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 10⁹ + 7.

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.

Print a single integer, the number of good sets modulo 10⁹ + 7.