結果
| 問題 | No.1302 Random Tree Score |
| ユーザー |
 uwi
|
| 提出日時 | 2020-11-27 22:18:03 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
AC
|
| 実行時間 | 1,647 ms / 3,000 ms |
| コード長 | 22,085 bytes |
| コンパイル時間 | 9,278 ms |
| コンパイル使用メモリ | 85,816 KB |
| 実行使用メモリ | 79,808 KB |
| 最終ジャッジ日時 | 2023-10-01 06:29:32 |
| 合計ジャッジ時間 | 22,799 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge14 |
（要ログイン）
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 | 69 ms
50,496 KB |
| testcase_01 | AC | 70 ms
50,620 KB |
| testcase_02 | AC | 574 ms
63,920 KB |
| testcase_03 | AC | 900 ms
69,168 KB |
| testcase_04 | AC | 556 ms
64,308 KB |
| testcase_05 | AC | 1,582 ms
74,480 KB |
| testcase_06 | AC | 1,580 ms
74,800 KB |
| testcase_07 | AC | 589 ms
64,416 KB |
| testcase_08 | AC | 926 ms
68,772 KB |
| testcase_09 | AC | 1,647 ms
79,136 KB |
| testcase_10 | AC | 1,531 ms
77,796 KB |
| testcase_11 | AC | 610 ms
61,732 KB |
| testcase_12 | AC | 1,574 ms
74,916 KB |
| testcase_13 | AC | 69 ms
50,736 KB |
| testcase_14 | AC | 1,587 ms
79,352 KB |
| testcase_15 | AC | 1,594 ms
79,808 KB |
| testcase_16 | AC | 71 ms
48,868 KB |
ソースコード
package contest201127;
import java.io.*;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;
public class E2 {
InputStream is;
FastWriter out;
String INPUT = "";
public void solve()
{
int n = ni();
final int mod = 998244353;
int[][] fif = enumFIF(n);
long[] a = new long[n-1];
for(int i = 1;i <= n-1;i++){
a[i-1] = (long)fif[1][i-1] * i % mod;
}
// 2n-2 - n
long[] b = pow(a, n);
out.println(b[n-2] * fif[0][n-2] % mod * invl(pow(n, n-2, mod), mod) % mod);
}
public static long[] powNaive(long[] a, int K)
{
int n = a.length;
long[] ret = {1};
for(int d = 31-Integer.numberOfLeadingZeros(K);d >= 0;d--) {
ret = mul(ret, ret, n);
if(K<<~d<0) {
ret = mul(ret, a, n);
}
}
return ret;
}
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 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;
}
public static final int mod = 998244353;
public static final int G = 3;
// only 998244353
public static long[] mul(long[] a, long[] b)
{
return Arrays.copyOf(convoluteSimply(a, b, mod, 3), a.length+b.length-1);
}
public static long[] mul(long[] a, long[] b, int lim)
{
return Arrays.copyOf(convoluteSimply(a, b, mod, 3), lim);
}
// public static final int mod = 1000000007;
// public static long[] mul(long[] a, long[] b)
// {
// if(Math.max(a.length, b.length) >= 3000){
// return Arrays.copyOf(NTTCRT.convolute(a, b, 3, mod), a.length+b.length-1);
// }else{
// return mulnaive(a, b);
// }
// }
// public static long[] mul(long[] a, long[] b, int lim)
// {
// if(Math.max(a.length, b.length) >= 3000){
// return Arrays.copyOf(NTTCRT.convolute(a, b, 3, mod), lim);
// }else{
// return mulnaive(a, b, lim);
// }
// }
public static final long big = (Long.MAX_VALUE/mod/mod-1)*mod*mod;
public static long[] mulnaive(long[] a, long[] b)
{
long[] c = new long[a.length+b.length-1];
for(int i = 0;i < a.length;i++){
for(int j = 0;j < b.length;j++){
c[i+j] += a[i]*b[j];
if(c[i+j] >= big)c[i+j] -= big;
}
}
for(int i = 0;i < c.length;i++)c[i] %= mod;
return c;
}
public static long[] mulnaive(long[] a, long[] b, int lim)
{
long[] c = new long[lim];
for(int i = 0;i < a.length;i++){
for(int j = 0;j < b.length && i+j < lim;j++){
c[i+j] += a[i]*b[j];
if(c[i+j] >= big)c[i+j] -= big;
}
}
for(int i = 0;i < c.length;i++)c[i] %= mod;
return c;
}
public static long[] mul_(long[] a, long k)
{
for(int i = 0;i < a.length;i++)a[i] = a[i] * k % mod;
return a;
}
public static long[] mul(long[] a, long k)
{
a = Arrays.copyOf(a, a.length);
for(int i = 0;i < a.length;i++)a[i] = a[i] * k % mod;
return a;
}
public static long[] add(long[] a, long[] b)
{
long[] c = new long[Math.max(a.length, b.length)];
for(int i = 0;i < a.length;i++)c[i] += a[i];
for(int i = 0;i < b.length;i++)c[i] += b[i];
for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod;
return c;
}
public static long[] add(long[] a, long[] b, int lim)
{
long[] c = new long[lim];
for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i];
for(int i = 0;i < b.length && i < lim;i++)c[i] += b[i];
for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod;
return c;
}
public static long[] sub(long[] a, long[] b)
{
long[] c = new long[Math.max(a.length, b.length)];
for(int i = 0;i < a.length;i++)c[i] += a[i];
for(int i = 0;i < b.length;i++)c[i] -= b[i];
for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod;
return c;
}
public static long[] sub(long[] a, long[] b, int lim)
{
long[] c = new long[lim];
for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i];
for(int i = 0;i < b.length && i < lim;i++)c[i] -= b[i];
for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod;
return c;
}
// F_{t+1}(x) = -F_t(x)^2*P(x) + 2F_t(x)
// if want p-destructive, comment out flipping p just before returning.
