Score : $1900$ points

Problem Statement

Snuke has a grid with $H$ rows and $W$ columns. The square at the $i$-th row and $j$-th column contains a character $S_{i,j}$.

He can perform the following two kinds of operation on the grid:

• Row-reverse: Reverse the order of the squares in a selected row.
• Column-reverse: Reverse the order of the squares in a selected column.

For example, reversing the $2$-nd row followed by reversing the $4$-th column will result as follows:

By performing these operations any number of times in any order, how many placements of characters on the grid can be obtained?

Constraints

• $1 \leq H,W \leq 200$
• $S_{i,j}$ is a lowercase English letter (a-z).

Input

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

$H$ $W$

$S_{1,1}$$S_{1,2}$$...$$S_{1,W}$

$S_{2,1}$$S_{2,2}$$...$$S_{2,W}$

$:$

$S_{H,1}$$S_{H,2}$$...$$S_{H,W}$

Output

Print the number of placements of characters on the grid that can be obtained, modulo $1000000007 (=10^9+7)$.

2 2
cf
cf

6

The following $6$ placements of characters can be obtained:

1 12
codefestival

2