"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;
const int maxnode = 2000;
int n, m;
int ch[maxnode][26], tot = 0, f[maxnode], last[maxnode], val[maxnode],
                     dp[1007][201][11];
char s[20];
void ins(char *s, int len) {
  int u = 0;
  for (int i = int(0); i <= int(len - 1); ++i) {
    int c = s[i] - 'A';
    if (!ch[u][c]) ch[u][c] = ++tot;
    u = ch[u][c];
  }
  val[u] = len;
}
void build() {
  queue<int> q;
  f[0] = 0;
  for (int i = int(0); i <= int(25); ++i) {
    int u = ch[0][i];
    if (u) {
      f[u] = last[u] = 0;
      q.push(u);
    }
  }
  while (!q.empty()) {
    int r = q.front();
    q.pop();
    for (int i = int(0); i <= int(25); ++i) {
      int u = ch[r][i];
      if (!u) {
        ch[r][i] = ch[f[r]][i];
        continue;
      }
      q.push(u);
      int v = f[r];
      while (v && !ch[v][i]) v = f[v];
      f[u] = ch[v][i];
      last[u] = val[f[u]] ? f[u] : last[f[u]];
      val[u] = max(val[u], val[last[u]]);
    }
  }
}
char DNA[4] = {'A', 'C', 'G', 'T'};
int main() {
  int n, m;
  cin >> n >> m;
  for (int i = int(1); i <= int(m); ++i) {
    scanf("%s", s);
    int len = strlen(s);
    ins(s, len);
  }
  build();
  dp[0][0][0] = 1;
  for (int i = int(0); i <= int(n); ++i)
    for (int j = int(0); j <= int(tot); ++j)
      for (int k = int(0); k <= int(9); ++k)
        if (dp[i][j][k]) {
          for (int l = int(0); l <= int(3); ++l) {
            int c = DNA[l] - 'A';
            int nxt = ch[j][c];
            if (val[nxt] >= k + 1)
              (dp[i + 1][nxt][0] += dp[i][j][k]) %= MOD;
            else
              (dp[i + 1][nxt][k + 1] += dp[i][j][k]) %= MOD;
          }
        }
  int ans = 0;
  for (int i = int(0); i <= int(tot); ++i) (ans += dp[n][i][0]) %= MOD;
  cout << ans << endl;
}
