結果
| 問題 | No.2750 Number of Prime Factors |
| ユーザー |
 VvyLw
|
| 提出日時 | 2024-05-10 22:58:41 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
AC
|
| 実行時間 | 116 ms / 2,000 ms |
| コード長 | 56,775 bytes |
| コンパイル時間 | 7,096 ms |
| コンパイル使用メモリ | 109,708 KB |
| 実行使用メモリ | 52,416 KB |
| 最終ジャッジ日時 | 2024-12-20 07:08:10 |
| 合計ジャッジ時間 | 8,824 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（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 | 104 ms
51,548 KB |
| testcase_01 | AC | 104 ms
51,732 KB |
| testcase_02 | AC | 113 ms
51,668 KB |
| testcase_03 | AC | 113 ms
51,616 KB |
| testcase_04 | AC | 112 ms
52,084 KB |
| testcase_05 | AC | 111 ms
52,064 KB |
| testcase_06 | AC | 101 ms
51,584 KB |
| testcase_07 | AC | 113 ms
51,564 KB |
| testcase_08 | AC | 111 ms
52,028 KB |
| testcase_09 | AC | 96 ms
51,600 KB |
| testcase_10 | AC | 115 ms
51,924 KB |
| testcase_11 | AC | 111 ms
51,576 KB |
| testcase_12 | AC | 104 ms
51,596 KB |
| testcase_13 | AC | 113 ms
51,660 KB |
| testcase_14 | AC | 103 ms
51,680 KB |
| testcase_15 | AC | 116 ms
52,284 KB |
| testcase_16 | AC | 116 ms
52,416 KB |
| testcase_17 | AC | 104 ms
51,836 KB |
| testcase_18 | AC | 107 ms
51,816 KB |
| testcase_19 | AC | 116 ms
51,980 KB |
| testcase_20 | AC | 101 ms
51,588 KB |
ソースコード
package yukicoder;
import static java.lang.Math.*;
import java.io.Closeable;
import java.io.Flushable;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Formatter;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.Random;
import java.util.function.DoublePredicate;
import java.util.function.IntPredicate;
import java.util.function.IntUnaryOperator;
import java.util.function.LongPredicate;
import java.util.function.LongUnaryOperator;
import java.util.function.UnaryOperator;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
class Main {
public static void main(final String[] args) {
final long begin = System.currentTimeMillis(), end;
IntStream.range(0, VvyLw.MULTI ? VvyLw.io.ni() : 1).mapToObj(VvyLw::solve).filter(Objects::nonNull).forEach(VvyLw.io::out);
end = System.currentTimeMillis();
VvyLw.io.dump(end - begin + "ms");
VvyLw.io.close();
}
}
final class VvyLw extends Utility {
static final IO io = new IO(System.in, System.out, System.err, false);
static final Random rd = new Random();
static final boolean MULTI = false;
static final int INF = 1 << 30;
static final long LINF = (1L << 61) - 1;
static final double EPS = 1e-18;
static final int MOD = 998244353;
static final int M0D = (int) 1e9 + 7;
static final int[] dx = {0, -1, 1, 0, 0, -1, -1, 1, 1};
static final int[] dy = {0, 0, 0, -1, 1, -1, 1, -1, 1};
static final Object solve(final int Huitloxopetl) {
final long[] p = {2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230L, 200560490130L, 7420738134810L, 304250263527210L, 13082761331670030L, 614889782588491410L};
final long n = io.nl();
return upperBound(p, n);
}
}
class Utility {
protected static final String yes(final boolean ok){ return ok ? "Yes" : "No"; }
protected static final String no(final boolean ok){ return yes(!ok); }
protected static final long sqr(final long x){ return x * x; }
protected static final long cub(final long x){ return x * x * x; }
protected static final int mod(long n, final int m) {
n %= m;
return (int) (n < 0 ? n + m : n);
}
protected static final long mod(long n, final long m) {
n %= m;
return n < 0 ? n + m : n;
}
protected static final double log(final double x, final long base){ return Math.log(x) / Math.log(base); }
protected static final long intCeil(final long a, final long b){ return a == 0 ? 0 : (a - 1) / b + 1; }
protected static final double intRound(final double a, final long b, final int c) {
final long d = powi(10, c);
return rint((a * d) / b) / d;
}
protected static final long powi(long a, int b) {
long res = 1;
while(b > 0) {
if(b % 2 == 1) {
res *= a;
}
a *= a;
b >>= 1;
}
return res;
}
protected static final long modPow(long a, long b, final long m) {
long res = 1;
while(b > 0) {
if(b % 2 == 1) {
res *= a;
res = mod(res, m);
}
a *= a;
a = mod(a, m);
b >>= 1;
}
return res;
}
protected static final long inv(long a, final long m) {
long b = m, u = 1, v = 0;
while(b > 0) {
final long t = a / b;
a -= t * b;
a ^= b;
b ^= a;
a ^= b;
u -= t * v;
u ^= v;
v ^= u;
u ^= v;
}
return mod(u, m);
}
protected static final long lcm(final long a, final long b){ return a / gcd(a, b) * b; }
protected static final long lcm(final int... a){ return Arrays.stream(a).asLongStream().reduce(1, (x, y) -> lcm(x, y)); }
protected static final long lcm(final long... a){ return Arrays.stream(a).reduce(1, (x, y) -> lcm(x, y)); }
protected static final long gcd(final long a, final long b){ return b > 0 ? gcd(b, a % b) : a; }
protected static final int gcd(final int... a){ return Arrays.stream(a).reduce(0, (x, y) -> (int) gcd(x, y)); }
protected static final long gcd(final long... a){ return Arrays.stream(a).reduce(0, (x, y) -> gcd(x, y)); }
protected static final int min(final int... a){ return Arrays.stream(a).min().getAsInt(); }
protected static final long min(final long... a){ return Arrays.stream(a).min().getAsLong(); }
protected static final double min(final double... a){ return Arrays.stream(a).min().getAsDouble(); }
protected static final int max(final int... a){ return Arrays.stream(a).max().getAsInt(); }
protected static final long max(final long... a){ return Arrays.stream(a).max().getAsLong(); }
protected static final double max(final double... a){ return Arrays.stream(a).max().getAsDouble(); }
protected static final long sum(final int... a){ return Arrays.stream(a).asLongStream().sum(); }
protected static final long sum(final long... a){ return Arrays.stream(a).sum(); }
protected static final double sum(final double... a){ return Arrays.stream(a).sum(); }
protected static final long prod(final int... a){ return Arrays.stream(a).asLongStream().reduce(1, (x, y) -> x * y); }
protected static final long prod(final long... a){ return Arrays.stream(a).reduce(1, (x, y) -> x * y); }
protected static final double prod(final double... a){ return Arrays.stream(a).reduce(1, (x, y) -> x * y); }
protected static final double ave(final int... a){ return Arrays.stream(a).average().getAsDouble(); }
protected static final double ave(final long... a){ return Arrays.stream(a).average().getAsDouble(); }
protected static final double ave(final double... a){ return Arrays.stream(a).average().getAsDouble(); }
protected static final double median(final int[] a) {
assert isSorted(a);
final int m = a.length / 2;
return a.length % 2 != 0 ? a[m] : (a[m - 1] + a[m]) / 2.0;
}
protected static final double median(final long[] a) {
assert isSorted(a);
final int m = a.length / 2;
return a.length % 2 != 0 ? a[m] : (a[m - 1] + a[m]) / 2.0;
}
