include <bits/stdc++.h>
using namespace std; // #define int long long
define push_b push_back
define push_f push_front
define pop_f pop_front
define pop_b pop_back
define sec second
define fir first
const int inf = 1e9 + 7;
signed main() {
ios::sync_with_stdio(0); cout.tie(0); cin.tie(0);
}