.next[cur] == -1) {
				base = sub(add(base, d11), d01);
			}else{
				// cycle上のときは2ではじまるやつしかないので調整不要
			}
			dp[cur] = base;
		}

		return dp;
	}

	long solveForTree(int[][] h)
	{
		int n = h.length;
		int[][] pars = parents(h, 0);
		int[] par = pars[0], ord = pars[1], dep = pars[2];

		Datum d01 = new Datum(2L*L%mod, L, L);
		Datum d00 = new Datum(1L, 0L, 1L);
		Datum d11 = new Datum(2L*K*L % mod, K*L % mod, K*L%mod);
		Datum[] dp = new Datum[n];
		long ans = 0;
		for(int i = n-1;i >= 0;i--){
			int cur = ord[i];
			Datum base = d01;
			Datum sum = d00;
			for(int e : h[cur]){
				if(par[cur] == e)continue;
				base = merge(base, promote(dp[e]));
				sum = add(sum, dp[e]);
			}
			Datum minus = merge(sum, d01);
			Datum plus = merge(sum, d11);

			ans += base.f0;
//			tr(cur, base, minus, plus);
			// +点ではじまるやつ(1,1)
			// 無に2ではじまるやつを引く (0,1)
			base = sub(add(base, d11), d01);
			dp[cur] = base;
			// n(012)
			ans -= minus.f0;
			ans += plus.f0;
			ans += mod;
//			tr(ans%mod);
		}
		return ans%mod;
	}

	public static class AnalyzeResult
	{
		public int[] par, next, ord, cycle, icycle, dep, roots;
	}

	public static AnalyzeResult analyze(int[][] g)
	{
		AnalyzeResult ret = new AnalyzeResult();

		int n = g.length;
		int[][] pn = split(g);
		int[] par = pn[0], next = pn[1];
		ret.par = par;
		ret.next = next;

		int[] ord = makeOrder(g, ret.par);
		ret.ord = ord;

		int[] cycle = cycle(g, ret.next);
		int[] icycle = new int[n];
		Arrays.fill(icycle, -1);
		for(int i = 0;i < cycle.length;i++)icycle[cycle[i]] = i;
		ret.cycle = cycle;
		ret.icycle = icycle;

		int[] depn = new int[n];
		int[] roots = new int[n];
		for(int i = 0;i < n;i++){
			int cur = ord[i];
			if(next[cur] != -1){
				roots[cur] = cur;
				depn[cur] = 0;
			}else{
				roots[cur] = roots[par[cur]];
				depn[cur] = depn[par[cur]] + 1;
			}
		}
		ret.dep = depn;
		ret.roots = roots;

		return ret;
	}

	public static class AnalyzeResultEx extends AnalyzeResult
	{
		public int[][] tspar;
		public int[] tdep;
	}

	public static int[][] makeTree(int[][] g, AnalyzeResult res)
	{
		int n = g.length;
		int[][] tree = new int[n][];
		int ngf = res.cycle[res.cycle.length-1], ngt = res.cycle[0];
		for(int i = 0;i < n;i++){
			int[] row = Arrays.copyOf(g[i], g[i].length);
			if(i == ngf || i == ngt){
				int p = 0;
				boolean processed = false;
				for(int j = 0;j < row.length;j++){
					if(row[j] == (ngf^ngt^i) && !processed || row[j] == i){
						processed = true;
					}else{
						row[p++] = row[j];
					}
				}
				row = Arrays.copyOf(row, p);
			}
			tree[i] = row;
		}
		return tree;
	}