protected static final double median(final double[] a) {
assert isSorted(a);
final int m = a.length / 2;
return a.length % 2 != 0 ? a[m] : (a[m - 1] + a[m]) / 2;
}
protected static final long[] div(final long n) {
final ArrayList<Long> d = new ArrayList<>();
for(long i = 1; i * i <= n; ++i) {
if(n % i == 0) {
d.add(i);
if(i * i != n) {
d.add(n / i);
}
}
}
return d.stream().mapToLong(i -> i).sorted().toArray();
}
protected static final IntPair[] primeFactor(long n) {
final ArrayList<IntPair> pf = new ArrayList<>();
for(long i = 2; i * i <= n; ++i) {
if(n % i != 0) {
continue;
}
int cnt = 0;
while(n % i == 0) {
cnt++;
n /= i;
}
pf.add(IntPair.of(i, cnt));
}
if(n != 1) {
pf.add(IntPair.of(n, 1));
}
return pf.toArray(IntPair[]::new);
}
protected static final long eulerPhi(long n) {
long res = n;
for(long i = 2; i * i <= n; ++i) {
if(n % i == 0) {
res -= res / i;
while(n % i == 0) {
n /= i;
}
}
}
if(n > 1) {
res -= res / n;
}
return res;
}
protected static final long sigma(final long n){ return n * (n + 1) / 2; }
protected static final long sigma(final long a, final long b) {
assert a <= b;
return sigma(b) - sigma(a - 1);
}
protected static final long fact(int n) {
long res = 1;
while(n > 0) {
res *= n--;
}
return res;
}
protected static final long fact(int n, final long mod) {
long res = 1;
while(n > 0) {
res *= n--;
res %= mod;
}
return res;
}
protected static final long perm(final int n, final int r) {
int m = n;
long res = 1;
while(m > n - r) {
res *= m--;
}
return res;
}
protected static final long perm(final int n, final int r, final long mod) {
int m = n;
long res = 1;
while(m > n - r) {
res *= m--;
res %= mod;
}
return res;
}
protected static final long binom(final int n, final int r) {
if(r < 0 || n < r) {
return 0;
}
int tmp = n;
long res = 1;
for(int i = 1; i <= min(n - r, r); ++i) {
res *= tmp--;
res /= i;
}
return res;
}
protected static final long binom(final int n, final int r, final long mod) {
if(r < 0 || n < r) {
return 0;
}
int tmp = n;
long res = 1;
for(int i = 1; i <= min(n - r, r); ++i) {
res *= tmp--;
res %= mod;
res /= i;
res %= mod;
}
return res;
}
protected static final boolean isInt(final double n){ return n == (long) floor(n); }
protected static final boolean isSqr(final long n){ return isInt(sqrt(n)); }
protected static final boolean isPrime(final long n) {
if(n == 1) {
return false;
}
for(long i = 2; i * i <= n; ++i) {
if(n % i == 0) {
return false;
}
}
return true;
}
protected static final boolean scope(final int l, final int x, final int r){ return l <= x && x <= r; }
protected static final boolean scope(final long l, final long x, final long r){ return l <= x && x <= r; }
protected static final boolean scope(final double l, final double x, final double r){ return l <= x && x <= r; }
protected static final boolean isBit(final long i, final long j){ return (i >> j & 1) == 1; }
protected static final boolean nextPerm(final int[] a) {
try {
final int[] res = nextPermutation(a);
System.arraycopy(res, 0, a, 0, a.length);
return true;
} catch(final NullPointerException e) {
Arrays.sort(a);
return false;
}
}
protected static final boolean nextPerm(final long[] a) {
try {
final long[] res = nextPermutation(a);
System.arraycopy(res, 0, a, 0, a.length);
return true;
} catch(final NullPointerException e) {
Arrays.sort(a);
return false;
}
}
protected static final boolean nextPerm(final double[] a) {
try {
final double[] res = nextPermutation(a);
System.arraycopy(res, 0, a, 0, a.length);
return true;
} catch(final NullPointerException e) {
Arrays.sort(a);
return false;
}
}
protected static final boolean nextPerm(final char[] a) {
try {
final char[] res = nextPermutation(a);
System.arraycopy(res, 0, a, 0, a.length);
return true;
} catch(final NullPointerException e) {
Arrays.sort(a);
return false;
}
}
protected static final boolean prevPerm(final int[] a) {
try {
final int[] res = prevPermutation(a);
System.arraycopy(res, 0, a, 0, a.length);
return true;
} catch(final NullPointerException e) {
final int[] res = reverse(sorted(a));
System.arraycopy(res, 0, a, 0, a.length);
return false;
}
}
protected static final boolean prevPerm(final long[] a) {
try {
final long[] res = prevPermutation(a);
System.arraycopy(res, 0, a, 0, a.length);
return true;
} catch(final NullPointerException e) {
final long[] res = reverse(sorted(a));
System.arraycopy(res, 0, a, 0, a.length);
return false;
}
}
protected static final boolean prevPerm(final double[] a) {
try {
final double[] res = prevPermutation(a);
System.arraycopy(res, 0, a, 0, a.length);
return true;
} catch(final NullPointerException e) {
final double[] res = reverse(sorted(a));
System.arraycopy(res, 0, a, 0, a.length);
return false;
}
}
protected static final boolean prevPerm(final char[] a) {
try {
final char[] res = prevPermutation(a);
System.arraycopy(res, 0, a, 0, a.length);
return true;
} catch(final NullPointerException e) {
final char[] res = reverse(sorted(a));
System.arraycopy(res, 0, a, 0, a.length);
return false;
}
}
private static final int[] nextPermutation(final int[] a) {
for(int i = a.length; --i > 0;) {
if(a[i - 1] < a[i]) {
final int j = find(a[i - 1], a, i, a.length - 1);
swap(a, i - 1, j);
Arrays.sort(a, i, a.length);
return a;
}
}
return null;
}
private static final long[] nextPermutation(final long[] a) {
for(int i = a.length; --i > 0;) {
if(a[i - 1] < a[i]) {
final int j = find(a[i - 1], a, i, a.length - 1);
swap(a, i - 1, j);
Arrays.sort(a, i, a.length);
return a;
}
}
return null;
}
private static final double[] nextPermutation(final double[] a) {
for(int i = a.length; --i > 0;) {
if(a[i - 1] < a[i]) {
final int j = find(a[i - 1], a, i, a.length - 1);
swap(a, i - 1, j);
Arrays.sort(a, i, a.length);
return a;
}
}
return null;
}
private static final char[] nextPermutation(final char[] a) {
for(int i = a.length; --i > 0;) {
if(a[i - 1] < a[i]) {
final int j = find(a[i - 1], a, i, a.length - 1);
swap(a, i - 1, j);
Arrays.sort(a, i, a.length);
return a;
}
}
return null;
}
private static final int[] prevPermutation(final int[] a) {
for(int i = a.length; --i > 0;) {
if(a[i - 1] > a[i]) {
final int j = findRev(a[i - 1], a, i, a.length - 1);
swap(a, i - 1, j);
Arrays.sort(a, i, a.length);
reverse(a, i, a.length - 1);
return a;
}
}
return null;
}
private static final long[] prevPermutation(final long[] a) {
for(int i = a.length; --i > 0;) {
if(a[i - 1] > a[i]) {
final int j = findRev(a[i - 1], a, i, a.length - 1);
swap(a, i - 1, j);
Arrays.sort(a, i, a.length);
reverse(a, i, a.length - 1);
return a;
}
}
return null;
}
private static final double[] prevPermutation(final double[] a) {
for(int i = a.length; --i > 0;) {
if(a[i - 1] > a[i]) {
final int j = findRev(a[i - 1], a, i, a.length - 1);
swap(a, i - 1, j);
Arrays.sort(a, i, a.length);
reverse(a, i, a.length - 1);
return a;
