#include <bits/stdc++.h>

using namespace std;

#define endl '\n'

#define TRACE 1 #define tcout TRACE && cout

#define fst ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);

#define int long long

const int P = 998244353; const int Base = 3221225477; const int INF = 0x3f3f3f3f3f3f3f3f;

const int N = 1e6 + 10, M = 2e6 + 10;

signed main() {

return 0;

}