"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 = 1E3 + 10;
const int mod = 1000000009;
int que[N];
char s[N];
int nxt[N][5];
int fail[N];
int cnt[N];
int tot, root;
int dp[N][N][11];
void build_trie(char *key) {
  int len = strlen(key), p = 0;
  for (int i = 0; i <= len - 1; i++) {
    char c = key[i];
    int v;
    if (c == 'A') v = 1;
    if (c == 'T') v = 2;
    if (c == 'C') v = 3;
    if (c == 'G') v = 0;
    if (nxt[p][v] == 0) nxt[p][v] = ++tot;
    p = nxt[p][v];
  }
  cnt[p] = len;
}
void build_AC_auto(int root) {
  int head = 0, tail = 0;
  for (int i = 0; i <= 3; i++)
    if (nxt[0][i]) fail[nxt[0][i]] = 0, que[head++] = nxt[0][i];
  while (head != tail) {
    int top = que[tail++];
    for (int i = 0; i <= 3; i++) {
      if (nxt[top][i]) {
        fail[nxt[top][i]] = nxt[fail[top]][i];
        cnt[nxt[top][i]] = max(cnt[nxt[top][i]], cnt[fail[nxt[top][i]]]);
        que[head++] = nxt[top][i];
      } else
        nxt[top][i] = nxt[fail[top]][i];
    }
  }
}
inline void add(int &a, int b) {
  a += b;
  if (a >= mod) a -= mod;
}
char str[20];
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= m; i++) {
    scanf("%s", str);
    build_trie(str);
  }
  fail[0] = 0;
  build_AC_auto(0);
  memset(dp, 0, sizeof dp);
  dp[0][0][0] = 1;
  for (int i = 0; i <= n - 1; i++)
    for (int j = 0; j <= tot; j++)
      for (int z = 0; z <= 9; z++)
        if (dp[i][j][z])
          for (int k = 0; k <= 3; k++) {
            int to = nxt[j][k];
            if (cnt[to] > z)
              add(dp[i + 1][to][0], dp[i][j][z]);
            else
              add(dp[i + 1][to][z + 1], dp[i][j][z]);
          }
  int ans = 0;
  for (int i = 0; i <= tot; i++) add(ans, dp[n][i][0]);
  printf("%d\n", ans);
}