}
}
return null;
}
private static final char[] prevPermutation(final char[] a) {
for(int i = a.length; --i > 0;) {
if(a[i - 1] > a[i]) {
final int j = findRev(a[i - 1], a, i, a.length - 1);
swap(a, i - 1, j);
Arrays.sort(a, i, a.length);
reverse(a, i, a.length - 1);
return a;
}
}
return null;
}
private static final int find(final int dest, final int[] a, final int s, final int e) {
if(s == e) {
return s;
}
final int m = (s + e + 1) / 2;
return a[m] <= dest ? find(dest, a, s, m - 1) : find(dest, a, m, e);
}
private static final int find(final long dest, final long[] a, final int s, final int e) {
if(s == e) {
return s;
}
final int m = (s + e + 1) / 2;
return a[m] <= dest ? find(dest, a, s, m - 1) : find(dest, a, m, e);
}
private static final int find(final double dest, final double[] a, final int s, final int e) {
if(s == e) {
return s;
}
final int m = (s + e + 1) / 2;
return a[m] <= dest ? find(dest, a, s, m - 1) : find(dest, a, m, e);
}
private static final int find(final char dest, final char[] a, final int s, final int e) {
if(s == e) {
return s;
}
final int m = (s + e + 1) / 2;
return a[m] <= dest ? find(dest, a, s, m - 1) : find(dest, a, m, e);
}
private static final int findRev(final int dest, final int[] a, final int s, final int e) {
if(s == e) {
return s;
}
final int m = (s + e + 1) / 2;
return a[m] > dest ? findRev(dest, a, s, m - 1) : findRev(dest, a, m, e);
}
private static final int findRev(final long dest, final long[] a, final int s, final int e) {
if(s == e) {
return s;
}
final int m = (s + e + 1) / 2;
return a[m] > dest ? findRev(dest, a, s, m - 1) : findRev(dest, a, m, e);
}
private static final int findRev(final double dest, final double[] a, final int s, final int e) {
if(s == e) {
return s;
}
final int m = (s + e + 1) / 2;
return a[m] > dest ? findRev(dest, a, s, m - 1) : findRev(dest, a, m, e);
}
private static final int findRev(final char dest, final char[] a, final int s, final int e) {
if(s == e) {
return s;
}
final int m = (s + e + 1) / 2;
return a[m] > dest ? findRev(dest, a, s, m - 1) : findRev(dest, a, m, e);
}
private static void reverse(final int[] arr, int start, int end) {
while(start < end) {
swap(arr, start, end);
start++;
end--;
}
}
private static void reverse(final long[] arr, int start, int end) {
while(start < end) {
swap(arr, start, end);
start++;
end--;
}
}
private static void reverse(final double[] arr, int start, int end) {
while(start < end) {
swap(arr, start, end);
start++;
end--;
}
}
private static void reverse(final char[] arr, int start, int end) {
while(start < end) {
swap(arr, start, end);
start++;
end--;
}
}
protected static final int find(final int[] a, final int x) {
for(int i = 0; i < a.length; ++i) {
if(a[i] == x) {
return i;
}
}
return -1;
}
protected static final int find(final long[] a, final long x) {
for(int i = 0; i < a.length; ++i) {
if(a[i] == x) {
return i;
}
}
return -1;
}
protected static final int find(final double[] a, final double x) {
for(int i = 0; i < a.length; ++i) {
if(a[i] == x) {
return i;
}
}
return -1;
}
protected static final int find(final char[] s, final char c) {
for(int i = 0; i < s.length; ++i) {
if(s[i] == c) {
return i;
}
}
return -1;
}
protected static final int find(final Object[] a, final Object x) {
for(int i = 0; i < a.length; ++i) {
if(a[i].equals(x)) {
return i;
}
}
return -1;
}
protected static final int findRev(final int[] a, final int x) {
for(int i = a.length; --i >= 0;) {
if(a[i] == x) {
return i;
}
}
return -1;
}
protected static final int findRev(final long[] a, final long x) {
for(int i = a.length; --i >= 0;) {
if(a[i] == x) {
return i;
}
}
return -1;
}
protected static final int findRev(final double[] a, final double x) {
for(int i = a.length; --i >= 0;) {
if(a[i] == x) {
return i;
}
}
return -1;
}
protected static final int findRev(final char[] s, final char c) {
for(int i = s.length; --i >= 0;) {
if(s[i] == c) {
return i;
}
}
return -1;
}
protected static final int findRev(final Object[] a, final Object x) {
for(int i = a.length; --i >= 0;) {
if(a[i].equals(x)) {
return i;
}
}
return -1;
}
protected static final boolean binarySearch(final int[] a, final int x){ return Arrays.binarySearch(a, x) >= 0; }
protected static final boolean binarySearch(final long[] a, final long x){ return Arrays.binarySearch(a, x) >= 0; }
protected static final <T extends Comparable<? super T>> boolean binarySearch(final T[] a, final T x){ return Arrays.binarySearch(a, x) >= 0; }
protected static final <T extends Comparable<? super T>> boolean binarySearch(final List<T> a, final T x){ return Collections.binarySearch(a, x, null) >= 0; }
protected static final int lowerBound(final int[] a, final int x){ return bins(a.length, -1, (IntPredicate) y -> a[y] >= x); }
protected static final int lowerBound(final long[] a, final long x){ return bins(a.length, -1, (IntPredicate) y -> a[y] >= x); }
protected static final <T extends Comparable<? super T>> int lowerBound(final T[] a, final T x){ return lowerBound(Arrays.asList(a), x); }
protected static final <T extends Comparable<? super T>> int lowerBound(final List<T> a, final T x){ return ~Collections.binarySearch(a, x, (p, q) -> p.compareTo(q) >= 0 ? 1 : -1); }
protected static final int upperBound(final int[] a, final int x){ return bins(a.length, -1, (IntPredicate) y -> a[y] > x); }
protected static final int upperBound(final long[] a, final long x){ return bins(a.length, -1, (IntPredicate) y -> a[y] > x); }
protected static final <T extends Comparable<? super T>> int upperBound(final T[] a, final T x){ return upperBound(Arrays.asList(a), x); }
protected static final <T extends Comparable<? super T>> int upperBound(final List<T> a, final T x){ return ~Collections.binarySearch(a, x, (p, q) -> p.compareTo(q) > 0 ? 1 : -1); }
protected static final String sorted(final String s){ return s.chars().sorted().mapToObj(Character::toString).collect(Collectors.joining()); }
protected static final int[] sorted(final int[] a){ return Arrays.stream(a).sorted().toArray(); }
protected static final long[] sorted(final long[] a){ return Arrays.stream(a).sorted().toArray(); }
protected static final double[] sorted(final double[] a){ return Arrays.stream(a).sorted().toArray(); }
protected static final char[] sorted(final char[] a){ return sorted(new String(a)).toCharArray(); }
protected static final <T extends Comparable<? super T>> T[] sorted(final T[] a){ return Arrays.stream(a).sorted().toArray(n -> Arrays.copyOf(a, n)); }
protected static final boolean isSorted(final String s){ return s.equals(sorted(s)); }
protected static final boolean isSorted(final int[] a){ return Arrays.equals(a, sorted(a)); }
protected static final boolean isSorted(final long[] a){ return Arrays.equals(a, sorted(a)); }
