結果
| 問題 | No.1600 Many Shortest Path Problems |
| ユーザー |
 uwi
|
| 提出日時 | 2021-07-09 23:01:56 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 29,906 bytes |
| コンパイル時間 | 5,071 ms |
| コンパイル使用メモリ | 90,800 KB |
| 実行使用メモリ | 148,872 KB |
| 最終ジャッジ日時 | 2023-09-14 10:37:13 |
| 合計ジャッジ時間 | 33,846 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / 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 | 67 ms
50,388 KB |
| testcase_01 | AC | 68 ms
50,480 KB |
| testcase_02 | AC | 69 ms
50,504 KB |
| testcase_03 | AC | 69 ms
50,884 KB |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | AC | 70 ms
50,512 KB |
| testcase_07 | AC | 70 ms
50,656 KB |
| testcase_08 | AC | 75 ms
50,480 KB |
| testcase_09 | AC | 70 ms
48,572 KB |
| testcase_10 | RE | - |
| testcase_11 | RE | - |
| testcase_12 | RE | - |
| testcase_13 | RE | - |
| testcase_14 | WA | - |
| testcase_15 | AC | 70 ms
48,616 KB |
| testcase_16 | AC | 69 ms
50,376 KB |
| testcase_17 | RE | - |
| testcase_18 | WA | - |
| testcase_19 | AC | 71 ms
48,900 KB |
| testcase_20 | AC | 70 ms
50,620 KB |
| testcase_21 | RE | - |
| testcase_22 | AC | 70 ms
50,676 KB |
| testcase_23 | AC | 70 ms
50,372 KB |
| testcase_24 | WA | - |
| testcase_25 | AC | 70 ms
50,616 KB |
| testcase_26 | AC | 70 ms
50,528 KB |
| testcase_27 | AC | 70 ms
50,544 KB |
| testcase_28 | AC | 70 ms
50,284 KB |
| testcase_29 | RE | - |
| testcase_30 | RE | - |
| testcase_31 | RE | - |
| testcase_32 | RE | - |
| testcase_33 | AC | 70 ms
50,392 KB |
| testcase_34 | AC | 69 ms
50,496 KB |
| testcase_35 | WA | - |
| testcase_36 | WA | - |
| testcase_37 | RE | - |
| testcase_38 | RE | - |
| testcase_39 | AC | 70 ms
50,384 KB |
| testcase_40 | RE | - |
| testcase_41 | WA | - |
| testcase_42 | RE | - |
| testcase_43 | RE | - |
| testcase_44 | RE | - |
| testcase_45 | WA | - |
| testcase_46 | RE | - |
| testcase_47 | WA | - |
| testcase_48 | RE | - |
| testcase_49 | AC | 71 ms
50,884 KB |
| testcase_50 | AC | 69 ms
50,896 KB |
| testcase_51 | AC | 71 ms
50,768 KB |
| testcase_52 | AC | 69 ms
50,496 KB |
| testcase_53 | AC | 70 ms
50,512 KB |
ソースコード
package contest210709;
import java.io.*;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
public class J {
InputStream is;
FastWriter out;
String INPUT = "";
public void solve()
{
int n = ni(), m = ni();
int[][] es = new int[m][];
for(int i = 0;i < m;i++){
es[i] = new int[]{ni()-1, ni()-1, i};
}
final int mod = 100000007;
DJSet ds = new DJSet(n);
int[] from = new int[n];
int[] to = new int[n];
int[] ws = new int[n];
boolean[] used = new boolean[m];
long[] p2 = enumPows(2, n+5, mod);
int p = 0;
for(int i = 0;i < m;i++){
if(!ds.union(es[i][0], es[i][1])){
from[p] = es[i][0];
to[p] = es[i][1];
ws[p] = i+1;
used[i] = true;
p++;
}
}
for(int i = 0;i < n;i++){
if(ds.upper[i] < 0){
from[p] = i;
to[p] = n;
ws[p] = -1;
p++;
}
}
assert p == n;
int[][][] g = packWU(n+1, from, to, ws);
int[][] pars = parents(g, n);
int[] ord = pars[1], par = pars[0], pw = pars[4], dep = pars[2];
