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 defaultdict

def E1():

    mod = 10 ** 9 + 7

    comb = [[1]]
    for i in range(1, 1010):
        x = [1]
        for j in range(1, i):
            x.append((comb[i - 1][j - 1] + comb[i - 1][j]) % mod)
        x.append(1)
        comb.append(x)

    dp = [1]
    for i in range(1, 1010):
        r = 0
        for k in range(i):
            r += dp[k] * comb[i - 1][k]
            r %= mod
        dp.append(r)

    m, n = map(int, input().split())

    ns = [0 for __ in range(m)]
    for j in range(n):
        temp = input()
        s = [int(i) for i in temp]
        for i in range(m):
            ns[i] |= s[i] << j

    dd = defaultdict(int)
    for e in ns:
        dd[e] += 1

    ans = 1
    for b in dd.values():
        ans = ans * dp[b] % mod

    print(ans)

if __name__=='__main__':
    E1()
	 	 	   	   			  				  	 	 	 	