結果
| 問題 | No.2606 Mirror Relay |
| ユーザー |
 uwi
|
| 提出日時 | 2024-01-12 22:25:56 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
AC
|
| 実行時間 | 553 ms / 2,000 ms |
| コード長 | 26,090 bytes |
| コンパイル時間 | 7,920 ms |
| コンパイル使用メモリ | 99,016 KB |
| 実行使用メモリ | 78,896 KB |
| 最終ジャッジ日時 | 2024-09-27 22:57:38 |
| 合計ジャッジ時間 | 29,163 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（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 | 99 ms
51,372 KB |
| testcase_01 | AC | 100 ms
51,376 KB |
| testcase_02 | AC | 93 ms
51,356 KB |
| testcase_03 | AC | 103 ms
51,564 KB |
| testcase_04 | AC | 117 ms
52,904 KB |
| testcase_05 | AC | 117 ms
52,824 KB |
| testcase_06 | AC | 117 ms
52,888 KB |
| testcase_07 | AC | 116 ms
52,440 KB |
| testcase_08 | AC | 119 ms
52,892 KB |
| testcase_09 | AC | 122 ms
52,780 KB |
| testcase_10 | AC | 118 ms
52,556 KB |
| testcase_11 | AC | 120 ms
52,676 KB |
| testcase_12 | AC | 122 ms
52,848 KB |
| testcase_13 | AC | 124 ms
52,512 KB |
| testcase_14 | AC | 116 ms
51,556 KB |
| testcase_15 | AC | 113 ms
52,472 KB |
| testcase_16 | AC | 111 ms
51,176 KB |
| testcase_17 | AC | 106 ms
51,796 KB |
| testcase_18 | AC | 114 ms
51,528 KB |
| testcase_19 | AC | 125 ms
53,080 KB |
| testcase_20 | AC | 134 ms
53,180 KB |
| testcase_21 | AC | 120 ms
52,896 KB |
| testcase_22 | AC | 119 ms
52,804 KB |
| testcase_23 | AC | 121 ms
52,800 KB |
| testcase_24 | AC | 127 ms
52,748 KB |
| testcase_25 | AC | 124 ms
52,908 KB |
| testcase_26 | AC | 129 ms
52,656 KB |
| testcase_27 | AC | 119 ms
52,644 KB |
| testcase_28 | AC | 116 ms
51,560 KB |
| testcase_29 | AC | 115 ms
52,752 KB |
| testcase_30 | AC | 126 ms
51,420 KB |
| testcase_31 | AC | 120 ms
52,976 KB |
| testcase_32 | AC | 122 ms
52,676 KB |
| testcase_33 | AC | 112 ms
51,188 KB |
| testcase_34 | AC | 124 ms
52,552 KB |
| testcase_35 | AC | 128 ms
52,968 KB |
| testcase_36 | AC | 123 ms
52,668 KB |
| testcase_37 | AC | 114 ms
52,660 KB |
| testcase_38 | AC | 130 ms
51,660 KB |
| testcase_39 | AC | 426 ms
63,852 KB |
| testcase_40 | AC | 494 ms
64,500 KB |
| testcase_41 | AC | 412 ms
63,884 KB |
| testcase_42 | AC | 443 ms
63,944 KB |
| testcase_43 | AC | 457 ms
64,208 KB |
| testcase_44 | AC | 476 ms
64,424 KB |
| testcase_45 | AC | 434 ms
64,392 KB |
| testcase_46 | AC | 429 ms
63,408 KB |
| testcase_47 | AC | 458 ms
64,832 KB |
| testcase_48 | AC | 464 ms
64,664 KB |
| testcase_49 | AC | 500 ms
64,604 KB |
| testcase_50 | AC | 513 ms
67,096 KB |
| testcase_51 | AC | 526 ms
66,968 KB |
| testcase_52 | AC | 438 ms
66,124 KB |
| testcase_53 | AC | 484 ms
67,004 KB |
| testcase_54 | AC | 496 ms
67,036 KB |
| testcase_55 | AC | 553 ms
77,464 KB |
| testcase_56 | AC | 484 ms
66,124 KB |
| testcase_57 | AC | 459 ms
65,984 KB |
| testcase_58 | AC | 519 ms
66,852 KB |
| testcase_59 | AC | 367 ms
63,720 KB |
| testcase_60 | AC | 368 ms
63,328 KB |
| testcase_61 | AC | 381 ms
63,076 KB |
| testcase_62 | AC | 355 ms
63,692 KB |
| testcase_63 | AC | 368 ms
63,464 KB |
| testcase_64 | AC | 367 ms
63,328 KB |
| testcase_65 | AC | 358 ms
63,364 KB |
| testcase_66 | AC | 362 ms
63,740 KB |
| testcase_67 | AC | 381 ms
64,372 KB |
| testcase_68 | AC | 367 ms
63,200 KB |
| testcase_69 | AC | 458 ms
78,896 KB |
| testcase_70 | AC | 104 ms
51,248 KB |
| testcase_71 | AC | 100 ms
