Template

#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <string.h>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <cmath>
#include <sstream>

#define pb push_back
#define mp make_pair
#define PI 3.1415926535897932384626433832795
#define sqr(x) (x)*(x)
#define ALL(x) x.begin(), x.end()
#define F first
#define S second
#define m0(x) memset(x,0,sizeof(x))
#define m1(x) memset(x,-1,sizeof(x))
#define pw(x) (1ull<<(x))

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int,int> pii;
const int INF = 2147483647;
const ll LLINF = 9223372036854775807LL;

int main() {
  //freopen("input.txt", "r", stdin);
  //freopen("output.txt", "w", stdout);

  return 0;
}