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Color the chessboard

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 524288/524288 K (Java/Others)
Total Submission(s): 335    Accepted Submission(s): 182


Problem Description
There is a chessboard with $n$ rows and $m$ columns, at first every position is colored red or blue or white. HazelFan want to change the color of every white position into red one or blue one, so that every rectangle in the chessboard with even rows and even colums, contains same number of red positions and blue positions. HazelFan wants to know how many ways are there to color the chessboard, module $998244353$.
 

Input
The first line contains a positive integer $T(1\leq T\leq5)$, denoting the number of test cases.
For each test case:
The first line contains two positive integers $n,m(1\leq n,m\leq10^3)$.
The next $n$ lines, the $i$th line contains a string of length $m$, the $j$th character describes the position in the $i$th row and the $j$th column as below:
'R': the position is colored red.
'B': the position is colored blue.
'?': the position is colored white.
 

Output
For each test case:
A single line contains a nonnegative integer, denoting the answer.
 

Sample Input
2 2 2 RB ?? 3 3 ??? ?R? ???
 

Sample Output
2 7
 

Source
 

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