A8429 | Pocket Book

One day little Vasya found mom's pocket book. The book had $n$ names of her friends and unusually enough, each name was exactly $m$ letters long. Let's number the names from $1$ to $n$ in the order in which they are written.

As mom wasn't home, Vasya decided to play with names: he chose three integers $i$ , $j$ , $k$ ( $1<=i<j<=n$ , $1<=k<=m$ ), then he took names number $i$ and $j$ and swapped their prefixes of length $k$ . For example, if we take names "CBDAD" and "AABRD" and swap their prefixes with the length of $3$ , the result will be names "AABAD" and "CBDRD".

You wonder how many different names Vasya can write instead of name number $1$ , if Vasya is allowed to perform any number of the described actions. As Vasya performs each action, he chooses numbers $i$ , $j$ , $k$ independently from the previous moves and his choice is based entirely on his will. The sought number can be very large, so you should only find it modulo $1000000007$ $(10^{9}+7)$ .

The first input line contains two integers $n$ and $m$ ( $1<=n,m<=100$ ) — the number of names and the length of each name, correspondingly. Then $n$ lines contain names, each name consists of exactly $m$ uppercase Latin letters.

Print the single number — the number of different names that could end up in position number $1$ in the pocket book after the applying the procedures described above. Print the number modulo $1000000007$ $(10^{9}+7)$ .