Problem Statement

For a grid with $N$ rows and $M$ columns, the cell in the $i$-th row and $j$-th column is called $(i,j)$.

A colored grid is defined to be a good grid if all of its cells can be made white by repeating the following operation.

• Choose $3$ cells enclosed by one of the following $4$ types of shapes (rotation is not allowed), and flip their colors.

Formally, perform one of the following operations.
• Choose integers $x,y \ (1 \leq x \leq N-2, \ 1 \leq y \leq M)$ and flip the colors of the $3$ cells $(x,y),(x+1,y),(x+2,y)$.
• Choose integers $x,y \ (1 \leq x \leq N, \ 1 \leq y \leq M-2)$ and flip the colors of the $3$ cells $(x,y),(x,y+1),(x,y+2)$.
• Choose integers $x,y \ (1 \leq x \leq N-1, \ 1 \leq y \leq M-1)$ and flip the colors of the $3$ cells $(x,y),(x+1,y),(x+1,y+1)$.
• Choose integers $x,y \ (1 \leq x \leq N-1, \ 1 \leq y \leq M-1)$ and flip the colors of the $3$ cells $(x,y),(x,y+1),(x+1,y+1)$.

You are given a grid with $N$ rows and $M$ columns. Each cell of the given grid is either painted white or black, or not painted.

If $S_{i,j}$ is W, B, then $(i,j)$ is a cell painted white, black, respectively; if it is ?, it is an unpainted cell.

Find the number, modulo $998244353$, of ways to paint each unpainted cell of the given grid white or black such that the resulting grid is a good grid.

Input

$N$ $M$
$S_{1,1}S_{1,2}\ldots S_{1,M}$
$\vdots$
$S_{N,1}S_{N,2}\ldots S_{N,M}$

• $3 \leq N,M \leq 500$
• $N,M$ are integers
• $S_{i,j}$ is one of W,B,?

Output

Output the answer as an integer.

Sample

Sample 1

Input

3 4
??BW
WBBW
WWWW

Output

1

The $2$ cells $(1,1),(1,2)$ are unpainted, so there are $2^2=4$ ways to paint in total.

If $(1,1)$ is painted black and $(1,2)$ is painted white, all cells can be made white with $2$ operations as shown in the figure below, so this is a good grid.

This $1$ way is the only painting that results in a good grid.

3 3
WWW
WBW
BBW

0

12 30
WW?W?BW??B??WBWBW?WWWWB?WBWWWW
BBB?WBBWWBBWW?WW?BWBWW?WBWW?WW
WBBBW?BW?WB?BWBWWWBBBWWWWB??WB
WW?WWBWWWWB?B?BBBWB?BBB?BB?W??
B?BB?WWBWWBW?BWBBBWWBBBB??B??B
WWBWWBWBWWW??W?WBBBWWWWW?WW?WW
WWWBB?B?BWB?WBWBW?W?BBBWB?WBBW
??BBWWBWW?WWBBBW?WWBWW?BWBBBWW
WBW?WW?B??BW?BWWBBBW?WWWWB??BB
W?BW?BWWBB?BW??BWWWWBB??BW?BWB
?WWW?WB?WWBBBWWBBBWWBW?BBWW?BB
?WWWBWBBWWWBWWWBBWWWB?WW?BWBWB

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