8809: [CSES Problem Set] Grid Completion
[Creator : ]
Description
Your task is to create an n×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?
Input
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.
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.
Output
Print one integer: the number of ways modulo $10^9+7$.
Constraints
$2 \leq n \leq 500$
Sample 1 Input
5
.....
..AB.
.....
B....
...A.
Sample 1 Output
16