protected static final boolean isSorted(final double[] a){ return Arrays.equals(a, sorted(a)); }
protected static final boolean isSorted(final char[] a){ return Arrays.equals(a, sorted(a)); }
protected static final <T extends Comparable<? super T>> boolean isSorted(final T[] a){ return Arrays.equals(a, sorted(a)); }
protected static final String reverse(final String s){ return new StringBuilder(s).reverse().toString(); }
protected static final int[] reverse(final int[] a) {
final int n = a.length;
final int[] b = new int[n];
for(int i = 0; i <= n / 2; ++i) {
b[i] = a[n - 1 - i];
b[n - 1 - i] = a[i];
}
return b;
}
protected static final long[] reverse(final long[] a) {
final int n = a.length;
final long[] b = new long[n];
for(int i = 0; i <= n / 2; ++i) {
b[i] = a[n - 1 - i];
b[n - 1 - i] = a[i];
}
return b;
}
protected static final double[] reverse(final double[] a) {
final int n = a.length;
final double[] b = new double[n];
for(int i = 0; i <= n / 2; ++i) {
b[i] = a[n - 1 - i];
b[n - 1 - i] = a[i];
}
return b;
}
protected static final char[] reverse(final char[] a) {
final int n = a.length;
final char[] b = new char[n];
for(int i = 0; i <= n / 2; ++i) {
b[i] = a[n - 1 - i];
b[n - 1 - i] = a[i];
}
return b;
}
protected static final Object[] reverse(final Object[] a) {
final int n = a.length;
final Object[] b = new Object[n];
for(int i = 0; i <= n / 2; ++i) {
b[i] = a[n - 1 - i];
b[n - 1 - i] = a[i];
}
return b;
}
protected static final int[] rotate(final int[] a, final int id) {
final int n = a.length, k = (int) mod(id, n);
final int[] res = new int[n];
System.arraycopy(a, k, res, 0, n - k);
System.arraycopy(a, 0, res, n - k, k);
return res;
}
protected static final long[] rotate(final long[] a, final int id) {
final int n = a.length, k = (int) mod(id, n);
final long[] res = new long[n];
System.arraycopy(a, k, res, 0, n - k);
System.arraycopy(a, 0, res, n - k, k);
return res;
}
protected static final double[] rotate(final double[] a, final int id) {
final int n = a.length, k = (int) mod(id, n);
final double[] res = new double[n];
System.arraycopy(a, k, res, 0, n - k);
System.arraycopy(a, 0, res, n - k, k);
return res;
}
protected static final char[] rotate(final char[] a, final int id) {
final int n = a.length, k = (int) mod(id, n);
final char[] res = new char[n];
System.arraycopy(a, k, res, 0, n - k);
System.arraycopy(a, 0, res, n - k, k);
return res;
}
protected static final boolean[] rotate(final boolean[] a, final int id) {
final int n = a.length, k = (int) mod(id, n);
final boolean[] res = new boolean[n];
System.arraycopy(a, k, res, 0, n - k);
System.arraycopy(a, 0, res, n - k, k);
return res;
}
protected static final Object[] rotate(final Object[] a, final int id) {
final int n = a.length, k = (int) mod(id, n);
final Object[] res = new Object[n];
System.arraycopy(a, k, res, 0, n - k);
System.arraycopy(a, 0, res, n - k, k);
return res;
}
protected static final String rotate(final String s, final int id) {
final List<Character> t = s.chars().mapToObj(i -> (char) i).collect(Collectors.toList());
Collections.rotate(t, id);
return t.stream().map(String::valueOf).collect(Collectors.joining());
}
protected static final int[][] rotateR(final int[][] a) {
final int h = a.length, w = a[0].length;
final int[][] b = new int[w][h];
IntStream.range(0, h).forEach(i -> {
Arrays.setAll(b[i], j -> a[j][i]);
});
IntStream.range(0, w).forEach(i -> b[i] = reverse(b[i]));
return b;
}
protected static final long[][] rotateR(final long[][] a) {
final int h = a.length, w = a[0].length;
final long[][] b = new long[w][h];
IntStream.range(0, h).forEach(i -> {
Arrays.setAll(b[i], j -> a[j][i]);
});
IntStream.range(0, w).forEach(i -> b[i] = reverse(b[i]));
return b;
}
protected static final double[][] rotateR(final double[][] a) {
final int h = a.length, w = a[0].length;
final double[][] b = new double[w][h];
IntStream.range(0, h).forEach(i -> {
Arrays.setAll(b[i], j -> a[j][i]);
});
IntStream.range(0, w).forEach(i -> b[i] = reverse(b[i]));
return b;
}
protected static final char[][] rotateR(final char[][] a) {
final int h = a.length, w = a[0].length;
final char[][] b = new char[w][h];
IntStream.range(0, h).forEach(i -> {
IntStream.range(0, w).forEach(j -> b[j][i] = a[i][j]);
});
IntStream.range(0, w).forEach(i -> b[i] = reverse(b[i]));
return b;
}
protected static final int[][] rotateL(final int[][] a) {
final int h = a.length, w = a[0].length;
final int[][] b = new int[w][h];
IntStream.range(0, h).forEach(i -> {
Arrays.setAll(b[i], j -> a[j][w - i - 1]);
});
return b;
}
protected static final long[][] rotateL(final long[][] a) {
final int h = a.length, w = a[0].length;
final long[][] b = new long[w][h];
IntStream.range(0, h).forEach(i -> {
Arrays.setAll(b[i], j -> a[j][w - i - 1]);
});
return b;
}
protected static final double[][] rotateL(final double[][] a) {
final int h = a.length, w = a[0].length;
final double[][] b = new double[w][h];
IntStream.range(0, h).forEach(i -> {
Arrays.setAll(b[i], j -> a[j][w - i - 1]);
});
return b;
}
protected static final char[][] rotateL(final char[][] a) {
final int h = a.length, w = a[0].length;
final char[][] b = new char[w][h];
IntStream.range(0, h).forEach(i -> {
IntStream.range(0, w).forEach(j -> b[w - j - 1][i] = a[i][j]);
});
return b;
}
protected static final void swap(final int[] a, final int i, final int j) {
a[i] ^= a[j];
a[j] ^= a[i];
a[i] ^= a[j];
}
protected static final void swap(final long[] a, final int i, final int j) {
a[i] ^= a[j];
a[j] ^= a[i];
a[i] ^= a[j];
}
protected static final void swap(final double[] a, final int i, final int j) {
final double tmp = a[i];
a[i] = a[j];
a[j] = tmp;
}
protected static final void swap(final char[] a, final int i, final int j) {
a[i] ^= a[j];
a[j] ^= a[i];
a[i] ^= a[j];
}
protected static final void swap(final boolean[] a, final int i, final int j) {
a[i] ^= a[j];
a[j] ^= a[i];
a[i] ^= a[j];
}
protected static final void swap(final Object[] a, final int i, final int j) {
final Object tmp = a[i];
a[i] = a[j];
a[j] = tmp;
}
protected static final void swap(final int[] a, final int[] b) {
assert a.length == b.length;
final int n = a.length;
final int[] c = a.clone();
System.arraycopy(b, 0, a, 0, n);
System.arraycopy(c, 0, b, 0, n);
}
protected static final void swap(final long[] a, final long[] b) {
assert a.length == b.length;
final int n = a.length;
final long[] c = a.clone();
System.arraycopy(b, 0, a, 0, n);
System.arraycopy(c, 0, b, 0, n);
}
protected static final void swap(final double[] a, final double[] b) {
assert a.length == b.length;
final int n = a.length;
final double[] c = a.clone();
System.arraycopy(b, 0, a, 0, n);
System.arraycopy(c, 0, b, 0, n);
}
protected static final void swap(final char[] a, final char[] b) {
assert a.length == b.length;
