New Year and Entity Enumeration

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 , then .
2. If , then
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.

Input

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

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

inputFormat

Input

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.

outputFormat

Output

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

样例

5 3
11010
00101
11000

4

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