51,484 KB |
| testcase_72 | AC | 95 ms
50,668 KB |
ソースコード
package no2xxx;
import java.io.*;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
public class No2606 {
InputStream is;
FastWriter out;
String INPUT = "";
public void solve()
{
char[] s = ns().toCharArray();
PalindromicTree pt = PalindromicTree.build(s);
List<Node> ns = new ArrayList<>();
// for(Node no : pt.nodes){
// tr(no);
// }
int[] sa = suffixArray(s);
int[] lcp = lcpArray(s, sa);
int n = s.length;
int[] isa = new int[n];
for(int i = 0;i < n;i++){
isa[sa[i]] = i;
}
SegmentTreeRMQ st = new SegmentTreeRMQ(lcp);
// tr(sa);
// tr(lcp);
SegmentTreeRMQL stl = new SegmentTreeRMQL(n);
Arrays.sort(pt.nodes, (l, r) -> l.len - r.len);
long[] dp = new long[pt.nodes.length];
for(int i = pt.nodes.length-1;i >= 2;i--){
Node no = pt.nodes[i];
int f = no.first;
int l = st.lastle(isa[f]-1, no.len-1);
int r = st.firstle(isa[f], no.len-1);
if(r == -1)r = n-1;
// (l,r]
int ind = isa[f];
// tr(l, r);
dp[i] = -Math.min(0L, stl.min(l+1, r+1)) + (long)no.len * no.freq;
stl.update(ind, -Math.max(dp[i], -stl.min(ind, ind+1)));
}
out.println(-stl.min(0, n));
}
public static class SegmentTreeRMQL {
public final int M, H, N;
public long[] vals;
public static final long I = Long.MAX_VALUE;
public SegmentTreeRMQL(int n)
{
N = n;
M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
H = M>>>1;
vals = new long[M];
Arrays.fill(vals, 0, M, I);
}
public SegmentTreeRMQL(int[] a)
{
this(a.length);
for(int i = 0;i < N;i++){
vals[H+i] = a[i];
}
// Arrays.fill(vals, H+N, M, I);
for(int i = H-1;i >= 1;i--)propagate(i);
}
public void update(int pos, long x)
{
vals[H+pos] = x;
for(int i = (H+pos)>>>1;i >= 1;i >>>= 1)propagate(i);
}
private void propagate(int i)
{
vals[i] = Math.min(vals[2*i], vals[2*i+1]);
}
public long min(int l, int r){
long min = I;
if(l >= r)return min;
l += H; r += H;
for(;l < r;l>>>=1,r>>>=1){
if((l&1) == 1)min = Math.min(min, vals[l++]);
if((r&1) == 1)min = Math.min(min, vals[--r]);
}
return min;
}
public int firstle(int l, long v) {
if(l >= H)return -1;
int cur = H+l;
while(true){
if(vals[cur] <= v){
if(cur >= H)return cur-H;
cur = 2*cur;
}else{
cur++;
if((cur&cur-1) == 0)return -1;
if((cur&1)==0)cur>>>=1;
}
}
}
public int lastle(int l, long v) {
if(l < 0)return -1;
int cur = H+l;
while(true){
if(vals[cur] <= v){
if(cur >= H)return cur-H;
cur = 2*cur + 1;
}else{
if((cur&cur-1) == 0)return -1;
cur--;
if((cur&1)==1)cur>>>=1;
}
}
}
}
public static class SegmentTreeRMQ {
public final int M, H, N;
public int[] vals;
public static final int I = Integer.MAX_VALUE;
public SegmentTreeRMQ(int n)
{
N = n;
M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
H = M>>>1;
vals = new int[M];
Arrays.fill(vals, 0, M, I);
}
public SegmentTreeRMQ(int[] a)
{
this(a.length);
for(int i = 0;i < N;i++){
vals[H+i] = a[i];
}
// Arrays.fill(vals, H+N, M, I);
for(int i = H-1;i >= 1;i--)propagate(i);
}
public void update(int pos, int x)
{
vals[H+pos] = x;
for(int i = (H+pos)>>>1;i >= 1;i >>>= 1)propagate(i);
}
private void propagate(int i)
{
vals[i] = Math.min(vals[2*i], vals[2*i+1]);
}
public int min(int l, int r){
int min = I;
if(l >= r)return min;
l += H; r += H;
for(;l < r;l>>>=1,r>>>=1){
if((l&1) == 1)min = Math.min(min, vals[l++]);
if((r&1) == 1)min = Math.min(min, vals[--r]);
