"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>
int n, m, size, mp[300], q[105], tail, dp[1005][105][11], ans;
char s[1005];
class TNode {
 public:
  int next[4], fail, len;
} tg[105];
int getTNode() {
  memset(tg[size].next, 0, sizeof(tg[size].next));
  tg[size].fail = tg[size].len = 0;
  return size++;
}
void insert(char *s) {
  int u = 0;
  for (int i = 0, c; s[i]; ++i) {
    c = mp[s[i]];
    if (!tg[u].next[c]) tg[u].next[c] = getTNode();
    u = tg[u].next[c];
  }
  tg[u].len = strlen(s);
}
void get_fail() {
  tail = 0;
  for (int i = 0; i < 4; ++i)
    if (tg[0].next[i]) q[tail++] = tg[0].next[i];
  for (int i = 0, top; i < tail; ++i) {
    top = q[i];
    tg[top].len = std::max(tg[top].len, tg[tg[top].fail].len);
    for (int j = 0; j < 4; ++j) {
      if (tg[top].next[j]) {
        tg[tg[top].next[j]].fail = tg[tg[top].fail].next[j];
        q[(tail++)] = tg[top].next[j];
      } else
        tg[top].next[j] = tg[tg[top].fail].next[j];
    }
  }
}
void add(int &a, int b) {
  a += b;
  if (a >= 1000000009) a -= 1000000009;
}
int main() {
  mp['A'] = 0, mp['C'] = 1, mp['G'] = 2, mp['T'] = 3;
  while (~scanf("%d%d", &n, &m)) {
    size = 0;
    getTNode();
    for (int i = 0; i < m; ++i) {
      scanf("%s", s);
      insert(s);
    }
    get_fail();
    memset(dp, 0, sizeof(dp));
    dp[0][0][0] = 1;
    for (int i = 0; i < n; ++i)
      for (int j = 0; j < size; ++j)
        for (int k = 0; k < 10; ++k)
          for (int c = 0; c < 4; ++c) {
            if (tg[tg[j].next[c]].len >= k + 1)
              dp[i + 1][tg[j].next[c]][0] =
                  (dp[i + 1][tg[j].next[c]][0] + dp[i][j][k]) % 1000000009;
            else
              dp[i + 1][tg[j].next[c]][k + 1] =
                  (dp[i + 1][tg[j].next[c]][k + 1] + dp[i][j][k]) % 1000000009;
          }
    ans = 0;
    for (int i = 0; i < size; ++i) ans = (ans + dp[n][i][0]) % 1000000009;
    printf("%d\n", ans);
  }
  return 0;
}
