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 $998244353$.

Constraints

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

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 $998244353$.