#include <bits/stdc++.h>

using namespace std;

#define ll long long
#define ull unsigned long long
#define ld long double
#define pb push_back
#define fi first
#define se second

const int N = 1e6;
const int mod = 1e9 + 7;

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
}