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 <image>, then <image>. 
  2. If <image>, then <image>
  3. <image>
  4. All elements of S are less than or equal to M. 



Here, <image> and <image> 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}.
from collections import*
n, m = map(int, raw_input().split())
a = [raw_input().strip() for i in xrange(m)]
d = defaultdict(int)
for c in zip(*a):
    d[c] += 1
mod = 1000000007
b = [1, 1]
p = [1]
for i in xrange(n):
    np = [p[-1]]
    for j in xrange(i + 1):
        x = p[j] + np[-1]
        if x >= mod:
            x -= mod
        np.append(x)
    p = np
    b.append(x)
ans = 1
for c in d.viewkeys():
    x = tuple('01'[x == '0'] for x in c)
    if x not in d:
        ans = ans * b[d[c]] % mod
    elif c[0] == '0':
        ans = ans * b[d[c]] % mod * b[d[x]] % mod
print(ans)