LCAFast2 lf = LCAFast2.build(packU(n+1, from, to), n);
HeavyLightDecomposition hld = new HeavyLightDecomposition(packU(n+1, from, to), par, ord, dep);
LST[] unpainted = new LST[hld.m];
for(int i = 0;i < hld.m;i++){
unpainted[i] = new LST(hld.cluspath[i].length);
unpainted[i].setRange(hld.cluspath[i].length);
}
long[] dp = new long[n+1];
for(int i = 1;i < n+1;i++){
int cur = ord[i];
if(par[cur] == n){
dp[cur] = 0;
}else{
dp[cur] = dp[par[cur]] + p2[pw[cur]];
if(dp[cur] >= mod)dp[cur] -= mod;
}
}
int[] alts = new int[n+1];
Arrays.fill(alts, -1);
for(int i = 0;i < m;i++){
if(!used[i]){
int f = es[i][0];
int t = es[i][1];
int lca = lf.lca(f, t);
for(int u : new int[]{f, t}) {
for (int x = u; ; ) {
int cx = hld.clus[x];
int l = cx == hld.clus[lca] ? hld.clusiind[lca] : -1;
int r = hld.clusiind[x];
while (true) {
int pr = unpainted[cx].prev(r);
if (pr != -1 && pr > l) {
unpainted[cx].unset(pr);
alts[hld.cluspath[cx][pr]] = i + 1;
} else {
break;
}
}
if (cx == hld.clus[lca]) break;
x = par[hld.cluspath[cx][0]];
}
}
}
}
for(int Q = ni();Q > 0;Q--){
int x = ni()-1, y = ni()-1, z = ni()-1;
if(!ds.equiv(x, y)){
out.println(-1);
continue;
}
int lca = lf.lca(x, y);
boolean hit = false;
int tar = dep[es[z][0]] > dep[es[z][1]] ? es[z][0] : es[z][1];
if(used[z]){
if(dep[x] >= dep[tar] && dep[tar] > dep[lca] && lf.anc(x, dep[x] - dep[tar]) == tar){
hit = true;
}
if(dep[y] >= dep[tar] && dep[tar] > dep[lca] && lf.anc(y, dep[y] - dep[tar]) == tar){
hit = true;
}
}
long ans = get(x, y, lf, dp);
if(hit){
if(alts[tar] == -1){
out.println(-1);
continue;
}
int s = es[alts[tar]-1][0], t = es[alts[tar]-1][1];
// x-tar-s?
boolean pass = false;
int ll = lf.lca(x, s);
if(dep[x] >= dep[tar] && dep[tar] > dep[ll] && lf.anc(x, dep[x] - dep[tar]) == tar){
pass = true;
}
if(dep[s] >= dep[tar] && dep[tar] > dep[ll] && lf.anc(s, dep[s] - dep[tar]) == tar){
pass = true;
}
if(pass){
int d = s; s = t; t = d;
}
// tr(x, s, y, t);
ans = (get(x, s, lf, dp) + get(y, t, lf, dp) + p2[alts[tar]]) % mod;
}
out.println(ans);
}
}
final int mod = 1000000007;
long get(int x, int y, LCAFast2 lf, long[] dp)
{
int lca = lf.lca(x, y);
return (dp[x] + dp[y] - 2*dp[lca] + 2*mod) % mod;
}
public static class LST {
public long[][] set;
public int n;
// public int size;
public LST(int n) {
this.n = n;
int d = 1;
for(int m = n;m > 1;m>>>=6, d++);
set = new long[d][];
for(int i = 0, m = n>>>6;i < d;i++, m>>>=6){
set[i] = new long[m+1];
}
// size = 0;
}
// [0,r)
public LST setRange(int r)
{
for(int i = 0;i < set.length;i++, r=r+63>>>6){
for(int j = 0;j < r>>>6;j++){
set[i][j] = -1L;
}
if((r&63) != 0)set[i][r>>>6] |= (1L<<r)-1;
}
return this;
}
// [0,r)
public LST unsetRange(int r)
{
if(r >= 0){
for(int i = 0;i < set.length;i++, r=r+63>>>6){
for(int j = 0;j < r+63>>>6;j++){
set[i][j] = 0;
}
if((r&63) != 0)set[i][r>>>6] &= ~((1L<<r)-1);
}
}
return this;
}
public LST set(int pos)
{
if(pos >= 0 && pos < n){
// if(!get(pos))size++;
