#include <fstream>
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <vector>
#include <stack>
#include <queue>
#include <deque>
#include <cstring>
#include <set>
#include <cstdlib>
#include <bitset>
#define pb push_back
#define x first
#define y second
#define mp make_pair
#define LL long long
#define ULL unsigned long long
#define ld long double
#define oo 2000000000
#define ooLL (1LL<<60)
using namespace std;

ifstream f(".in");
ofstream g(".out");

typedef  pair<int,int> PP;




int main()
{


    return 0;
}