#include <bits/stdc++.h>
#include <cstdint>
#include <sys/time.h>

typedef std::int_fast32_t  s32;
typedef std::uint_fast32_t u32;
typedef std::int_fast64_t  s64;
typedef std::uint_fast64_t u64;

const unsigned long mod = 1000000007;

int main() {

  return 0;
}