Problem Statement

We have a grid with H rows and W columns. Let (i, j) denote the square at the i-th row and j-th column.
You are given $H strings S_1, S_2, S_3, \dots, S_H$ that describe the square, as follows:

• if the j-th character of S_i is R, (i, j) is painted red;
• if the j-th character of S_i is B, (i, j) is painted blue;
• if the j-th character of S_i is ., (i, j) is unpainted.

Let k be the number of unpainted squares. Among the 2^k ways to paint each of those squares red or blue, how many satisfy the following condition?

• The number of red squares visited while getting from (1, 1) to (H, W) by repeatedly moving one square right or down, including (1, 1) and (H, W), is always the same regardless of the path taken.

Since the count may be enormous, print it modulo 998244353.

Input

Input is given from Standard Input in the following format:
H W
S_1
S_2
S_3
$\hspace{3pt} \vdots$
S_H

Output

Print the count modulo 998244353.

Constraints

• $2 \le H \le 500$
• $2 \le W \le 500$
• S_i is a string of length W consisting of R, B, and ..

Sample Input 1

2 2
B.
.R

Sample Output 1

2

There are two ways to get from (1, 1) to (2, 2) by repeatedly moving right or down, as follows:

• $(1, 1) \rightarrow (1, 2) \rightarrow (2, 2)$
• $(1, 1) \rightarrow (2, 1) \rightarrow (2, 2)$

If we paint (1, 2) and (2, 1) in different colors, the above two paths will contain different numbers of red squares, violating the condition.
On the other hand, if we paint (1, 2) and (2, 1) in the same color, the two paths will contain the same numbers of red squares, satisfying the condition.
Thus, there are two ways to satisfy the condition.

Sample Input 2

3 3
R.R
BBR
...

Sample Output 2

0

There may be no way to satisfy the condition.

Sample Input 3

2 2
BB
BB

Sample Output 3

1

There is no unpainted square, and the current grid satisfies the condition, so the answer is 1.

见题面 Input 部分

见题面 Output 部分