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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        static final long MODULO = (long) (1e9 + 7);

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int m = in.nextInt();
            int n = in.nextInt();
            String[] t = new String[n];
            for (int i = 0; i < n; ++i) {
                t[i] = in.next();
            }
            long[] code = new long[m];
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < m; ++j) {
                    code[j] |= ((long) (t[i].charAt(j) - '0')) << i;
                }
            }
            Arrays.sort(code);
            int[][] comb = new int[code.length + 2][code.length + 2];
            comb[0][0] = 1;
            for (int i = 1; i < comb.length; ++i) {
                comb[i][0] = 1;
                for (int j = 1; j < comb.length; ++j) {
                    comb[i][j] = (comb[i - 1][j - 1] + comb[i - 1][j]) % (int) MODULO;
                }
            }
            long[] ways = new long[code.length + 1];
            ways[0] = 1;
            for (int i = 1; i < ways.length; ++i) {
                for (int j = 1; j <= i; ++j) {
                    ways[i] = (ways[i] + ways[i - j] * comb[i - 1][j - 1]) % MODULO;
                }
            }
            long res = 1;
            int block = 1;
            for (int i = 1; i < code.length; ++i) {
                if (code[i] == code[i - 1]) {
                    ++block;
                } else {
                    res = res * ways[block] % MODULO;
                    block = 1;
                }
            }
            res = res * ways[block] % MODULO;
            out.println(res);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

