Header
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <string>
#include <sstream>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <ctime>
#define inf 0x3f3f3f3f
#define Inf 0x3FFFFFFFFFFFFFFFLL
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define Rep(i, n) for (int i = 1; i <= (n); ++i)
#define clr(x, a) memset(x, (a), sizeof x)
typedef double db;
typedef long long ll;
using namespace std;
int main() {
return 0;
}