This documentation is automatically generated by competitive-verifier/competitive-verifier
#include "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template <typename T1, typename T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
os << p.first << " " << p.second;
return os;
}
template <typename T1, typename T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
for (T& in : v) is >> in;
return is;
}
template <typename T1, typename T2>
inline bool chmax(T1& a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2>
inline bool chmin(T1& a, T2 b) {
return a > b && (a = b, true);
}
template <typename T = int64>
vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T& t, const V& v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T& t, const V& v) {
for (auto& e : t) fill_v(e, v);
}
template <typename F>
struct FixPoint : F {
explicit FixPoint(F&& f) : F(std::forward<F>(f)) {}
template <typename... Args>
decltype(auto) operator()(Args&&... args) const {
return F::operator()(*this, std::forward<Args>(args)...);
}
};
template <typename F>
inline decltype(auto) MFP(F&& f) {
return FixPoint<F>{std::forward<F>(f)};
}
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template <typename T1, typename T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
os << p.first << " " << p.second;
return os;
}
template <typename T1, typename T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
for (T& in : v) is >> in;
return is;
}
template <typename T1, typename T2>
inline bool chmax(T1& a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2>
inline bool chmin(T1& a, T2 b) {
return a > b && (a = b, true);
}
template <typename T = int64>
vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T& t, const V& v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T& t, const V& v) {
for (auto& e : t) fill_v(e, v);
}
template <typename F>
struct FixPoint : F {
explicit FixPoint(F&& f) : F(std::forward<F>(f)) {}
template <typename... Args>
decltype(auto) operator()(Args&&... args) const {
return F::operator()(*this, std::forward<Args>(args)...);
}
};
template <typename F>
inline decltype(auto) MFP(F&& f) {
return FixPoint<F>{std::forward<F>(f)};
}