final int n = a.length;
final char[] c = a.clone();
System.arraycopy(b, 0, a, 0, n);
System.arraycopy(c, 0, b, 0, n);
}
protected static final void swap(final boolean[] a, final boolean[] b) {
assert a.length == b.length;
final int n = a.length;
final boolean[] c = a.clone();
System.arraycopy(b, 0, a, 0, n);
System.arraycopy(c, 0, b, 0, n);
}
protected static final void swap(final Object[] a, final Object[] b) {
assert a.length == b.length;
final int n = a.length;
final Object[] c = a.clone();
System.arraycopy(b, 0, a, 0, n);
System.arraycopy(c, 0, b, 0, n);
}
protected static final <F extends Comparable<? super F>, S extends Comparable<? super S>> Pair<S, F>[] swap(final Pair<F, S>[] p) {
@SuppressWarnings("unchecked")
final Pair<S, F>[] q = new Pair[p.length];
Arrays.setAll(q, i -> p[i].swap());
return q;
}
protected static final IntPair[] swap(final IntPair[] p) {
final IntPair[] q = new IntPair[p.length];
Arrays.setAll(q, i -> p[i].swap());
return q;
}
protected static final FloatPair[] swap(final FloatPair[] p) {
final FloatPair[] q = new FloatPair[p.length];
Arrays.setAll(q, i -> p[i].swap());
return q;
}
@SuppressWarnings("unchecked")
protected static final <F extends Comparable<? super F>, S extends Comparable<? super S>> F[] first(final Pair<F, S>[] p){ return (F[]) Arrays.stream(p).map(i -> i.first).toArray(); }
protected static final long[] first(final IntPair[] p){ return Arrays.stream(p).mapToLong(i -> i.first).toArray(); }
protected static final double[] first(final FloatPair[] p){ return Arrays.stream(p).mapToDouble(i -> i.first).toArray(); }
@SuppressWarnings("unchecked")
protected static final <F extends Comparable<? super F>, S extends Comparable<? super S>> S[] second(final Pair<F, S>[] p){ return (S[]) Arrays.stream(p).map(i -> i.second).toArray(); }
protected static final long[] second(final IntPair[] p){ return Arrays.stream(p).mapToLong(i -> i.second).toArray(); }
protected static final double[] second(final FloatPair[] p){ return Arrays.stream(p).mapToDouble(i -> i.second).toArray(); }
protected static final IntStream iota(final int n){ return IntStream.range(0, n); }
protected static final IntStream iota(final int n, final int init){ return IntStream.range(0 + init, n + init); }
protected static final Integer[] boxed(final int[] a){ return Arrays.stream(a).boxed().toArray(Integer[]::new); }
protected static final Long[] boxed(final long[] a){ return Arrays.stream(a).boxed().toArray(Long[]::new); }
protected static final Double[] boxed(final double[] a){ return Arrays.stream(a).boxed().toArray(Double[]::new); }
protected static final int bins(int ok, int ng, final IntPredicate fn) {
while(abs(ok - ng) > 1) {
final int mid = (ok + ng) / 2;
if(fn.test(mid)) {
ok = mid;
}
else {
ng = mid;
}
}
return ok;
}
protected static final long bins(long ok, long ng, final LongPredicate fn) {
while(abs(ok - ng) > 1) {
final long mid = (ok + ng) / 2;
if(fn.test(mid)) {
ok = mid;
}
else {
ng = mid;
}
}
return ok;
}
protected static final double bins(double ok, double ng, final DoublePredicate fn) {
while(abs(ok - ng) > VvyLw.EPS) {
final double mid = (ok + ng) / 2;
if(fn.test(mid)) {
ok = mid;
}
else {
ng = mid;
}
}
return ok;
}
protected static final Map<Integer, Integer> counter(final int[] a) {
final Map<Integer, Integer> res = new HashMap<>();
for(final int i: a) {
res.merge(i, 1, (x, y) -> x + y);
}
return res;
}
protected static final Map<Long, Integer> counter(final long[] a) {
final Map<Long, Integer> res = new HashMap<>();
for(final long i: a) {
res.merge(i, 1, (x, y) -> x + y);
}
return res;
}
protected static final long innerProd(final IntPair... p){ return iota(p.length).mapToLong(i -> p[i].first.longValue() * p[i].second.longValue()).sum(); }
protected static final double innerProd(final FloatPair... p){ return iota(p.length).mapToDouble(i -> p[i].first.doubleValue() * p[i].second.doubleValue()).sum(); }
protected static final FloatPair intersection(final IntPair a, final long sec1, final IntPair b, final long sec2) {
double m1, m2, b1, b2;
if(a.second.longValue() == 0 && b.second.longValue() == 0) {
return null;
} else if(a.second.longValue() == 0) {
m2 = -b.first.doubleValue() / b.second.longValue();
b2 = -sec2 / b.second.doubleValue();
final double x = -sec1 / a.first.doubleValue(), y = b2 + m2 * x;
return FloatPair.of(x, y);
} else if(b.second.longValue() == 0) {
m1 = -a.first.doubleValue() / a.second.longValue();
b1 = -sec1 / a.second.doubleValue();
final double x = -sec2 / b.first.doubleValue(), y = b1 + m1 * x;
return FloatPair.of(x, y);
}
m1 = -a.first.doubleValue() / a.second.longValue();
m2 = -b.first.doubleValue() / b.second.longValue();
b1 = -sec1 / a.second.doubleValue();
b2 = -sec2 / b.second.doubleValue();
assert m1 != m2;
final double x = (b1 - b2) / (m2 - m1), y = m1 * x + b1;
return FloatPair.of(x, y);
}
protected static final FloatPair intersection(final FloatPair a, final double sec1, final FloatPair b, final double sec2) {
double m1, m2, b1, b2;
if(a.second.doubleValue() == 0 && b.second.doubleValue() == 0) {
return null;
} else if(a.second.doubleValue() == 0) {
m2 = -b.first.doubleValue() / b.second.doubleValue();
b2 = -sec2 / b.second.doubleValue();
final double x = -sec1 / a.first.doubleValue(), y = b2 + m2 * x;
return FloatPair.of(x, y);
} else if(b.second.doubleValue() == 0) {
m1 = -a.first.doubleValue() / a.second.doubleValue();
b1 = -sec1 / a.second.doubleValue();
final double x = -sec2 / b.first.doubleValue(), y = b1 + m1 * x;
return FloatPair.of(x, y);
}
m1 = -a.first.doubleValue() / a.second.doubleValue();
m2 = -b.first.doubleValue() / b.second.doubleValue();
b1 = -sec1 / a.second.doubleValue();
b2 = -sec2 / b.second.doubleValue();
assert m1 != m2;
final double x = (b1 - b2) / (m2 - m1), y = m1 * x + b1;
return FloatPair.of(x, y);
}
protected static final int[] corPress(final int[] a) {
final int[] res = new int[a.length];
final int[] x = Arrays.stream(a).sorted().distinct().toArray();
Arrays.setAll(res, i -> lowerBound(x, a[i]));
return res;
}
protected static final int[] corPress(final long[] a) {
final int[] res = new int[a.length];
final long[] x = Arrays.stream(a).sorted().distinct().toArray();
Arrays.setAll(res, i -> lowerBound(x, a[i]));
return res;
}
protected static final String runLenPress(final String s) {
final int n = s.length();
final StringBuilder sb = new StringBuilder();
for(int l = 0; l < n;) {
int r = l + 1;
for(; r < n && s.charAt(l) == s.charAt(r); ++r){}
sb.append(s.charAt(l));
sb.append(r - l);
l = r;
}
return sb.toString();
}
protected static final String runLenRev(final String s) {
final int n = s.length();
final StringBuilder sb = new StringBuilder();
for(int l = 0; l < n;) {
int r = l + 1;
for(; r < n && scope('0', s.charAt(r), '9'); ++r){}
