#include <bits/stdc++.h>
using namespace std;
 
#define fora(i, n) for (int i = 0; i < n; ++i)
#define forb(i, n) for (int i = 1; i <= n; ++i)
#define all(x) begin(x), end(x) 
#define sz(x) (ll)(x).size()
#define _ << " " <<
#define debug(x) #x << " = " << (x)
 
using ll = long long;
using ld = long double;
using pii = std::pair<int, int>;

int main() {
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);
}