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E. New Year and Entity Enumeration

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

- If , then .
- If , then
- 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.

Examples

Input

5 3

11010

00101

11000

Output

4

Input

30 2

010101010101010010101010101010

110110110110110011011011011011

Output

860616440

Note

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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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