sb.append(String.valueOf(s.charAt(l)).repeat(Integer.parseInt(s.substring(l + 1, r))));
l = r;
}
return sb.toString();
}
protected static final int[] zAlgorithm(final String s) {
final int n = s.length();
int j = 0;
final int[] pre = new int[n];
for(int i = 0; ++i < n;) {
if(i + pre[i - j] < j + pre[j]) {
pre[i] = pre[i - j];
}
else {
int k = max(0, j + pre[j] - i);
while(i + k < n && s.charAt(k) == s.charAt(i + k)) {
++k;
}
pre[i] = k;
j = i;
}
}
pre[0] = n;
return pre;
}
protected static final int[] manacher(final String s_, final boolean calcEven) {
int n = s_.length();
final char[] s;
if(calcEven) {
s = new char[2 * n - 1];
IntStream.range(0, n).forEach(i -> s[i] = s_.charAt(i));
for(int i = n; --i >= 0;) {
s[2 * i] = s_.charAt(i);
}
final char d = Collections.min(s_.chars().mapToObj(c -> (char) c).collect(Collectors.toList()));
for(int i = 0; i < n - 1; ++i) {
s[2 * i + 1] = d;
}
} else {
s = new char[n];
IntStream.range(0, n).forEach(i -> s[i] = s_.charAt(i));
}
n = s.length;
final int[] rad = new int[n];
for(int i = 0, j = 0; i < n;) {
while(i - j >= 0 && i + j < n && s[i - j] == s[i + j]) {
++j;
}
rad[i] = j;
int k = 1;
while(i - k >= 0 && i + k < n && k + rad[i - k] < j) {
rad[i + k] = rad[i - k];
++k;
}
i += k;
j -= k;
}
if(calcEven) {
for(int i = 0; i < n; ++i) {
if(((i ^ rad[i]) & 1) == 0) {
rad[i]--;
}
}
} else {
for(int x: rad) {
x = 2 * x - 1;
}
}
return rad;
}
protected static final long kthRoot(final long n, final int k) {
if(k == 1) {
return n;
}
final LongPredicate chk = x -> {
long mul = 1;
for(int j = 0; j < k; ++j) {
try {
mul = multiplyExact(mul, x);
} catch(final ArithmeticException e) {
return false;
}
}
return mul <= n;
};
long ret = 0;
for(int i = 32; --i >= 0;) {
if(chk.test(ret | (1L << i))) {
ret |= 1L << i;
}
}
return ret;
}
protected static final long tetration(final long a, final long b, final long m) {
if(m == 1) {
return 0;
}
if(a == 0) {
return (b & 1) == 0 ? 1 : 0;
}
if(b == 0) {
return 1;
}
if(b == 1) {
return a % m;
}
if(b == 2) {
return modPow(a, a, m);
}
final long phi = eulerPhi(m);
long tmp = tetration(a, b - 1, phi);
if(tmp == 0) {
tmp += phi;
}
return modPow(a, tmp, m);
}
protected static final long floorSum(final long n, final long m, long a, long b) {
long ans = 0;
if(a >= m) {
ans += (n - 1) * n * (a / m) / 2;
a %= m;
}
if(b >= m) {
ans += n * (b / m);
b %= m;
}
final long ym = (a * n + b) / m, xm = (ym * m - b);
if(ym == 0) {
return ans;
}
ans += (n - (xm + a - 1) / a) * ym;
ans += floorSum(ym, a, m, (a - xm % a) % a);
return ans;
}
}
interface TriFunction<T, U, V, R> {
R apply(final T a, final U b, final V c);
}
interface QuadFunction<A, B, C, D, R> {
R apply(final A a, final B b, final C c, final D d);
}
interface TriConsumer<T, U, V> {
void accept(final T a, final U b, final V c);
}
interface TriPredicate<T, U, V> {
boolean test(final T a, final U b, final V c);
}
interface RecursiveFunction<T, R> {
R apply(final RecursiveFunction<T, R> rec, final T n);
}
interface RecursiveBiFunction<T, U, R> {
R apply(final RecursiveBiFunction<T, U, R> rec, final T n, final U m);
}
interface RecursiveTriFunction<T, U, V, R> {
R apply(final RecursiveTriFunction<T, U, V, R> rec, final T p, final U q, final V r);
}
interface RecursiveUnaryOperator<T> {
T apply(final RecursiveUnaryOperator<T> rec, final T n);
}
interface RecursiveBinaryOperator<T> {
T apply(final RecursiveBinaryOperator<T> rec, final T a, final T b);
}
interface RecursiveConsumer<T> {
void accept(final RecursiveConsumer<T> rec, final T x);
}
interface RecursiveBiConsumer<T, U> {
void accept(final RecursiveBiConsumer<T, U> rec, final T x, final U y);
}
interface RecursiveTriConsumer<T, U, V> {
void accept(final RecursiveTriConsumer<T, U, V> rec, final T x, final U y, final V z);
}
interface RecursivePredicate<T> {
boolean test(final RecursivePredicate<T> rec, final T n);
}
interface RecursiveBiPredicate<T, U> {
boolean test(final RecursiveBiPredicate<T, U> rec, final T x, final U y);
}
interface RecursiveTriPredicate<T, U, V> {
boolean test(final RecursiveTriPredicate<T, U, V> rec, final T x, final U y, final V z);
}
interface RecursiveIntFunction<R> {
R apply(final RecursiveIntFunction<R> rec, final int n);
}
interface RecursiveLongFunction<R> {
R apply(final RecursiveLongFunction<R> rec, final long n);
}
interface RecursiveDoubleFunction<R> {
R apply(final RecursiveDoubleFunction<R> rec, final double n);
}
interface RecursiveIntUnaryOperator {
int apply(final RecursiveIntUnaryOperator rec, final int n);
}
interface RecursiveLongUnaryOperator {
long apply(final RecursiveLongUnaryOperator rec, final long n);
}
interface RecursiveDoubleUnaryOperator {
double apply(final RecursiveDoubleUnaryOperator rec, final double n);
}
interface RecursiveIntBinaryOperator {
int apply(final RecursiveIntBinaryOperator rec, final int a, final int b);
}
interface RecursiveLongBinaryOperator {
long apply(final RecursiveLongBinaryOperator rec, final long a, final long b);
}
interface RecursiveDoubleBinaryOperator {
double apply(final RecursiveDoubleBinaryOperator rec, final double a, final double b);
}
interface RecursiveIntConsumer {
void accept(final RecursiveIntConsumer rec, final int n);
}
interface RecursiveLongConsumer {
void accept(final RecursiveLongConsumer rec, final long n);
}
interface RecursiveDoubleConsumer {
void accept(final RecursiveDoubleConsumer rec, final double n);
}
interface RecursiveIntPredicate {
boolean test(final RecursiveIntPredicate rec, final int n);
}
interface RecursiveLongPredicate {
boolean test(final RecursiveLongPredicate rec, final long n);
}
interface RecursiveDoublePredicate {
boolean test(final RecursiveDoublePredicate rec, final double n);
}
final class IO implements Closeable, AutoCloseable {
private final MyScanner in;
private final MyPrinter out, err;
IO(final InputStream in, final OutputStream out, final OutputStream err, final boolean autoFlush) {
this.in = new MyScanner(in);
this.out = new MyPrinter(out, autoFlush);
this.err = new MyPrinter(err, true);
}
final int ni(){ return in.ni(); }
final long nl(){ return in.nl(); }
final double nd(){ return in.nd(); }
final char nc(){ return in.nc(); }
final String ns(){ return in.ns(); }
final char[] nt(){ return in.nt(); }
final BigInteger nb(){ return in.nb(); }
final IntPair pi(){ return in.pi(); }
final FloatPair pf(){ return in.pf(); }
final int[] ni(final int n) {
final int[] a = new int[n];
Arrays.setAll(a, i -> ni());
return a;
}
final int[] ni(final int n, final IntUnaryOperator f){ return Arrays.stream(ni(n)).map(f).toArray(); }
final long[] nl(final int n) {
final long[] a = new long[n];
Arrays.setAll(a, i -> nl());
return a;
}
final long[] nl(final int n, final LongUnaryOperator f){ return Arrays.stream(nl(n)).map(f).toArray(); }
