// #pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,sse4.1,sse4.2,popcnt,abm,mmx,avx")

#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <set>
#include <map>
#include <queue>
#include <random>
#include <chrono>
#include <cassert>
#include <sstream>
#include <fstream>
#include <iomanip>
#include <tuple>

#define fi first
#define se second
#define pb push_back
#define ll long long
#define ld long double
#define hm unordered_map
#define pii pair<int, int>
#define sz(a) (int)a.size()
#define all(a) a.begin(), a.end()
#define cinv(v) for (auto& x: v) cin >> x
#define fr(i, n) for (int i = 0; i < n; ++i)
#define fl(i, l, n) for (int i = l; i < n; ++i)

// #define int ll

template <typename T1, typename T2> inline bool chkmin(T1 &x, const T2 &y) {if (x > y) {x = y; return 1;} return 0;}
template <typename T1, typename T2> inline bool chkmax(T1 &x, const T2 &y) {if (x < y) {x = y; return 1;} return 0;}

using namespace std;

#ifdef LOCAL
	#define dbg(x) cerr << #x << " : " << x << '\n'
#else
	#define dbg(x)
#endif

//tg: @runningcherry

template <typename Collection> string Join (const Collection& col) {
	bool first = true;
	stringstream ss;
	for (const auto& x: col) {
		if (!first) ss << ", ";
		first = false;
		ss << x;
	}
	return ss.str ();
}

template <typename T1, typename T2> ostream& operator << (ostream& out, const pair<T1, T2>& v) {
	return out << '{' << v.fi << ", " << v.se << '}';
}

template<typename T> ostream& operator << (ostream& out, const vector<T>& v) {
	return out << '[' << Join (v) << ']';
}

template <typename T1, typename T2> ostream& operator << (ostream& out, const map<T1, T2>& v) {
	return out << '{' << Join (v) << '}';
}

template<typename T> ostream& operator << (ostream& out, const set<T>& v) {
	return out << '(' << Join (v) << ')';
}

template<typename T> ostream& operator << (ostream& out, const multiset<T>& v) {
	return out << '(' << Join (v) << ')';
}

template <typename T1, typename T2> istream& operator >> (istream& in, pair<T1, T2>& a) {
	return in >> a.fi >> a.se;
}

const ll inf = (ll) 2e9;
const ll mod = (ll)1e9 + 7;

const int maxn = 2e5 + 20;

mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());



signed main () {
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);






}