Mock CCC '18 Contest 2 J5/S3 - A Coloring Problem

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Points: 10 (partial)
Time limit: 5.0s
Memory limit: 1G

Problem type

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.


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

Sample Output 1


Sample Input 2

7 6

Sample Output 2


Sample Input 3

2 2

Sample Output 3



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