final double[] nd(final int n) {
final double[] a = new double[n];
Arrays.setAll(a, i -> nd());
return a;
}
final char[] nc(final int n) {
final char[] a = new char[n];
IntStream.range(0, n).forEach(i -> a[i] = nc());
return a;
}
final String[] ns(final int n) {
final String[] a = new String[n];
Arrays.setAll(a, i -> ns());
return a;
}
final char[][] nt(final int n) {
final char[][] a = new char[n][];
Arrays.setAll(a, i -> nt());
return a;
}
final BigInteger[] nb(final int n) {
final BigInteger[] a = new BigInteger[n];
Arrays.setAll(a, i -> nb());
return a;
}
final IntPair[] pi(final int n) {
final IntPair[] a = new IntPair[n];
Arrays.setAll(a, i -> pi());
return a;
}
final IntPair[] pi(final int n, final UnaryOperator<IntPair> f){ return Arrays.stream(pi(n)).map(f).toArray(IntPair[]::new); }
final FloatPair[] pf(final int n) {
final FloatPair[] a = new FloatPair[n];
Arrays.setAll(a, i -> pf());
return a;
}
final int[][] ni(final int h, final int w) {
final int[][] a = new int[h][w];
Arrays.setAll(a, i -> ni(w));
return a;
}
final long[][] nl(final int h, final int w) {
final long[][] a = new long[h][w];
Arrays.setAll(a, i -> nl(w));
return a;
}
final double[][] nd(final int h, final int w) {
final double[][] a = new double[h][w];
Arrays.setAll(a, i -> nd(w));
return a;
}
final char[][] nc(final int h, final int w) {
final char[][] a = new char[h][w];
Arrays.setAll(a, i -> nc(w));
return a;
}
final String[][] ns(final int h, final int w) {
final String[][] a = new String[h][w];
Arrays.setAll(a, i -> ns(w));
return a;
}
final BigInteger[][] nb(final int h, final int w) {
final BigInteger[][] a = new BigInteger[h][w];
Arrays.setAll(a, i -> nb(w));
return a;
}
final String line(){ return in.line(); }
final void print(final Object arg){ out.print(arg); }
final void printf(final String fmt, final Object... args){ out.printf(fmt, args); }
final void out(){ out.out(); }
final void out(final Object head, final Object... tail){ out.out(head, tail); }
final void out(final int[][] args){ IntStream.range(0, args.length).forEach(i -> out(args[i])); }
final void out(final long[][] args){ IntStream.range(0, args.length).forEach(i -> out(args[i])); }
final void out(final double[][] args){ IntStream.range(0, args.length).forEach(i -> out(args[i])); }
final void out(final boolean[][] args){ IntStream.range(0, args.length).forEach(i -> out(args[i])); }
final void out(final char[][] args){ IntStream.range(0, args.length).forEach(i -> out(args[i])); }
final void out(final Object[][] args){ IntStream.range(0, args.length).forEach(i -> out(args[i])); }
final void outl(final Object head, final Object... tail){ out.outl(head, tail); }
final void dump(final Object head, final Object... tail){ err.out(head, tail); }
final void dump(final int[][] args){ IntStream.range(0, args.length).forEach(i -> dump(args[i])); }
final void dump(final long[][] args){ IntStream.range(0, args.length).forEach(i -> dump(args[i])); }
final void dump(final double[][] args){ IntStream.range(0, args.length).forEach(i -> dump(args[i])); }
final void dump(final boolean[][] args){ IntStream.range(0, args.length).forEach(i -> dump(args[i])); }
final void dump(final char[][] args){ IntStream.range(0, args.length).forEach(i -> dump(args[i])); }
final void dump(final Object[][] args){ IntStream.range(0, args.length).forEach(i -> dump(args[i])); }
final void dumpl(final Object head, final Object... tail){ err.outl(head, tail); }
@Override
public final void close() {
out.flush();
in.close();
out.close();
err.close();
}
private final class MyScanner implements Closeable, AutoCloseable {
private int pos, lim;
private final byte[] buf;
private final InputStream is;
private boolean check;
MyScanner(final InputStream is) {
this.is = is;
pos = lim = 0;
buf = new byte[1 << 17];
check = false;
}
private final boolean isPunct(final byte bt){ return !Utility.scope(33, bt, 126); }
private final boolean isNum(final byte bt){ return Utility.scope('0', bt, '9'); }
private final byte read() {
if(pos == lim && lim != -1) {
try {
lim = is.read(buf);
pos = 0;
} catch(final IOException e) {
e.printStackTrace();
}
}
return buf[pos++];
}
private final byte next() {
byte bt;
if(check) {
check = false;
bt = buf[pos - 1];
if(!isPunct(bt)) {
return bt;
}
}
while(isPunct(bt = read())){}
return bt;
}
final int ni(){ return toIntExact(nl()); }
final long nl() {
byte c = next();
final boolean neg = c == '-';
if(neg) {
c = next();
}
assert isNum(c);
long res = c - '0';
while(isNum(c = read())) {
res = 10 * res + c - '0';
}
check = !isNum(c);
return neg ? -res : res;
}
final double nd() {
byte c = next();
final boolean neg = c == '-';
if(neg) {
c = next();
}
assert isNum(c);
double res = c - '0';
while(isNum(c = read())) {
res = 10 * res + c - '0';
}
if(c != '.') {
check = true;
return res;
}
int i;
for(i = 0; isNum(c = read()); ++i) {
res = res * 10 + c - '0';
}
res /= pow(10, i);
check = true;
return neg ? -res : res;
}
final char nc(){ return (char) next(); }
final String ns() {
final StringBuilder sb = new StringBuilder();
byte c = next();
while(!isPunct(c)) {
sb.append((char) c);
c = read();
}
return sb.toString();
}
final char[] nt(){ return ns().toCharArray(); }
final BigInteger nb(){ return new BigInteger(ns()); }
final IntPair pi(){ return IntPair.of(nl(), nl()); }
final FloatPair pf(){ return FloatPair.of(nd(), nd()); }
final String line() {
final StringBuilder sb = new StringBuilder();
byte c;
while((c = read()) != '\n') {
sb.append((char) c);
}
return sb.toString();
}
@Override
public final void close() {
try {
is.close();
} catch(final IOException e) {
e.printStackTrace();
}
}
}
private final class MyPrinter implements Closeable, Flushable, AutoCloseable {
private OutputStream os;
private final boolean autoFlush;
private final byte[] buf;
private int pos;
private final boolean debug;
MyPrinter(final OutputStream os, final boolean autoFlush){
this.os = os;
this.autoFlush = autoFlush;
buf = new byte[1 << 17];
pos = 0;
debug = os == System.err;
}
private final void write(final byte bt) {
buf[pos++] = bt;
if(pos == buf.length) {
flush();
}
}
private final void newLine() {
write((byte) '\n');
if(autoFlush) {
flush();
}
}
final void print(final Object arg) {
if(arg instanceof final String s) {
for(final char c: s.toCharArray()) {
write((byte) c);
}
} else {
final StringBuilder sb = new StringBuilder();
if(arg instanceof final int[] a) {
if(debug) {
print(Arrays.toString(a));
return;
}
if(a.length == 0) {
return;
}
sb.append(a[0]);
for(int i = 0; ++i < a.length;) {
sb.append(" " + a[i]);
}
} else if(arg instanceof final long[] a) {
if(debug) {
print(Arrays.toString(a));
return;
}
if(a.length == 0) {
return;
}
sb.append(a[0]);
for(int i = 0; ++i < a.length;) {
sb.append(" " + a[i]);
}
