presets

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef vector<bool> vb;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef pair<int, int> pi;

#define F first
#define S second
#define PB push_back
#define MP make_pair
#define max(a, b) (a > b ? a : b)
#define min(a, b) (a < b ? a : b)


int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.setf(ios::fixed);
    cout.precision(6);
//    freopen("input.txt", "r", stdin);
//    freopen("output.txt", "w", stdout);




    return 0;
}