public static long[] inv(long[] p)
{
int n = p.length;
long[] f = {invl(p[0], mod)};
for(int i = 0;i < p.length;i++){
if(p[i] == 0)continue;
p[i] = mod-p[i];
}
for(int i = 1;i < 2*n;i*=2){
long[] f2 = mul(f, f, Math.min(n, 2*i));
long[] f2p = mul(f2, Arrays.copyOf(p, i), Math.min(n, 2*i));
for(int j = 0;j < f.length;j++){
f2p[j] += 2L*f[j];
if(f2p[j] >= mod)f2p[j] -= mod;
if(f2p[j] >= mod)f2p[j] -= mod;
}
f = f2p;
}
for(int i = 0;i < p.length;i++){
if(p[i] == 0)continue;
p[i] = mod-p[i];
}
return f;
}
// differentiate
public static long[] d(long[] p)
{
long[] q = new long[p.length];
for(int i = 0;i < p.length-1;i++){
q[i] = p[i+1] * (i+1) % mod;
}
return q;
}
// integrate
public static long[] i(long[] p)
{
long[] q = new long[p.length];
for(int i = 0;i < p.length-1;i++){
q[i+1] = p[i] * invl(i+1, mod) % mod;
}
return q;
}
static long[] exp(long[] a) { return exp(a, a.length); }
/**
* https://cs.uwaterloo.ca/~eschost/publications/BoSc09-final.pdf
* @verified https://judge.yosupo.jp/problem/exp_of_formal_power_series
* @param a
* @param lim
* @return
*/
static long[] exp(long[] a, int lim)
{
long[] F = {1L};
long[] G = {1L};
long[] da = d(a);
for(int m = 1;;m *= 2) {
long[] G2 = mul(G, G, m);
G = sub(mul_(G, 2), mul(F, G2, m));
long[] Q = Arrays.copyOf(da, m-1);
long[] W = add(Q, mul(G, sub(d(F), mul(F, Q, m), m-1)));
F = mul(F, add(new long[] {1}, sub(Arrays.copyOf(a, m), i(W))), m);
if(m >= lim)break;
}
return Arrays.copyOf(F, lim);
}
//
// // F_{t+1}(x) = F_t(x)-(ln F_t(x) - P(x)) * F_t(x)
// public static long[] exp(long[] p)
// {
// int n = p.length;
// long[] f = {p[0]};
// for(int i = 1;i < 2*n;i*=2){
// long[] ii = ln(f);
// long[] sub = sub(ii, p, Math.min(n, 2*i));
// if(--sub[0] < 0)sub[0] += mod;
// for(int j = 0;j < 2*i && j < n;j++){
// sub[j] = mod-sub[j];
// if(sub[j] == mod)sub[j] = 0;
// }
// f = mul(sub, f, Math.min(n, 2*i));
//// f = sub(f, mul(sub(ii, p, 2*i), f, 2*i));
// }
// return f;
// }
// \int f'(x)/f(x) dx
public static long[] ln(long[] f)
{
return i(mul(d(f), inv(f)));
}
// ln F(x) - k ln P(x) = 0
public static long[] pow(long[] p, long K)
{
int n = p.length;
int tz = trailingZeros(p);
if((long)tz*K >= n)return new long[n];
long[] pa = Arrays.copyOfRange(p, tz, n);
int m = pa.length;
// pa[0] must be 1
long base = pa[0];
long scale = invl(base, mod);
for(int i = 0;i < m;i++)pa[i] = pa[i] * scale % mod;
long[] lnp = Arrays.copyOf(ln(pa), m);
for(int i = 0;i < m;i++)lnp[i] = lnp[i] * K % mod;
long[] reta = exp(lnp);
long kscale = pow(base, K, mod);
for(int i = 0;i < m;i++)reta[i] = reta[i] * kscale % mod;
long[] ret = new long[n];
System.arraycopy(reta, 0, ret, (int)(tz*K), (int)(n-tz*K));
return ret;
}
public static int trailingZeros(long[] a)
{
int ret = 0;
for(long v : a) {
if(v == 0) {
ret++;
}else {
break;
}
}
return ret;
}
public static long[] convoluteSimply(long[] a, long[] b, int P, int g)
{
int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
long[] fa = nttmb(a, m, false, P, g);
long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
for(int i = 0;i < m;i++){
fa[i] = fa[i]*fb[i]%P;
}
return nttmb(fa, m, true, P, g);
}
// static int[] wws = new int[270000]; // outer faster
// Modifed Montgomery + Barrett
private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g)
{
long[] dst = Arrays.copyOf(src, n);
int h = Integer.numberOfTrailingZeros(n);
long K = Integer.highestOneBit(P)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/P;
int[] wws = new int[1<<h-1];
long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);
long w = (1L<<32)%P;
