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#include "utils/utils.hpp"
#pragma once
#include <bits/stdc++.h>
using namespace std;
template <class T>
auto vect(const T& v, int n) { return vector<T>(n, v); }
template <class T, class... D>
auto vect(const T& v, int n, D... m) {
return vector<decltype(vect(v, m...))>(n, vect(v, m...));
}
template <typename T>
static constexpr T inf = numeric_limits<T>::max() / 2;
mt19937_64 mrand(random_device{}());
long long rnd(long long x) { return mrand() % x; }
int lg2(long long x) { return sizeof(long long) * 8 - 1 - __builtin_clzll(x); }
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef pair<int, int> pii;
typedef tree<pii, null_type, less<pii>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
#line 2 "utils/utils.hpp"
#include <bits/stdc++.h>
using namespace std;
template <class T>
auto vect(const T& v, int n) { return vector<T>(n, v); }
template <class T, class... D>
auto vect(const T& v, int n, D... m) {
return vector<decltype(vect(v, m...))>(n, vect(v, m...));
}
template <typename T>
static constexpr T inf = numeric_limits<T>::max() / 2;
mt19937_64 mrand(random_device{}());
long long rnd(long long x) { return mrand() % x; }
int lg2(long long x) { return sizeof(long long) * 8 - 1 - __builtin_clzll(x); }
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef pair<int, int> pii;
typedef tree<pii, null_type, less<pii>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;