Problem Statement

There is a grid with $H$ rows and $W$ columns where each square has one of the characters X and Y written on it. Let $(i, j)$ denote the square at the $i$-th row from the top and $j$-th column from the left. The characters on the grid are given as $H$ strings $S_1, S_2, \dots, S_H$: the $j$-th character of $S_i$ is the character on square $(i, j)$.

For a path $P$ from square $(1, 1)$ to square $(H, W)$ obtained by repeatedly moving down or right to the adjacent square, the score is defined as follows.

• Let $\mathrm{str}(P)$ be the string of length $(H + W - 1)$ obtained by concatenating the characters on the squares visited by $P$ in the order they are visited.
• The score of $P$ is the square of the number of pairs of consecutive Ys in $\mathrm{str}(P)$.

There are $\displaystyle\binom{H + W - 2}{H - 1}$ such paths. Find the sum of the scores over all those paths, modulo $998244353$.

What is $\binom{N}{K}$? $\displaystyle\binom{N}{K}$ is the binomial coefficient representing the number of ways to choose $K$ from $N$ distinct elements.

Constraints

• $1 \leq H \leq 2000$
• $1 \leq W \leq 2000$
• $S_i \ (1 \leq i \leq H)$ is a string of length $W$ consisting of X and Y.

Input

The input is given from Standard Input in the following format:

H W
S_1
S_2
\vdots
S_H

Output

Print the sum of the scores over all possible paths, modulo $998244353$.