Reverse Grid

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≦H,W≦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).

Examples

Input

2 2 cf cf

Output

6

Input

1 12 codefestival

Output

2

inputFormat

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}

outputFormat

Output

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

Examples

Input

2 2 cf cf

Output

6

Input

1 12 codefestival

Output

2

样例

2 2
cf
cf

6