**Time limit:**1.00 s**Memory limit:**512 MB

**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.

**Output**

Print one integer: the number of ways modulo $10^9+7$.

**Constraints**

- $2 \le n \le 500$

**Example**

Input:

`5`

.....

..AB.

.....

B....

...A.

Output:

`16`