This documentation is automatically generated by online-judge-tools/verification-helper
#include "template/template.hpp"
#pragma once
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
#include"utility.hpp"
// math
#include"math.hpp"
// inout
#include"inout.hpp"
// macro
#include"macro.hpp"
#line 2 "template/template.hpp"
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
#line 2 "template/utility.hpp"
using ll = long long;
// a ← max(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmax(T &a, const U b){
return (a < b ? a = b, 1: 0);
}
// a ← min(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmin(T &a, const U b){
return (a > b ? a = b, 1: 0);
}
#line 59 "template/template.hpp"
// math
#line 2 "template/math.hpp"
// 除算に関する関数
// floor(x / y) を求める.
template<typename T, typename U>
T div_floor(T x, U y){ return (x > 0 ? x / y: (x - y + 1) / y); }
// ceil(x / y) を求める.
template<typename T, typename U>
T div_ceil(T x, U y){ return (x > 0 ? (x + y - 1) / y: x / y) ;}
// x を y で割った余りを求める.
template<typename T, typename U>
T mod(T x, U y){
T q = div_floor(x, y);
return x - q * y ;
}
// x を y で割った商と余りを求める.
template<typename T, typename U>
pair<T, T> divmod(T x, U y){
T q = floor(x, y);
return {q, x - q * y};
}
// 指数に関する関数
// x の y 乗を求める.
ll intpow(ll x, ll y){
ll a = 1;
while (y){
if (y & 1) { a *= x; }
x *= x;
y >>= 1;
}
return a;
}
// x の y 乗を z で割った余りを求める.
ll modpow(ll x, ll y, ll z){
ll a = 1;
while (y){
if (y & 1) { (a *= x) %= z; }
(x *= x) %= z;
y >>= 1;
}
return a;
}
// vector の要素の総和を求める.
ll sum(vector<ll> &X){
ll y = 0;
for (auto &&x: X) { y+=x; }
return y;
}
// vector の要素の総和を求める.
template<typename T>
T sum(vector<T> &X){
T y = T(0);
for (auto &&x: X) { y += x; }
return y;
}
#line 62 "template/template.hpp"
// inout
#line 1 "template/inout.hpp"
// 入出力
template<class... T>
void input(T&... a){ (cin >> ... >> a); }
void print(){ cout << "\n"; }
template<class T, class... Ts>
void print(const T& a, const Ts&... b){
cout << a;
(cout << ... << (cout << " ", b));
cout << "\n";
}
template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &P){
is >> P.first >> P.second;
return is;
}
template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &P){
os << P.first << " " << P.second;
return os;
}
template<typename T>
vector<T> vector_input(int N, int index){
vector<T> X(N+index);
for (int i=index; i<index+N; i++) cin >> X[i];
return X;
}
template<typename T>
istream &operator>>(istream &is, vector<T> &X){
for (auto &x: X) { is >> x; }
return is;
}
template<typename T>
ostream &operator<<(ostream &os, const vector<T> &X){
int s = (int)X.size();
for (int i = 0; i < s; i++) { os << (i ? " " : "") << X[i]; }
return os;
}
template<typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &S){
int i = 0;
for (T a: S) {os << (i ? " ": "") << a; i++;}
return os;
}
template<typename T>
ostream &operator<<(ostream &os, const set<T> &S){
int i = 0;
for (T a: S) { os << (i ? " ": "") << a; i++; }
return os;
}
template<typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &S){
int i = 0;
for (T a: S) { os << (i ? " ": "") << a; i++; }
return os;
}
template<typename T>
ostream &operator<<(ostream &os, const multiset<T> &S){
int i = 0;
for (T a: S) { os << (i ? " ": "") << a; i++; }
return os;
}
#line 65 "template/template.hpp"
// macro
#line 2 "template/macro.hpp"
// マクロの定義
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define unless(cond) if (!(cond))
// オーバーロードマクロ
#define overload2(_1, _2, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload5(_1, _2, _3, _4, _5, name, ...) name
// 繰り返し系
#define rep1(n) for (ll i = 0; i < n; i++)
#define rep2(i, n) for (ll i = 0; i < n; i++)
#define rep3(i, a, b) for (ll i = a; i < b; i++)
#define rep4(i, a, b, c) for (ll i = a; i < b; i += c)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define foreach1(x, a) for (auto &&x: a)
#define foreach2(x, y, a) for (auto &&[x, y]: a)
#define foreach3(x, y, z, a) for (auto &&[x, y, z]: a)
#define foreach4(x, y, z, w, a) for (auto &&[x, y, z, w]: a)
#define foreach(...) overload5(__VA_ARGS__, foreach4, foreach3, foreach2, foreach1)(__VA_ARGS__)
#line 68 "template/template.hpp"