	/**
	 * gから親リンクとringの次のリンクを取り出す。ringを含んでいなくても可能。森も取り出す。
	 * 重複辺は事前に除いておかないといけない。
	 * 重複辺を含んでいても大丈夫だとおもう
	 * par!=-1,next==-1 : 木部ノード
	 * par==-1,next!=-1 : 環部ノード
	 * par==-1,next==-1 : 森のルート
	 * @param g 重複辺を除いたpseudoforest
	 * @return {par, next}
	 */
	public static int[][] split(int[][] g)
	{
		int n = g.length;
		int[] deg = new int[n];
		int[] par = new int[n];
		Arrays.fill(par, -1);
		for(int i = 0;i < n;i++){
			deg[i] = g[i].length;
		}
		Queue<Integer> q = new ArrayDeque<Integer>();
		for(int i = 0;i < n;i++){
			if(deg[i] == 1){
				q.add(i);
			}
		}
		while(!q.isEmpty()){
			int cur = q.poll();
			deg[cur] = -9999999;
			for(int e : g[cur]){
				deg[e]--;
				if(deg[e] >= 0){
					par[cur] = e;
				}
				if(deg[e] >= 0 && deg[e] <= 1){
					q.add(e);
				}
			}
		}
		boolean[] ved = new boolean[n];
		int[] next = new int[n];
		Arrays.fill(next, -1);
		for(int i = 0;i < n;i++){
			if(!ved[i] && deg[i] == 2){
				ved[i] = true;
				int cur = i;
				outer:
				while(true){
					for(int e : g[cur]){
						if(deg[e] == 2 && !ved[e]){
							next[cur] = e;
							ved[e] = true;
							cur = e;
							continue outer;
						}
					}
					next[cur] = i;
					break;
				}
			}
		}

		return new int[][]{par, next};
	}

	/**
	 * cycle側が先頭にくる
	 * @param g
	 * @param par
	 * @return
	 */
	public static int[] makeOrder(int[][] g, int[] par)
	{
		int n = g.length;
		int[] ord = new int[n];
		int p = 0;
		boolean[] ved = new boolean[n];
		for(int i = 0;i < n;i++){
			if(par[i] == -1){
				ord[p++] = i;
				ved[i] = true;
			}
		}
		for(int r = 0;r < n;r++){
			for(int e : g[ord[r]]){
				if(!ved[e]){
					ved[e] = true;
					ord[p++] = e;
				}
			}
		}
		return ord;
	}

	// cycle部分を取り出す
	public static int[] cycle(int[][] g, int[] next)
	{
		int n = g.length;
		int[] which = new int[n];
		int p = 0;
		for(int i = 0;i < n;i++){
			if(next[i] != -1){
				int u = i;
				while(true){
					which[p++] = u;
					u = next[u];
					if(u == i)break;
				}
				break;
			}
		}
		return Arrays.copyOf(which, p);
	}

	public static int[][] parents(int[][] g, int[] clus)
	{
		int n = g.length;
		int[] par = new int[n];
		Arrays.fill(par, -1);
		int[] q = new int[n];
		int[] depth = new int[n];

		int p = 0;
		for(int i = 0;i < n;i++){
			if(clus[i] == 0){
				int root = i;
				q[p] = root;
				depth[root] = 0;
				par[root] = -1;
				for(int r = p++;r < p;r++){
					int cur = q[r];
					for(int nex : g[cur]){
						if(par[cur] != nex && clus[nex] != 0){
							q[p++] = nex;
							par[nex] = cur;
							depth[nex] = depth[cur] + 1;
						}
					}
				}
			}
		}

		return new int[][] {par, q, depth};
	}


	public static long pow(long a, long n, long mod) {
		//		a %= mod;
		long ret = 1;
		int x = 63 - Long.numberOfLeadingZeros(n);
		for (; x >= 0; x--) {
			ret = ret * ret % mod;
			if (n << 63 - x < 0) ret = ret * a % mod;
		}
		return ret;
	}


	static class Datum
	{
		long f1; // (y+1)K^xL^y
		long f0; // yK^xL^y
		long fp; // K^xL^y

		public Datum(long f1, long f0, long fp) {
			this.f1 = f1;
			this.f0 = f0;
			this.fp = fp;
		}

