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}.
#include <bits/stdc++.h>
using namespace std;
vector<vector<long long> > comb(int n, int mod = 1e9 + 7) {
  vector<vector<long long> > comb(n + 1, vector<long long>(n + 1));
  comb[0][0] = 1;
  for (int i = 0; i <= n; i++) {
    comb[i][0] = 1;
    for (int j = 1; j <= i; j++) {
      comb[i][j] = (comb[i - 1][j] + comb[i - 1][j - 1]) % mod;
    }
  }
  return comb;
}
vector<long long> bell(int n, vector<vector<long long> > comb,
                       int mod = 1e9 + 7) {
  vector<long long> B(n + 1);
  B[0] = 1;
  for (int i = 1; i <= n; i++) {
    for (int k = 0; k < i; k++) {
      B[i] = (B[i] + B[k] * comb[i - 1][k] % mod) % mod;
    }
  }
  return B;
}
int main() {
  int m, n;
  cin >> m >> n;
  vector<string> T(n);
  for (int i = 0; i < n; i++) {
    cin >> T[i];
  }
  vector<long long> masks(m);
  for (int j = 0; j < m; j++) {
    for (int i = 0; i < n; i++) {
      if (T[i][j] == '1') {
        masks[j] |= 1LL << i;
      }
    }
  }
  vector<int> sizes_to_partition;
  vector<bool> included(m);
  for (int bit = 0; bit < m; bit++) {
    if (included[bit]) {
      continue;
    }
    included[bit] = true;
    int cur_size = 1;
    for (int j = bit + 1; j < m; j++) {
      if (masks[bit] == masks[j]) {
        included[j] = true;
        cur_size++;
      }
    }
    sizes_to_partition.push_back(cur_size);
  }
  if (sizes_to_partition.empty()) {
    sizes_to_partition.push_back(m);
  }
  int ans = 1;
  vector<long long> B = bell(m, comb(m));
  for (int cur_size : sizes_to_partition) {
    ans = ans * B[cur_size] % (long long)(1e9 + 7);
  }
  cout << ans << '\n';
}