} else if(arg instanceof final double[] a) {
if(debug) {
print(Arrays.toString(a));
return;
}
if(a.length == 0) {
return;
}
for(int i = 0; i < a.length; ++i) {
sb.append(a[i]);
}
} else if(arg instanceof final boolean[] a) {
if(debug) {
print(Arrays.toString(a));
return;
}
if(a.length == 0) {
return;
}
sb.append(a[0]);
for(int i = 0; ++i < a.length;) {
sb.append(" " + a[i]);
}
} else if(arg instanceof final char[] a) {
if(a.length == 0) {
return;
}
sb.append(a[0]);
for(int i = 0; ++i < a.length;) {
sb.append(" " + a[i]);
}
} else if(arg instanceof final Object[] a) {
if(debug) {
print(Arrays.toString(a));
return;
}
if(a.length == 0) {
return;
}
print(a[0]);
for(int i = 0; ++i < a.length;) {
print(" ");
print(a[i]);
}
return;
} else {
if(debug) {
print(arg.toString());
return;
} else if(arg instanceof final Pair<?, ?> p) {
sb.append(p.first + " " + p.second);
} else if(arg instanceof final Collection<?> c) {
int i = 0;
for(final Object el: c) {
print(el);
if(++i != c.size()) {
print(" ");
}
}
return;
} else if(sb.isEmpty()) {
print(arg.toString());
return;
}
}
print(sb.toString());
}
if(autoFlush) {
flush();
}
}
final void printf(final String fmt, final Object... args){ print(new Formatter().format(fmt, args)); }
final void out(){ newLine(); }
final void out(final Object head, final Object... tail) {
print(head);
for(final Object el: tail) {
print(" ");
print(el);
}
newLine();
}
private final void p(final Object obj) {
switch(obj) {
case int[] a: Arrays.stream(a).forEach(this::out); break;
case long[] a: Arrays.stream(a).forEach(this::out); break;
case double[] a: Arrays.stream(a).forEach(this::out); break;
case boolean[] a: IntStream.range(0, a.length).mapToObj(i -> a[i]).forEach(this::out); break;
case char[] a: IntStream.range(0, a.length).mapToObj(i -> a[i]).forEach(this::out); break;
case Object[] a: Arrays.stream(a).forEach(this::out); break;
case Collection<?> a: a.stream().forEach(this::out); break;
default: out(obj);
}
}
final void outl(final Object head, final Object... tail) {
p(head);
for(final Object el: tail) {
p(el);
}
}
@Override
public final void flush() {
try {
os.write(buf, 0, pos);
pos = 0;
} catch(final IOException e) {
e.printStackTrace();
}
}
@Override
public final void close() {
if(os == null) {
return;
}
try {
os.close();
os = null;
} catch(final IOException e) {
e.printStackTrace();
}
}
}
}
class Pair<F extends Comparable<? super F>, S extends Comparable<? super S>> implements Comparable<Pair<F, S>>, Cloneable {
public F first;
public S second;
protected Pair(final F first, final S second) {
this.first = first;
this.second = second;
}
static final <F extends Comparable<? super F>, S extends Comparable<? super S>> Pair<F, S> of(final F a, final S b){ return new Pair<>(a, b); }
Pair<S, F> swap(){ return Pair.of(second, first); }
@Override
public final boolean equals(final Object o) {
if(this == o) {
return true;
}
if(o == null || getClass() != o.getClass()) {
return false;
}
final Pair<?, ?> p = (Pair<?, ?>) o;
return first.equals(p.first) && second.equals(p.second);
}
@Override
public final int hashCode(){ return Objects.hash(first, second); }
@Override
public final String toString(){ return "(" + first + ", " + second + ")"; }
@SuppressWarnings("unchecked")
@Override
public final Pair<F, S> clone() {
try {
return (Pair<F, S>) super.clone();
} catch(final CloneNotSupportedException e){
e.printStackTrace();
}
throw new Error();
}
@Override
public final int compareTo(final Pair<F, S> p) {
if(first.compareTo(p.first) == 0) {
return second.compareTo(p.second);
}
return first.compareTo(p.first);
}
}
final class IntPair extends Pair<Long, Long> {
private IntPair(final long first, final long second){ super(first, second); }
static final IntPair ZERO = new IntPair(0, 0);
static final IntPair ONE = new IntPair(1, 1);
static final IntPair of(final long a, final long b){ return new IntPair(a, b); }
@Override
final IntPair swap(){ return new IntPair(second, first); }
final IntPair add(final IntPair p){ return new IntPair(first + p.first, second + p.second); }
final IntPair sub(final IntPair p){ return new IntPair(first - p.first, second - p.second); }
final IntPair mul(final IntPair p){ return new IntPair(first * p.first, second * p.second); }
final IntPair div(final IntPair p){ return new IntPair(first / p.first, second / p.second); }
final IntPair mod(final IntPair p){ return new IntPair(first % p.first, second % p.second); }
final IntPair rotate(){ return new IntPair(-second, first); }
final FloatPair rotate(final int ang) {
final double rad = toRadians(Utility.mod(ang, 360));
return FloatPair.of(first * cos(rad) - second * sin(rad), first * sin(rad) + second * cos(rad));
}
final long dot(final IntPair p){ return first * p.first + second * p.second; }
final long cross(final IntPair p){ return rotate().dot(p); }
final long sqr(){ return dot(this); }
final double grad() {
try {
return 1.0 * second / first;
} catch(final ArithmeticException e) {
e.printStackTrace();
}
throw new Error();
}
final double abs(){ return hypot(first, second); }
final long lcm(){ return Utility.lcm(first, second); }
final long gcd(){ return Utility.gcd(first, second); }
final IntPair extgcd() {
long x = 1, y = 0, t1 = 0, t2 = 0, t3 = 1, a = first, b = second;
while(b > 0) {
t1 = a / b;
a -= t1 * b;
a ^= b;
b ^= a;
a ^= b;
x -= t1 * t2;
x ^= t2;
t2 ^= x;
x ^= t2;
y -= t1 * t3;
y ^= t3;
t3 ^= y;
y ^= t3;
}
return new IntPair(x, y);
}
}
final class FloatPair extends Pair<Double, Double> {
private FloatPair(final double first, final double second){ super(first, second); }
static final FloatPair of(final double a, final double b){ return new FloatPair(a, b); }
@Override
final FloatPair swap(){ return new FloatPair(second, first); }
final FloatPair add(final FloatPair p){ return new FloatPair(first + p.first, second + p.second); }
final FloatPair sub(final FloatPair p){ return new FloatPair(first - p.first, second - p.second); }
final FloatPair mul(final FloatPair p){ return new FloatPair(first * p.first, second * p.second); }
final FloatPair div(final FloatPair p){ return new FloatPair(first / p.first, second / p.second); }
final FloatPair rotate(){ return new FloatPair(-second, first); }
final FloatPair rotate(final int ang) {
final double rad = toRadians(Utility.mod(ang, 360));
return FloatPair.of(first * cos(rad) - second * sin(rad), first * sin(rad) + second * cos(rad));
}
final double dot(final FloatPair p){ return first * p.first + second * p.second; }
final double cross(final FloatPair p){ return rotate().dot(p); }
final double sqr(){ return dot(this); }
final double grad() {
try {
return second / first;
} catch(final ArithmeticException e) {
e.printStackTrace();
}
throw new Error();
}
final double abs(){ return hypot(first, second); }
}