"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 read() {
  int x = 0, f = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while ('0' <= c && c <= '9') {
    x = x * 10 + c - '0';
    c = getchar();
  }
  return x * f;
}
int n, m, cnt, maxx, tab[300], f[1005][105][105];
char s[15];
struct Trie {
  int bj, len, fail, ch[4];
} tree[105];
void Insert() {
  int len = strlen(s + 1), now = 1;
  maxx = max(maxx, len);
  for (int i = 1; i <= len; ++i) {
    int v = tab[s[i]];
    int &o = tree[now].ch[v];
    if (!o) o = ++cnt;
    now = o;
  }
  tree[now].bj = 1;
  tree[now].len = len;
}
void Build() {
  queue<int> q;
  for (int i = 0; i <= 3; ++i) tree[0].ch[i] = 1;
  q.push(1);
  while (!q.empty()) {
    int x = q.front(), fail = tree[x].fail;
    q.pop();
    tree[x].bj |= tree[fail].bj;
    tree[x].len = max(tree[x].len, tree[fail].len);
    for (int i = 0; i <= 3; ++i) {
      int &y = tree[x].ch[i];
      if (!y)
        y = tree[fail].ch[i];
      else
        tree[y].fail = tree[fail].ch[i], q.push(y);
    }
  }
}
inline int Mod(int x) { return x >= 1000000009 ? x - 1000000009 : x; }
int main() {
  tab['A'] = 0;
  tab['C'] = 1;
  tab['G'] = 2;
  tab['T'] = 3;
  n = read();
  m = read();
  cnt = 1;
  for (int i = 1; i <= m; ++i) scanf("%s", s + 1), Insert();
  Build();
  f[0][0][1] = 1;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j <= maxx; ++j)
      for (int k = 1; k <= cnt; ++k)
        if (f[i][j][k])
          for (int p = 0; p <= 3; ++p) {
            int y = tree[k].ch[p];
            if (j + 1 <= tree[y].len)
              f[i + 1][0][y] = Mod(f[i + 1][0][y] + f[i][j][k]);
            else
              f[i + 1][j + 1][y] = Mod(f[i + 1][j + 1][y] + f[i][j][k]);
          }
  int ans = 0;
  for (int k = 1; k <= cnt; ++k) ans = Mod(ans + f[n][0][k]);
  cout << ans << '\n';
}
