Piece Chessboard

A square grid of height $N$ and width $M$ has each cell painted either black or white. Hyeonchae, whose head is full of chess, wonders how many ways there are to cut this grid so that the result is a chessboard.

A chessboard must have black and white painted alternately. Specifically, each cell is painted one of black and white, and any two squares that share an edge must be painted different colors. The shape of a chessboard must be a square, and it does not have to be $8 \times 8$.

Let us satisfy Hyeonchae's curiosity.

The input is given as follows.

$N\ M$
$C_{1,1} C_{1,2} \cdots C_{1,M}$
$C_{2,1} C_{2,2} \cdots C_{2,M}$
$\vdots$
$C_{N,1} C_{N,2} \cdots C_{N,M}$

• $1 \leq N,M \leq 3\,000$
• $C_{i,j}$ is a character meaning the color painted on $\left(i,j\right)$, and it is one of B and W. If $C_{i,j}$ is B, then $\left(i,j\right)$ is painted black, and if it is W, then $\left(i,j\right)$ is painted white.

Output how many ways there are to cut the given grid so that the result is a chessboard.