Description:
You are given an integer m.
Let M = 2m - 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 $$a \in S$$, then $$a \text{ XOR } M \in S$$.
2. If $$a,b\in S$$, then $$a \text{ AND } b \in S$$
3. $$T \subseteq S$$
4. All elements of S are less than or equal to M.
Here, $$\text{XOR}$$ and $$AND$$ refer to the bitwise XOR and bitwise AND operators, respectively.
Count the number of good sets S, modulo 109 + 7.
Input Format:
The first line will contain two integers m and n (1 ≤ m ≤ 1 000, 1 ≤ n ≤ min(2m, 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 Format:
Print a single integer, the number of good sets modulo 109 + 7.
Note:
An example of a valid set S is {00000, 00101, 00010, 00111, 11000, 11010, 11101, 11111}.