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}.

#Nice now I'm sumproduct of gps times bell function
mod=10**9+7
def Blist(m):
    A = [0 for i in range(0, m)]
    A[0] = 1
    R = [1, 1]
    for n in range(1, m):
        A[n] = A[0]
        for k in range(n, 0, -1):
            A[k-1] += A[k]
            A[k-1]%=mod
        R.append(A[0])
    return R
    
    
m,n=[int(k) for k in raw_input().split(" ")]
t=[]
for i in range(n):
    t+=[[k for k in raw_input()]]

ti=[int("".join([t[i][k] for i in range(n)]),2) for k in range(m)]

left=set(range(m))
potes=[]
gps=[]
mxl=0
for k in range(m):
    if k in left:
        totej=set()
        for j in left:
            if ti[k]^ti[j]==0:
                totej.add(j)
        left=left-totej
        gps+=[len(totej)]  
        mxl=max(mxl,len(totej))

bl=Blist(m)

res=1

for k in gps:
    res*=bl[k]
    res%=mod

print res