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.