#include <iostream>

#include <array>
#include <vector>
#include <list>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>

#include <string>
#include <sstream>

#include <memory>
#include <cassert>

#include <functional>

using namespace std;

const int MOD = 1000000007;

typedef unsigned long long ull;

int main()
{

}