		@Override
		public String toString() {
			return "Datum{" +
					"f1=" + f1 +
					", f0=" + f0 +
					", fp=" + fp +
					'}';
		}
	}

	public static Datum merge(Datum A, Datum B)
	{
		long nfp = A.fp * B.fp % mod;
		long nf0 = ((A.f1 * B.f1 - A.f0 * B.f0 - nfp) % mod + mod) % mod;
		long nf1 = ((A.f1 * B.f1 - A.f0 * B.f0) % mod + mod) % mod;
		return new Datum(nf1, nf0, nfp);
	}

	public static Datum add(Datum A, Datum B)
	{
		long nfp = (A.fp + B.fp) % mod;
		long nf0 = (A.f0 + B.f0) % mod;
		long nf1 = (A.f1 + B.f1) % mod;
		return new Datum(nf1, nf0, nfp);
	}

	public static Datum sub(Datum A, Datum B)
	{
		long nfp = (A.fp - B.fp + mod) % mod;
		long nf0 = (A.f0 - B.f0 + mod) % mod;
		long nf1 = (A.f1 - B.f1 + mod) % mod;
		return new Datum(nf1, nf0, nfp);
	}



	public static Datum promote(Datum A)
	{
		return new Datum(
				(A.f1 + 1) % mod,
				A.f0,
				(A.fp + 1) % mod
		);
	}

	public static long invl(long a, long mod) {
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		return p < 0 ? p + mod : p;
	}


	public static int[][] parents(int[][] g, int root) {
		int n = g.length;
		int[] par = new int[n];
		Arrays.fill(par, -1);

		int[] depth = new int[n];
		depth[0] = 0;

		int[] q = new int[n];
		q[0] = root;
		for (int p = 0, r = 1; p < r; p++) {
			int cur = q[p];
			for (int nex : g[cur]) {
				if (par[cur] != nex) {
					q[r++] = nex;
					par[nex] = cur;
					depth[nex] = depth[cur] + 1;
				}
			}
		}
		return new int[][]{par, q, depth};
	}


	public static int[][] packU(int n, int[] from, int[] to) {
		return packU(n, from, to, from.length);
	}

	public static int[][] packU(int n, int[] from, int[] to, int sup) {
		int[][] g = new int[n][];
		int[] p = new int[n];
		for (int i = 0; i < sup; i++) p[from[i]]++;
		for (int i = 0; i < sup; i++) p[to[i]]++;
		for (int i = 0; i < n; i++) g[i] = new int[p[i]];
		for (int i = 0; i < sup; i++) {
			g[from[i]][--p[from[i]]] = to[i];
			g[to[i]][--p[to[i]]] = from[i];
		}
		return g;
	}


	public static void main(String[] args) {
		new H2().run();
	}

	public void run()
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);

		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
		//		Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
		//			@Override
		//			public void run() {
		//				long s = System.currentTimeMillis();
		//				solve();
		//				out.flush();
		//				if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
		//			}
		//		};
		//		t.start();
		//		t.join();
	}

	private boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;

		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}

	private final byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}

	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	//	private boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }

	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}

	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}

	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}

	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}

		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}

		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;

		private FastWriter(){out = null;}

		public FastWriter(OutputStream os)
		{
			this.out = os;
		}

		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}

		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}

		public FastWriter write(char c)
		{
			return write((byte)c);
		}

		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}

		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}

		private static int countDigits(int l) {
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}

		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}

		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}

		public FastWriter writeln(char c){ return write(c).writeln(); }
		public FastWriter writeln(int x){ return write(x).writeln(); }
		public FastWriter writeln(long x){ return write(x).writeln(); }
		public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); }

		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(IntUnaryOperator f, int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(f.applyAsInt(x));
			}
			return this;
		}

		public FastWriter write(LongUnaryOperator f, long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(f.applyAsLong(x));
			}
			return this;
		}

		public FastWriter writeln()
		{
			return write((byte)'\n');
		}

		public FastWriter writeln(int... xs) { return write(xs).writeln(); }
		public FastWriter writeln(long... xs) { return write(xs).writeln(); }
		public FastWriter writeln(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); }
		public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, xs).writeln(); }
		public FastWriter writeln(char[] line) { return write(line).writeln(); }
		public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln();return this; }
		public FastWriter writeln(String s) { return write(s).writeln(); }

		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}

		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}

		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter print(IntUnaryOperator f, int... xs) { return write(f, xs); }
		public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); }
		public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}

	public static void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}

	// print ids which are 1
	public static void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}

	public static void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}

	public static void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}

	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}

	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}

	private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}
0