Problem Statement

We have a grid with N horizontal rows and N vertical columns.
Let (i, j) denote the square at the i-th row from the top and j-th column from the left. A character c_{i,j} describes the color of (i, j).
B means the square is painted black; W means the square is painted white; ? means the square is not yet painted.
Takahashi will complete the black-and-white grid by painting each unpainted square black or white.
Let the zebraness of the grid be the number of pairs of a black square and a white square sharing a side.
Find the maximum possible zebraness of the grid that Takahashi can achieve.

Input

Input is given from Standard Input in the following format:
N
$c_{1,1} \dots c_{1,N}$
$\hspace{20pt}\vdots$
$c_{N,1} \dots c_{N,N}$

Output

Print the answer.

Constraints

• 1 ≤ N ≤ 100
• c_{i, j} is B, W, or ?.

Sample Input 1

2
BB
BW

Sample Output 1

2

We have two pairs of a black square and a white square sharing a side: (1, 2), (2, 2) and (2, 1), (2, 2), so the zebraness of this grid is 2.

Sample Input 2

3
BBB
BBB
W?W

Sample Output 2

4

Painting (3, 2) white makes the zebraness 3, and painting it black makes the zebraness 4.

Sample Input 3

5
?????
?????
?????
?????
?????

Sample Output 3

40

见题面 Input 部分

见题面 Output 部分