F - Zebraness

Score : $600$ points

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.

Constraints

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

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.

2
BB
BW

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 $2$.

3
BBB
BBB
W?W

4

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

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

40