}
return min;
}
public int firstle(int l, int v) {
if(l >= H)return -1;
int cur = H+l;
while(true){
if(vals[cur] <= v){
if(cur >= H)return cur-H;
cur = 2*cur;
}else{
cur++;
if((cur&cur-1) == 0)return -1;
if((cur&1)==0)cur>>>=1;
}
}
}
public int lastle(int l, int v) {
if(l < 0)return -1;
int cur = H+l;
while(true){
if(vals[cur] <= v){
if(cur >= H)return cur-H;
cur = 2*cur + 1;
}else{
if((cur&cur-1) == 0)return -1;
cur--;
if((cur&1)==1)cur>>>=1;
}
}
}
}
private static int[] saNaive(int[] s) {
int n = s.length;
int[] sa = new int[n];
for(int i = 0;i < n;i++){
sa[i] = i;
}
insertionsortUsingComparator(sa, (l, r) -> {
while (l < n && r < n) {
if (s[l] != s[r]) return s[l] - s[r];
l++;
r++;
}
return -(l - r);
});
return sa;
}
private static int[] saDoubling(int[] s) {
int n = s.length;
int[] sa = new int[n];
for(int i = 0;i < n;i++){
sa[i] = i;
}
int[] rnk = java.util.Arrays.copyOf(s, n);
int[] tmp = new int[n];
for (int k = 1; k < n; k *= 2) {
final int _k = k;
final int[] _rnk = rnk;
java.util.function.IntBinaryOperator cmp = (x, y) -> {
if (_rnk[x] != _rnk[y]) return _rnk[x] - _rnk[y];
int rx = x + _k < n ? _rnk[x + _k] : -1;
int ry = y + _k < n ? _rnk[y + _k] : -1;
return rx - ry;
};
mergesortUsingComparator(sa, cmp);
tmp[sa[0]] = 0;
for (int i = 1; i < n; i++) {
tmp[sa[i]] = tmp[sa[i - 1]] + (cmp.applyAsInt(sa[i - 1], sa[i]) < 0 ? 1 : 0);
}
int[] buf = tmp;
tmp = rnk;
rnk = buf;
}
return sa;
}
private static void insertionsortUsingComparator(int[] a, java.util.function.IntBinaryOperator comparator) {
final int n = a.length;
for (int i = 1; i < n; i++) {
final int tmp = a[i];
if (comparator.applyAsInt(a[i - 1], tmp) > 0) {
int j = i;
do {
a[j] = a[j - 1];
j--;
} while (j > 0 && comparator.applyAsInt(a[j - 1], tmp) > 0);
a[j] = tmp;
}
}
}
private static void mergesortUsingComparator(int[] a, java.util.function.IntBinaryOperator comparator) {
final int n = a.length;
final int[] work = new int[n];
for (int block = 1; block <= n; block <<= 1) {
final int block2 = block << 1;
for (int l = 0, max = n - block; l < max; l += block2) {
int m = l + block;
int r = Math.min(l + block2, n);
System.arraycopy(a, l, work, 0, block);
for (int i = l, wi = 0, ti = m;; i++) {
if (ti == r) {
System.arraycopy(work, wi, a, i, block - wi);
break;
}
if (comparator.applyAsInt(work[wi], a[ti]) > 0) {
a[i] = a[ti++];
} else {
a[i] = work[wi++];
if (wi == block) break;
}
}
}
}
}
private static final int THRESHOLD_NAIVE = 50;
private static final int THRESHOLD_DOUBLING = 0;
private static int[] sais(int[] s, int upper) {
int n = s.length;
if (n == 0) return new int[0];
if (n == 1) return new int[]{0};
if (n == 2) {
if (s[0] < s[1]) {
return new int[]{0, 1};
} else {
return new int[]{1, 0};
}
}
if (n < THRESHOLD_NAIVE) {
return saNaive(s);
}
// if (n < THRESHOLD_DOUBLING) {
// return saDoubling(s);
// }
int[] sa = new int[n];
boolean[] ls = new boolean[n];
for (int i = n - 2; i >= 0; i--) {
ls[i] = s[i] == s[i + 1] ? ls[i + 1] : s[i] < s[i + 1];
}
int[] sumL = new int[upper + 1];
int[] sumS = new int[upper + 1];
for (int i = 0; i < n; i++) {
if (ls[i]) {
sumL[s[i] + 1]++;
} else {
sumS[s[i]]++;
}
}
for (int i = 0; i <= upper; i++) {
sumS[i] += sumL[i];
if (i < upper) sumL[i + 1] += sumS[i];
}
java.util.function.Consumer<int[]> induce = lms -> {