for(int i = 0;i < set.length;i++, pos>>>=6){
set[i][pos>>>6] |= 1L<<pos;
}
}
return this;
}
public LST unset(int pos)
{
if(pos >= 0 && pos < n){
// if(get(pos))size--;
for(int i = 0;i < set.length && (i == 0 || set[i-1][pos] == 0L);i++, pos>>>=6){
set[i][pos>>>6] &= ~(1L<<pos);
}
}
return this;
}
public boolean get(int pos)
{
return pos >= 0 && pos < n && set[0][pos>>>6]<<~pos<0;
}
public LST toggle(int pos)
{
return get(pos) ? unset(pos) : set(pos);
}
public int prev(int pos)
{
for(int i = 0;i < set.length && pos >= 0;i++, pos>>>=6, pos--){
int pre = prev(set[i][pos>>>6], pos&63);
if(pre != -1){
pos = pos>>>6<<6|pre;
while(i > 0)pos = pos<<6|63-Long.numberOfLeadingZeros(set[--i][pos]);
return pos;
}
}
return -1;
}
public int next(int pos)
{
for(int i = 0;i < set.length && pos>>>6 < set[i].length;i++, pos>>>=6, pos++){
int nex = next(set[i][pos>>>6], pos&63);
if(nex != -1){
pos = pos>>>6<<6|nex;
while(i > 0)pos = pos<<6|Long.numberOfTrailingZeros(set[--i][pos]);
return pos;
}
}
return -1;
}
private static int prev(long set, int n)
{
long h = set<<~n;
if(h == 0L)return -1;
return -Long.numberOfLeadingZeros(h)+n;
}
private static int next(long set, int n)
{
long h = set>>>n;
if(h == 0L)return -1;
return Long.numberOfTrailingZeros(h)+n;
}
@Override
public String toString()
{
List<Integer> list = new ArrayList<Integer>();
for(int pos = next(0);pos != -1;pos = next(pos+1)){
list.add(pos);
}
return list.toString();
}
}
public static class HeavyLightDecomposition {
public int[][] g;
public int[] clus;
public int[][] cluspath;
public int[] clusiind;
public int[] par, dep;
public int m;
public HeavyLightDecomposition(int[][] g, int[] par, int[] ord, int[] dep) {
init(g, par, ord, dep);
}
public void init(int[][] g, int[] par, int[] ord, int[] dep) {
clus = decomposeToHeavyLight(g, par, ord);
cluspath = clusPaths(clus, ord);
clusiind = clusIInd(cluspath, g.length);
this.m = cluspath.length;
this.par = par;
this.dep = dep;
this.g = g;
}
public static int[] decomposeToHeavyLight(int[][] g, int[] par, int[] ord) {
int n = g.length;
int[] size = new int[n];
Arrays.fill(size, 1);
for (int i = n - 1; i > 0; i--) size[par[ord[i]]] += size[ord[i]];
int[] clus = new int[n];
Arrays.fill(clus, -1);
int p = 0;
for (int i = 0; i < n; i++) {
int u = ord[i];
if (clus[u] == -1) clus[u] = p++;
// centroid path (not heavy path)
int argmax = -1;
for (int v : g[u]) {
if (par[u] != v && (argmax == -1 || size[v] > size[argmax])) argmax = v;
}
if (argmax != -1) clus[argmax] = clus[u];
}
return clus;
}
public static int[][] clusPaths(int[] clus, int[] ord) {
int n = clus.length;
int[] rp = new int[n];
int sup = 0;
for (int i = 0; i < n; i++) {
rp[clus[i]]++;
sup = Math.max(sup, clus[i]);
}
sup++;
int[][] row = new int[sup][];
for (int i = 0; i < sup; i++) row[i] = new int[rp[i]];
for (int i = n - 1; i >= 0; i--) {
row[clus[ord[i]]][--rp[clus[ord[i]]]] = ord[i];
}
return row;
}
public static int[] clusIInd(int[][] clusPath, int n) {
