"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 mod = 1e9 + 9;
queue<int> q;
struct node {
  int ch[4], end, dep, fail;
} nodes[110];
int turn[1000], dp[1010][110][20], ans;
int n, m, len, tot, nel[110];
char s[20];
void ins() {
  int now = 0;
  for (int i = 1; i <= len; ++i) {
    if (!nodes[now].ch[turn[s[i]]]) {
      nodes[now].ch[turn[s[i]]] = ++tot;
      nodes[tot].dep = nodes[now].dep + 1;
    }
    now = nodes[now].ch[turn[s[i]]];
  }
  nel[now] = nodes[now].dep;
  nodes[now].end = 1;
}
void build() {
  for (int i = 0; i < 4; ++i) {
    if (nodes[0].ch[i]) {
      q.push(nodes[0].ch[i]);
      nodes[nodes[0].ch[i]].dep = 1;
    }
  }
  while (!q.empty()) {
    int now = q.front();
    q.pop();
    for (int i = 0; i < 4; ++i) {
      if (nodes[now].ch[i]) {
        q.push(nodes[now].ch[i]);
        nodes[nodes[now].ch[i]].dep = nodes[now].dep + 1;
        nodes[nodes[now].ch[i]].fail = nodes[nodes[now].fail].ch[i];
      } else
        nodes[now].ch[i] = nodes[nodes[now].fail].ch[i];
    }
    nel[now] = max(nel[now], nel[nodes[now].fail]);
  }
}
int main() {
  turn['A'] = 0;
  turn['G'] = 1;
  turn['T'] = 2;
  turn['C'] = 3;
  scanf("%d %d", &n, &m);
  for (int i = 1; i <= m; ++i) {
    scanf("%s", s + 1);
    len = strlen(s + 1);
    ins();
  }
  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 <= nodes[j].dep; ++k) {
        for (int z = 0; z < 4; ++z) {
          if (nel[nodes[j].ch[z]] > k) {
            dp[i + 1][nodes[j].ch[z]][0] += dp[i][j][k];
            dp[i + 1][nodes[j].ch[z]][0] %= mod;
          } else {
            dp[i + 1][nodes[j].ch[z]][k + 1] += dp[i][j][k];
            dp[i + 1][nodes[j].ch[z]][k + 1] %= mod;
          }
        }
      }
    }
  }
  for (int j = 0; j <= tot; ++j) {
    ans += dp[n][j][0];
    ans %= mod;
  }
  printf("%d\n", ans);
  return 0;
}