java.util.Arrays.fill(sa, -1);
int[] buf = new int[upper + 1];
System.arraycopy(sumS, 0, buf, 0, upper + 1);
for (int d : lms) {
if (d == n) continue;
sa[buf[s[d]]++] = d;
}
System.arraycopy(sumL, 0, buf, 0, upper + 1);
sa[buf[s[n - 1]]++] = n - 1;
for (int i = 0; i < n; i++) {
int v = sa[i];
if (v >= 1 && !ls[v - 1]) {
sa[buf[s[v - 1]]++] = v - 1;
}
}
System.arraycopy(sumL, 0, buf, 0, upper + 1);
for (int i = n - 1; i >= 0; i--) {
int v = sa[i];
if (v >= 1 && ls[v - 1]) {
sa[--buf[s[v - 1] + 1]] = v - 1;
}
}
};
int[] lmsMap = new int[n + 1];
java.util.Arrays.fill(lmsMap, -1);
int m = 0;
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lmsMap[i] = m++;
}
}
int[] lms = new int[m];
{
int p = 0;
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms[p++] = i;
}
}
}
induce.accept(lms);
if (m > 0) {
int[] sortedLms = new int[m];
{
int p = 0;
for (int v : sa) {
if (lmsMap[v] != -1) {
sortedLms[p++] = v;
}
}
}
int[] recS = new int[m];
int recUpper = 0;
recS[lmsMap[sortedLms[0]]] = 0;
for (int i = 1; i < m; i++) {
int l = sortedLms[i - 1], r = sortedLms[i];
int endL = (lmsMap[l] + 1 < m) ? lms[lmsMap[l] + 1] : n;
int endR = (lmsMap[r] + 1 < m) ? lms[lmsMap[r] + 1] : n;
boolean same = true;
if (endL - l != endR - r) {
same = false;
} else {
while (l < endL && s[l] == s[r]) {
l++;
r++;
}
if (l == n || s[l] != s[r]) same = false;
}
if (!same) {
recUpper++;
}
recS[lmsMap[sortedLms[i]]] = recUpper;
}
int[] recSA = sais(recS, recUpper);
for (int i = 0; i < m; i++) {
sortedLms[i] = lms[recSA[i]];
}
induce.accept(sortedLms);
}
return sa;
}
public static int[] suffixArray(int[] s, int upper) {
assert (0 <= upper);
for (int d : s) {
assert (0 <= d && d <= upper);
}
return sais(s, upper);
}
public static int[] suffixArray(int[] s)
{
int n = s.length;
int[] vals = Arrays.copyOf(s, n);
java.util.Arrays.sort(vals);
int p = 1;
for(int i = 1;i < n;i++){
if(vals[i] != vals[i-1]){
vals[p++] = vals[i];
}
}
int[] s2 = new int[n];
for(int i = 0;i < n;i++){
s2[i] = java.util.Arrays.binarySearch(vals, 0, p, s[i]);
}
return sais(s2, p);
}
public static int[] suffixArray(char[] s) {
int n = s.length;
int[] s2 = new int[n];
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return sais(s2, 255);
}
public static int[] suffixArray(java.lang.String s) {
return suffixArray(s.toCharArray());
}
public static int[] lcpArray(int[] s, int[] sa) {
int n = s.length;
assert (n >= 1);
int[] rnk = new int[n];
for (int i = 0; i < n; i++) {
rnk[sa[i]] = i;
}
int[] lcp = new int[n - 1];
int h = 0;
for (int i = 0; i < n; i++) {
if (h > 0) h--;
if (rnk[i] == 0) {
continue;
}
int j = sa[rnk[i] - 1];
for (; j + h < n && i + h < n; h++) {
if (s[j + h] != s[i + h]) break;
}
lcp[rnk[i] - 1] = h;
}
return lcp;
}
public static int[] lcpArray(char[] s, int[] sa) {
int n = s.length;
int[] s2 = new int[n];
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return lcpArray(s2, sa);
}
public static int[] lcpArray(java.lang.String s, int[] sa) {
return lcpArray(s.toCharArray(), sa);
}
public static int[] zAlgorithm(int[] s) {
int n = s.length;
if (n == 0) return new int[0];
int[] z = new int[n];
for (int i = 1, j = 0; i < n; i++) {
int k = j + z[j] <= i ? 0 : Math.min(j + z[j] - i, z[i - j]);
while (i + k < n && s[k] == s[i + k]) k++;
z[i] = k;
