An $m$-by-$n$ grid $G$ is good if every square is colored either red or blue, and if the square in row $i$, column $j$ is blue, then every square in row $k$, column $l$ that satisfies $k\le i$ and $l\le j$ must also be colored blue.

You are given a grid that is partially colored in. Count the number of ways to color the remaining squares of the grid such that the grid is good.

Constraints

$1\le m,n\le 30$

At least one square in the grid will be ..

Input Specification

The first line contains two space-separated integers $m$ and $n$.

Each of the next $m$ lines contains $n$ characters representing the grid. Each character is either R to represent a red square, B to represent a blue square, or . to indicate a square that has not been colored.

Output Specification

Print, on a single line, the number of distinct colorings possible.

Sample Input 1

3 2
..
B.
.R

Sample Output 1

6

Sample Input 2

7 6
......
.....B
.B..R.
......
...B..
.R....
...R..

Sample Output 2

3

Sample Input 3

2 2
R.
.B

Sample Output 3

0