#include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for (auto (i) = a; i < (b); ++(i))
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;

int main() {
#ifdef LOCAL
    freopen("input.txt", "r", stdin);
#endif
    cin.tie(0)->sync_with_stdio(0);
    cin.exceptions(cin.failbit);

}