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 is given from Standard Input in the following format:

```
$N$
$c_{1,1} \dots c_{1,N}$
$\hspace{20pt}\vdots$
$c_{N,1} \dots c_{N,N}$
```

Print the answer.

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

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.

4

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