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}.
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
    private static final int REM = 1000000007;

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        int m = in.nextInt();
        int n = in.nextInt();

        String[] T = new String[n];

        for (int i=0; i<n; ++i) {
            T[i] = in.next();
        }

        boolean[] found = new boolean[m];
        List<Integer> groups = new ArrayList<>();
        for (int i=0; i<m; ++i) {
            if (!found[i]) {
                List<Integer> bits = new ArrayList<>();
                bits.add(i);
                found[i] = true;
                int count = 0;
                while (!bits.isEmpty()) {
                    ++count;
                    int bit = bits.remove(bits.size()-1);

                    for (int j=0; j<m; ++j) {
                        if (!found[j]) {
                            boolean samegroup = true;

                            for (int k=0; k<n; ++k) {
                                if (T[k].charAt(bit) != T[k].charAt(j)) {
                                    samegroup = false;
                                }
                            }
                            if (samegroup) {
                                found[j] = true;
                                bits.add(j);
                            }
                        }
                    }
                }
                //System.out.println(count);
                groups.add(count);
            }
        }

        int[][] dp = new int[m+1][m+1];
        int[] total = new int[m+1];

        dp[0][0] = 1;
        for (int i=1; i<=m; ++i) {
            for (int j=1; j<=i; ++j) {
                dp[i][j] = (int)(((long)dp[i-1][j] * j % REM + dp[i-1][j-1]) % REM);
                total[i] = (total[i] + dp[i][j]) % REM;
            }
        }

        int ans = 1;
        for (int size : groups) {
            ans = (int)((long)ans * total[size] % REM);
        }
        System.out.println(ans);
    }
}
