You are given an integer $*m*$.

Let $*M* = 2^{*m*} - 1$.

You are also given a set of $*n*$ integers denoted as the set $*T*$. The integers will be provided in base 2 as $*n*$ binary strings of length $*m*$.

A set of integers $*S*$ is called "good" if the following hold.

1. If , then .
2. If , then
3. 
4. All elements of $*S*$ are less than or equal to $*M*$.

Here, and refer to the bitwise XOR and bitwise AND operators, respectively.

Count the number of good sets $*S*$, modulo $10^{9} + 7$.

Input

The first line will contain two integers $*m*$ and $*n*$ ($1 ≤ *m* ≤ 1 000$, $1 ≤ *n* ≤ *min*(2^{*m*}, 50)$).

The next $*n*$ lines will contain the elements of $*T*$. Each line will contain exactly $*m*$ zeros and ones. Elements of $*T*$ will be distinct.

Output

Print a single integer, the number of good sets modulo $10^{9} + 7$.

Note

An example of a valid set $*S*$ is {00000, 00101, 00010, 00111, 11000, 11010, 11101, 11111}.