#include <bits/stdc++.h>

using namespace std;

ifstream in("input.in");
ofstream out("output.out");

#define for0(AAA, BBB) for(ll AAA = 0; AAA < BBB; ++AAA)
#define for1(AAA, BBB) for(ll AAA = 1; AAA <= BBB; ++AAA)

#ifndef ONLINE_JUDGE
#else
#define in cin
#define out cout
#endif

typedef long long ll;
typedef unsigned long long ull;

const ll NMX = 2e5 + 5;
const ll MOD = 1e9 + 7;
const string YES = "YES";
const string NO = "NO";


int main() {
    ios::sync_with_stdio(0);




    return 0;
}