#define REP(i, n) for(int (i) = 0; (i) < (n); ++(i))
#define REPR(i, n) for(int (i) = (n); (i) >= 0; --(i))
#define FOR(i, n, m) for(int (i) = (n); (i) < (m); ++(i))

// constexpr int INF = 1e9;
constexpr ll INF = 1LL<<61;
constexpr ll mod = 1e9+7;

int main(){
  
  return 0;
}