for(int k = 0;k < 1<<h-1;k++){
wws[k] = (int)w;
w = modh(w*dw, M, H, P);
}
long J = invl(P, 1L<<32);
for(int i = 0;i < h;i++){
for(int j = 0;j < 1<<i;j++){
for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){
long u = (dst[s] - dst[t] + 2*P)*wws[k];
dst[s] += dst[t];
if(dst[s] >= 2*P)dst[s] -= 2*P;
// long Q = (u&(1L<<32)-1)*J&(1L<<32)-1;
long Q = (u<<32)*J>>>32;
dst[t] = (u>>>32)-(Q*P>>>32)+P;
}
}
if(i < h-1){
for(int k = 0;k < 1<<h-i-2;k++)wws[k] = wws[k*2];
}
}
for(int i = 0;i < n;i++){
if(dst[i] >= P)dst[i] -= P;
}
for(int i = 0;i < n;i++){
int rev = Integer.reverse(i)>>>-h;
if(i < rev){
long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;
}
}
if(inverse){
long in = invl(n, P);
for(int i = 0;i < n;i++)dst[i] = modh(dst[i]*in, M, H, P);
}
return dst;
}
// Modified Shoup + Barrett
private static long[] nttsb(long[] src, int n, boolean inverse, int P, int g)
{
long[] dst = Arrays.copyOf(src, n);
int h = Integer.numberOfTrailingZeros(n);
long K = Integer.highestOneBit(P)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/P;
long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);
long[] wws = new long[1<<h-1];
long[] ws = new long[1<<h-1];
long w = 1;
for(int k = 0;k < 1<<h-1;k++){
wws[k] = (w<<32)/P;
ws[k] = w;
w = modh(w*dw, M, H, P);
}
for(int i = 0;i < h;i++){
for(int j = 0;j < 1<<i;j++){
for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){
long ndsts = dst[s] + dst[t];
if(ndsts >= 2*P)ndsts -= 2*P;
long T = dst[s] - dst[t] + 2*P;
long Q = wws[k]*T>>>32;
dst[s] = ndsts;
dst[t] = ws[k]*T-Q*P&(1L<<32)-1;
}
}
// dw = dw * dw % P;
if(i < h-1){
for(int k = 0;k < 1<<h-i-2;k++){
wws[k] = wws[k*2];
ws[k] = ws[k*2];
}
}
}
for(int i = 0;i < n;i++){
if(dst[i] >= P)dst[i] -= P;
}
for(int i = 0;i < n;i++){
int rev = Integer.reverse(i)>>>-h;
if(i < rev){
long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;
}
}
if(inverse){
long in = invl(n, P);
for(int i = 0;i < n;i++){
dst[i] = modh(dst[i] * in, M, H, P);
}
}
return dst;
}
static final long mask = (1L<<31)-1;
public static long modh(long a, long M, int h, int mod)
{
long r = a-((M*(a&mask)>>>31)+M*(a>>>31)>>>h-31)*mod;
return r < mod ? r : r-mod;
}
private static long[] garnerPrepare(int[] m)
{
int n = m.length;
assert n == m.length;
if(n == 0)return new long[0];
long[] gamma = new long[n];
for(int k = 1;k < n;k++){
long prod = 1;
for(int i = 0;i < k;i++){
prod = prod * m[i] % m[k];
}
gamma[k] = invl(prod, m[k]);
}
return gamma;
}
private static long[] garnerBatch(int[] u, int[] m, long[] gamma)
{
int n = u.length;
assert n == m.length;
long[] v = new long[n];
v[0] = u[0];
for(int k = 1;k < n;k++){
long temp = v[k-1];
for(int j = k-2;j >= 0;j--){
temp = (temp * m[j] + v[j]) % m[k];
}
v[k] = (u[k] - temp) * gamma[k] % m[k];
if(v[k] < 0)v[k] += m[k];
}
return v;
}
public static int[][] enumFIF(int n) {
int[] f = new int[n + 1];
int[] invf = new int[n + 1];
f[0] = 1;
for (int i = 1; i <= n; i++) {
f[i] = (int) ((long) f[i - 1] * i % mod);
}
long a = f[n];
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;
}
invf[n] = (int) (p < 0 ? p + mod : p);
for (int i = n - 1; i >= 0; i--) {
invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
}
return new int[][]{f, invf};
}
public static void main(String[] args) {
new E2().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 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(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 println(int... xs) { return writeln(xs); }
public FastWriter println(long... xs) { return writeln(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)); }
}