int[] iind = new int[n];
for (int[] path : clusPath) {
for (int i = 0; i < path.length; i++) {
iind[path[i]] = i;
}
}
return iind;
}
public int lca(int x, int y) {
int rx = cluspath[clus[x]][0];
int ry = cluspath[clus[y]][0];
while (clus[x] != clus[y]) {
if (dep[rx] > dep[ry]) {
x = par[rx];
rx = cluspath[clus[x]][0];
} else {
y = par[ry];
ry = cluspath[clus[y]][0];
}
}
return clusiind[x] > clusiind[y] ? y : x;
}
public int ancestor(int x, int v) {
while (x != -1) {
if (v <= clusiind[x]) return cluspath[clus[x]][clusiind[x] - v];
v -= clusiind[x] + 1;
x = par[cluspath[clus[x]][0]];
}
return x;
}
// [iord[x], right[x])
public int[][] makeRights() {
int root = -1;
int n = g.length;
for (int i = 0; i < n; i++) if (par[i] == -1) root = i;
int[] ord = new int[n];
int[] right = new int[n];
int[] curs = new int[n];
int[] inds = new int[n];
int sp = 0, p = 0;
curs[sp++] = root;
while (sp > 0) {
int cur = curs[sp - 1];
int ind = inds[sp - 1];
inds[sp - 1]++;
if (ind == 0) {
ord[p++] = cur;
for (int e : g[cur]) {
if (par[cur] == e) continue;
if (clus[cur] == clus[e]) {
curs[sp] = e;
inds[sp] = 0;
sp++;
break;
}
}
} else if (ind - 1 < g[cur].length) {
int e = g[cur][ind - 1];
if (e == par[cur]) continue;
if (clus[cur] == clus[e]) continue;
curs[sp] = e;
inds[sp] = 0;
sp++;
} else {
right[cur] = p;
sp--;
}
}
int[] iord = new int[n];
for (int i = 0; i < n; i++) iord[ord[i]] = i;
return new int[][]{ord, iord, right};
}
///// templates
public void queryNew(int u, int anc, int v) {
// for(int x = u;;){
// int cx = hld.clus[x];
// int l = cx == hld.clus[anc] ? hld.clusiind[anc] : 0;
// int r = hld.clusiind[x];
//
// st[cx].add(l, r+1, v); // path query
// ans += sumRangeFenwick(ft0, ft1, iord[x]) - sumRangeFenwick(ft0, ft1, iord[hld.cluspath[cx][0]] + l - 1); // subtree query
//
// if(cx == hld.clus[anc])break;
// x = par[hld.cluspath[cx][0]];
// }
}
/**
* xとその先祖ancについて経路x-ancでのクエリを処理するテンプレ
* @param x
* @param anc
*/
// public void query(int x, int anc)
// {
// int cx = hld.clus[x]; // cluster
// int ind = hld.clusiind[x]; // pos in cluster
// while(cx != hld.clus[anc]){
// // TODO クラスタcxの0~indについて逆向きにクエリ処理
// // st[cx].add(0, ind+1, v);
// int con = par[hld.cluspath[cx][0]];
// ind = hld.clusiind[con];
// cx = hld.clus[con];
// }
// // TODO clusiind[anc]~indについて逆向きにクエリ処理
// // st[cx].add(hld.clusiind[anc], ind+1, v);
// }
}
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 class LCAFast2 {
public int n, h;
public int[][] bigst;
public int[][] bigind;
public long[][] smallb;
public int[] vs, first, deps;
public int lca(int a, int b)
{
return vs[rmqpos(Math.min(first[a], first[b]), Math.max(first[a], first[b]))];
}
public int pointOnPath(int a, int b, int dfroma)
{
int lca = lca(a, b);
if(dfroma <= dep(a) - dep(lca)){
return anc(a, dfroma);
}
int dfromb = dep(b) - dep(lca) - (dfroma - (dep(a) - dep(lca)));
if(dfromb < 0)return -1;
return anc(b, dfromb);
}
public int anc(int a, int d)
{
int da = dep(a);
