Your task is to create an $n \times n$ grid whose each row and column has exactly one A and B. Some of the characters have already been placed. In how many ways can you complete the grid?
The first input line has an integer $n$ : the size of the grid.
After this, there are $n$ lines that describe the grid. Each line has $n$ characters: . means an empty square, and A and B show the characters already placed.
You can assume that every row and column has at most one A and B.
Print one integer: the number of ways modulo $10^9+7$ .