if (j + z[j] < i + z[i]) j = i;
}
z[0] = n;
return z;
}
public static int[] zAlgorithm(char[] s) {
int n = s.length;
if (n == 0) return new int[0];
int[] z = new int[n];
for (int i = 1, j = 0; i < n; i++) {
int k = j + z[j] <= i ? 0 : Math.min(j + z[j] - i, z[i - j]);
while (i + k < n && s[k] == s[i + k]) k++;
z[i] = k;
if (j + z[j] < i + z[i]) j = i;
}
z[0] = n;
return z;
}
public static int[] zAlgorithm(String s) {
return zAlgorithm(s.toCharArray());
}
public static class Node
{
public int id, first, len, freq;
public char c;
public Node firstChild;
public Node next;
public Node link;
private Node(int first, int len, char c, int id) {
this.first = first;
this.len = len;
this.c = c;
this.id = id;
this.freq = 0;
}
public Node next(char x)
{
for(Node ch = this.firstChild;ch != null;ch = ch.next){
if(ch.c == x)return ch;
}
return null;
}
public void add(Node x)
{
Node ch = this.firstChild;
this.firstChild = x;
x.next = ch;
}
@Override
public String toString() {
return "Node [id=" + id + ", first=" + first + ", len=" + len + ", freq=" + freq + ", c=" + c
+ ", firstChild=" + (firstChild != null ? firstChild.id : null) + ", sibling=" + (next != null ? next.id : null)
+ ", link=" + (link != null ? link.id : null) + "]";
}
}
public static class PalindromicTree {
public Node[] nodes; // [0]=hell, [1]=len0
public static PalindromicTree build(char[] s)
{
int n = s.length;
Node zero = new Node(-1, 0, (char)0, 1);
Node hell = new Node(-1, -1, (char)0, 0);
zero.link = hell;
hell.link = hell;
hell.add(zero);
Node[] nodes = new Node[n+2];
int p = 0;
nodes[p++] = hell;
nodes[p++] = zero;
Node cur = zero; // current suffix palindrome
for(int i = 0;i < n;i++){
char x = s[i];
while(i-cur.len-1 < 0 || s[i-cur.len-1] != x)cur = cur.link; // find xAx
Node xax = cur.next(x); // already exists
if(xax == null){
// new subpalindrome
xax = new Node(i-cur.len-1, cur.len+2, x, p);
nodes[p++] = xax;
cur.add(xax);
// make suffix link
if(xax.len == 1){
xax.link = zero;
}else{
Node b = cur.link;
while(true){
while(i-b.len-1 < 0 || s[i-b.len-1] != x)b = b.link; // find xBx
Node xbx = b.next(x);
if(xbx != null){
xax.link = xbx;
break;
}
}
}
}
// [i-cur.len-1, i]
xax.freq++; // increment regardless new or not
cur = xax;
}
for(int i = p-1;i >= 2;i--){
nodes[i].link.freq += nodes[i].freq;
}
PalindromicTree pt = new PalindromicTree();
pt.nodes = Arrays.copyOf(nodes, p);
return pt;
}
public String toDot(boolean next, boolean suffixLink)
{
StringBuilder sb = new StringBuilder("digraph{\n");
sb.append("graph[rankdir=LR];\n");
sb.append("node[shape=circle];\n");
for(Node n : nodes){
if(n != null){
if(suffixLink && n.link != null){
sb.append("\"" + n.id + "\"")
.append("->")
.append("\"" + n.link.id + "\"")
.append("[style=dashed];\n");
}
if(next){
for(Node ch = n.firstChild;ch != null;ch = ch.next){
sb.append("\"" + n.id + "\"")
.append("->")
.append("\"" + ch.id + "\"")
.append("[label=\"")
.append(ch.c == 0 ? ' ' : ch.c)
.append("\"];\n");
}
}
}
}
sb.append("}\n");
return sb.toString();
}
}
public static void main(String[] args) {
new No2606().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[][] nmi(int n, int m)
{
int[][] map = new int[n][];
for(int i = 0;i < n;i++)map[i] = na(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)); }
}