#include <algorithm>
#include <bitset>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <ctime>
#include <deque>
#include <functional>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <utility>
#include <vector>
#include <string>

#define FOR(I, A, B) for(int I = (A); I < (B); ++I)
#define REP(I, N) FOR(I, 0, N)
#define ALL(A) (A).begin(), (A).end()
#define SZ(A) int((A).size())
#define PB push_back
#define FST(A) (A).first
#define SEC(A) (A).second
#define DEBUG

typedef long long int ll;
typedef unsigned long long int ull;

using namespace std;

typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef vector<int> vi;
typedef vector<bool> vb;

int main(void) {
  //Write your code here

	return 0;
}