"Multidimensional spaces are completely out of style these days, unlike genetics problems" — thought physicist Woll and changed his subject of study to bioinformatics. Analysing results of sequencing he faced the following problem concerning DNA sequences. We will further think of a DNA sequence as an arbitrary string of uppercase letters "A", "C", "G" and "T" (of course, this is a simplified interpretation).

Let w be a long DNA sequence and s1, s2, ..., sm — collection of short DNA sequences. Let us say that the collection filters w iff w can be covered with the sequences from the collection. Certainly, substrings corresponding to the different positions of the string may intersect or even cover each other. More formally: denote by |w| the length of w, let symbols of w be numbered from 1 to |w|. Then for each position i in w there exist pair of indices l, r (1 ≤ l ≤ i ≤ r ≤ |w|) such that the substring w[l ... r] equals one of the elements s1, s2, ..., sm of the collection.

Woll wants to calculate the number of DNA sequences of a given length filtered by a given collection, but he doesn't know how to deal with it. Help him! Your task is to find the number of different DNA sequences of length n filtered by the collection {si}.

Answer may appear very large, so output it modulo 1000000009.

Input

First line contains two integer numbers n and m (1 ≤ n ≤ 1000, 1 ≤ m ≤ 10) — the length of the string and the number of sequences in the collection correspondently. 

Next m lines contain the collection sequences si, one per line. Each si is a nonempty string of length not greater than 10. All the strings consist of uppercase letters "A", "C", "G", "T". The collection may contain identical strings.

Output

Output should contain a single integer — the number of strings filtered by the collection modulo 1000000009 (109 + 9).

Examples

Input

2 1
A


Output

1


Input

6 2
CAT
TACT


Output

2

Note

In the first sample, a string has to be filtered by "A". Clearly, there is only one such string: "AA".

In the second sample, there exist exactly two different strings satisfying the condition (see the pictures below).

<image> <image>
#include <bits/stdc++.h>
using namespace std;
int ch[101][4], b[101], fa[101], mx[101], tot, n, m, ans, f[1001][101][11];
char s[200];
struct AC {
  int p;
  void insert(char *s) {
    int l = strlen(s);
    p = 0;
    for (int i = 0; i < l; i++) {
      int id = s[i] == 'A' ? 0 : (s[i] == 'C' ? 1 : (s[i] == 'T' ? 2 : 3));
      if (!ch[p][id]) ch[p][id] = ++tot;
      p = ch[p][id];
    }
    b[p] = l;
  }
  void getfail() {
    queue<int> q;
    for (int i = 0; i < 4; i++)
      if (ch[0][i]) q.push(ch[0][i]), mx[ch[0][i]] = b[ch[0][i]];
    while (!q.empty()) {
      int r = q.front();
      q.pop();
      for (int i = 0; i < 4; i++) {
        int u = ch[r][i], v = fa[r];
        if (!u) {
          ch[r][i] = ch[v][i];
          continue;
        }
        q.push(u);
        while (v && !ch[v][i]) v = fa[v];
        fa[u] = ch[v][i];
        mx[u] = max(mx[fa[u]], b[u]);
      }
    }
  }
} ac;
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 0; i < m; i++) {
    scanf("%s", s);
    ac.insert(s);
  }
  ac.getfail();
  f[0][0][0] = 1;
  for (int i = 0; i < n; i++)
    for (int j = 0; j <= tot; j++)
      for (int k = 0; k < 10; k++)
        for (int c = 0; c < 4; c++)
          if (ch[j][c]) {
            if (mx[ch[j][c]] >= k + 1)
              (f[i + 1][ch[j][c]][0] += f[i][j][k]) %= 1000000009;
            else
              (f[i + 1][ch[j][c]][k + 1] += f[i][j][k]) %= 1000000009;
          }
  for (int i = 0; i <= tot; i++) (ans += f[n][i][0]) %= 1000000009;
  printf("%d\n", ans);
}
