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}.
#Problem Set E: Collaborated with no one
from collections import defaultdict

mod_v = 1000000007

temp_arr = [[1]]
for i in range(1,1010):
    a = [1]
    for k in range(1,i):
        a.append((temp_arr[i-1][k-1]+temp_arr[i-1][k]) % mod_v)
    a.append(1)
    temp_arr.append(a)


ans_arr = [1]
for i in range(1,1010):
    res = 0
    for j in range(i):
        res += ans_arr[j] * temp_arr[i-1][j]
        res %= mod_v
    ans_arr.append(res)


n_list=list(map(int, input().split()))

n = n_list[0]
lines = n_list[1]

new_list = [0 for __ in range(n)]

for i in range(lines):
    input1 = list(map(int, input()))
    for k in range(n):
        new_list[k] |= input1[k] << i

default_d = defaultdict(int)
for k in new_list:
    default_d[k] += 1

answer = 1
for n in default_d.values():
    answer = answer * ans_arr[n] % mod_v

print(answer)
  		 	 	  	    	 	 		   		 	  	