if(da < d)return -1;
int danc = da - d;
int low = 0, high = first[a] + 1;
while(high - low > 1){
int h = high+low>>1;
if(rmqval(h, first[a]) <= danc){
low = h;
}else {
high = h;
}
}
return vs[low];
}
public int d(int a, int b)
{
return dep(a) + dep(b) - 2 * rmqval(Math.min(first[a], first[b]), Math.max(first[a], first[b]));
}
public int dep(int x)
{
return deps[first[x]];
}
public int rmqpos(int l, int r)
{
if(l > r)return -1;
int cl = l>>>6;
int cr = r>>>6;
if(cl == cr){
return argmax(smallb[l&63][cl], r-l+1) + l;
}else{
int min = deps[l] - max(smallb[l&63][cl], 63-(l&63)+1);
int pos = argmax(smallb[l&63][cl], 63-(l&63)+1) + l;
{
int can = deps[r>>>6<<6] - max(smallb[0][cr], (r&63)-0+1);
if(can < min){
min = can;
pos = argmax(smallb[0][cr], (r&63)-0+1) + (r>>>6<<6);
}
}
if(cl+1 <= cr-1){
int len = (cr-1)-(cl+1)+1;
int h = 31-Integer.numberOfLeadingZeros(len);
{
int can = bigst[h][cl+1];
if(can < min){
min = can;
pos = bigind[h][cl+1];
}
}
{
int can = bigst[h][cr-1-(1<<h)+1];
if(can < min){
min = can;
pos = bigind[h][cr-1-(1<<h)+1];
}
}
}
return pos;
}
}
public int rmqval(int l, int r)
{
if(l > r)return -1;
int cl = l>>>6;
int cr = r>>>6;
if(cl == cr){
return deps[l] - max(smallb[l&63][cl], r-l+1);
}else{
int min = deps[l] - max(smallb[l&63][cl], 63-(l&63)+1);
min = Math.min(min, deps[r>>>6<<6] - max(smallb[0][cr], (r&63)-0+1));
if(cl+1 <= cr-1){
int len = (cr-1)-(cl+1)+1;
int h = 31-Integer.numberOfLeadingZeros(len);
min = Math.min(min, bigst[h][cl+1]);
min = Math.min(min, bigst[h][cr-1-(1<<h)+1]);
}
return min;
}
}
public static LCAFast2 build(int[][] g, int root)
{
LCAFast2 ret = new LCAFast2();
int[][] et = eulerTour(g, root);
int[] vs = et[0], deps = et[1], first = et[2];
ret.vs = vs;
ret.first = first;
ret.deps = deps;
int n = deps.length;
int u = n+63>>>6;
int h = 31-Integer.numberOfLeadingZeros(u) + 1;
int[][] bigst = new int[h][];
int[][] bigind = new int[h][];
int[] cup = new int[u];
int[] cupind = new int[u];
Arrays.fill(cup, Integer.MAX_VALUE);
for(int i = 0;i < n;i++){
if(deps[i] < cup[i>>>6]){
cup[i>>>6] = deps[i];
cupind[i>>>6] = i;
}
}
bigst[0] = cup;
bigind[0] = cupind;
for(int i = 1;i < h;i++){
bigst[i] = new int[u-(1<<i)+1];
bigind[i] = new int[u-(1<<i)+1];
for(int j = 0;j + (1<<i) <= u;j++){
if(bigst[i-1][j] < bigst[i-1][j+(1<<i-1)]){
bigst[i][j] = bigst[i-1][j];
bigind[i][j] = bigind[i-1][j];
}else{
bigst[i][j] = bigst[i-1][j+(1<<i-1)];
bigind[i][j] = bigind[i-1][j+(1<<i-1)];
}
}
}
long[][] smallb = new long[64][u];
for(int i = 0;i < u;i++){
long x = 0;
for(int j = 0;j < 63 && (i<<6|j+1) < n;j++){
if(deps[i<<6|j] > deps[i<<6|j+1]){
x |= 1L<<j;
}
}
long val = 0;
for(int j = 63;j >= 0;j--){
val <<= 1;
if(x<<~j<0){
val |= 1L;
}else{
val &= val - 1;
}
smallb[j][i] = val;
}
//
// for(int j = 0;j < 64;j++){
// smallb[j][i] = make(x>>>j);
// }
}
ret.n = n; ret.h = h;
ret.bigst = bigst;
ret.bigind = bigind;
ret.smallb = smallb;
return ret;
}
public static int[][] eulerTour(int[][] g, int root)
