"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;
const int N = 1005;
const long long MOD = 1e9 + 9;
const int Len = 11;
map<char, int> parsing = {{'A', 0}, {'T', 1}, {'C', 2}, {'G', 3}};
char c[Len];
int tr[1005][4], tot;
int e[1005], fail[1005];
void insert(char *s) {
  int u = 0;
  for (int i = 0; s[i]; i++) {
    int t = parsing[s[i]];
    if (!tr[u][t]) tr[u][t] = ++tot;
    u = tr[u][t];
  }
  if (strlen(s) > e[u]) e[u] = strlen(s);
}
queue<int> q;
void build() {
  for (int i = 0; i < 4; i++)
    if (tr[0][i]) q.push(tr[0][i]);
  while (q.size()) {
    int u = q.front();
    q.pop();
    for (int i = 0; i < 4; i++) {
      if (tr[u][i])
        fail[tr[u][i]] = tr[fail[u]][i], q.push(tr[u][i]),
        e[tr[u][i]] = max(e[tr[u][i]], e[fail[tr[u][i]]]);
      else
        tr[u][i] = tr[fail[u]][i];
    }
  }
}
long long dp[N][N][12];
int main() {
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    cin >> c;
    insert(c);
  }
  build();
  dp[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 t = 0; t < 4; t++) {
          int u = tr[j][t];
          if (e[u] > k)
            dp[i + 1][u][0] = (dp[i + 1][u][0] + dp[i][j][k]) % MOD;
          else
            dp[i + 1][u][k + 1] = (dp[i + 1][u][k + 1] + dp[i][j][k]) % MOD;
        }
      }
    }
  }
  long long ans = 0;
  for (int i = 0; i <= tot; i++) {
    ans = (ans + dp[n][i][0]) % MOD;
  }
  cout << ans << endl;
  return 0;
}
