Contest Duration: ~ (local time)
I - Reverse Grid

Time Limit: 2 sec / Memory Limit: 256 MB

問題文

H 行、横 W 列のマス目があり、i 行目の j 列目のマスには文字 S_{i,j} が書かれています。

すぬけくんはこのマス目に対して以下の 2 種類の操作を行うことが出来ます。

• 行リバース：行を 1 つ選び、その行をリバースする。
• 列リバース：列を 1 つ選び、その列をリバースする。

制約

• 1≦H,W≦200
• S_{i,j} は小文字アルファベット（a-z）である。

入力

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}


入力例 1

2 2
cf
cf


出力例 1

6


入力例 2

1 12
codefestival


出力例 2

2


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≦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).

Sample Input 1

2 2
cf
cf


Sample Output 1

6


The following 6 placements of characters can be obtained:

Sample Input 2

1 12
codefestival


Sample Output 2

2