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;
using ll = long long;
constexpr ll mod = 1000000007;
ll st2[1007][1007];
ll bell[1007];
string s[50];
vector<int> unions;
vector<int> size;
void init(int n) {
  unions = vector<int>(n, -1);
  size = vector<int>(n, 1);
}
int findSet(int n) {
  if (unions[n] < 0) return n;
  return unions[n] = findSet(unions[n]);
}
void linkSets(int a, int b) {
  size[a] += size[b];
  size[b] = size[a];
  if (unions[a] > unions[b])
    unions[a] = b;
  else if (unions[b] > unions[a])
    unions[b] = a;
  else {
    unions[a] = b;
    unions[b]--;
  }
}
void unionSets(int a, int b) {
  if (findSet(a) != findSet(b)) linkSets(findSet(a), findSet(b));
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  for (int n = 1; n <= 1000; ++n) {
    st2[n][1] = 1;
    for (int k = 2; k <= n; ++k) {
      st2[n][k] = k * st2[n - 1][k] + st2[n - 1][k - 1];
      st2[n][k] %= mod;
    }
  }
  for (int n = 1; n <= 1000; ++n) {
    for (int k = 0; k <= n; ++k) {
      bell[n] += st2[n][k];
      bell[n] %= mod;
    }
  }
  int m, n;
  cin >> m >> n;
  for (int i = 0; i < n; i++) cin >> s[i];
  init(m);
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < m; j++) {
      bool all = true;
      for (int k = 0; k < n; k++) all &= s[k][i] == s[k][j];
      if (all) unionSets(i, j);
    }
  }
  ll res = 1;
  for (int i = 0; i < m; i++) {
    res *= bell[size[findSet(i)]];
    res %= mod;
    size[findSet(i)] = 1;
  }
  cout << res << endl;
}