{
int n = g.length;
int[] vs = new int[2*n-1];
int[] deps = new int[2*n-1];
int[] first = new int[n];
Arrays.fill(first, -1);
int p = 0;
int[] stack = new int[n];
int[] inds = new int[n];
int sp = 0;
stack[sp++] = root;
outer:
while(sp > 0){
int cur = stack[sp-1], ind = inds[sp-1];
vs[p] = cur;
deps[p] = sp-1;
if(first[cur] == -1)first[cur] = p;
p++;
while(ind < g[cur].length){
int nex = g[cur][ind++];
if(first[nex] == -1){
inds[sp-1] = ind;
stack[sp] = nex;
inds[sp] = 0;
sp++;
continue outer;
}
}
inds[sp-1] = ind;
if(ind == g[cur].length)sp--;
}
return new int[][]{vs, deps, first};
}
// TinyRMQ
public static long make(long x)
{
int h = 0;
int max = 0;
long ret = 0;
for(int i = 0;i < 64;i++){
if(x<<~i<0){
h++;
}else{
h--;
}
if(h > max){
max = h;
ret |= 1L<<i;
}
}
return ret;
}
public static int max(long x, int r)
{
assert r > 0;
return Long.bitCount(x&(1L<<r-1)-1);
}
public static int argmax(long x, int r)
{
assert r > 0;
return 64-Long.numberOfLeadingZeros(x&(1L<<r-1)-1);
}
}
public static long[] enumPows(int a, int n, int mod)
{
a %= mod;
long[] pows = new long[n+1];
pows[0] = 1;
for(int i = 1;i <= n;i++)pows[i] = pows[i-1] * a % mod;
return pows;
}
public static int[][][] packWU(int n, int[] from, int[] to, int[] w) {
return packWU(n, from, to, w, from.length);
}
public static int[][][] packWU(int n, int[] from, int[] to, int[] w, 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]][2];
for (int i = 0; i < sup; i++) {
--p[from[i]];
g[from[i]][p[from[i]]][0] = to[i];
g[from[i]][p[from[i]]][1] = w[i];
--p[to[i]];
g[to[i]][p[to[i]]][0] = from[i];
g[to[i]][p[to[i]]][1] = w[i];
}
return g;
}
public static int[][] parents(int[][][] g, int root) {
int n = g.length;
int[] par = new int[n];
Arrays.fill(par, -1);
int[] dw = new int[n];
int[] pw = new int[n];
int[] dep = new int[n];
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[0]) {
q[r++] = nex[0];
par[nex[0]] = cur;
dep[nex[0]] = dep[cur] + 1;
dw[nex[0]] = dw[cur] + nex[1];
pw[nex[0]] = nex[1];
}
}
}
return new int[][]{par, q, dep, dw, pw};
}
public static class DJSet {
public int[] upper;
public DJSet(int n) {
upper = new int[n];
Arrays.fill(upper, -1);
}
public int root(int x) {
return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
}
public boolean equiv(int x, int y) {
return root(x) == root(y);
}
public boolean union(int x, int y) {
x = root(x);
y = root(y);
if (x != y) {
if (upper[y] < upper[x]) {
int d = x;
x = y;
y = d;
}
upper[x] += upper[y];
upper[y] = x;
}
return x == y;
}
public int count() {
int ct = 0;
for (int u : upper) if (u < 0) ct++;
return ct;
}
public int[][] toBucket() {
int n = upper.length;
int[][] ret = new int[n][];
int[] rp = new int[n];
for (int i = 0; i < n; i++) if (upper[i] < 0) ret[i] = new int[-upper[i]];
for (int i = 0; i < n; i++) {
int r = root(i);
ret[r][rp[r]++] = i;
}
return ret;
}
}
public static void main(String[] args) {
new J().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)); }
}