"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 maxn = 1500;
const int MOD = 1e9 + 9;
int ing[128];
long long dp[1005][105][15];
int n, m;
struct ac_auto {
  int nxt[maxn][4], fail[maxn], ed[maxn], q[maxn];
  int L = 0;
  void inserta(char buf[]) {
    int now = 0;
    int len = strlen(buf);
    for (int i = 0; buf[i]; i++) {
      int son = ing[(int)buf[i]];
      if (!nxt[now][son]) nxt[now][son] = ++L;
      now = nxt[now][son];
    }
    ed[now] = len;
  }
  void getfail() {
    int front = 0, back = 0, now = 0;
    for (int i = 0; i < 4; i++)
      if (nxt[now][i]) q[++back] = nxt[now][i];
    while (front < back) {
      now = q[++front];
      for (int i = 0; i < 4; i++) {
        if (nxt[now][i]) {
          fail[nxt[now][i]] = nxt[fail[now]][i];
          q[++back] = nxt[now][i];
        } else
          nxt[now][i] = nxt[fail[now]][i];
        ed[nxt[now][i]] = max(ed[nxt[now][i]], ed[nxt[fail[now]][i]]);
      }
    }
  }
  void work() {
    memset(dp, 0, sizeof dp);
    dp[0][0][0] = 1;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j <= L; j++) {
        for (int k = 0; k <= 10; k++)
          for (int f = 0; f < 4; f++) {
            if (ed[nxt[j][f]] > k) {
              dp[i + 1][nxt[j][f]][0] += dp[i][j][k];
              dp[i + 1][nxt[j][f]][0] %= MOD;
            } else {
              dp[i + 1][nxt[j][f]][k + 1] += dp[i][j][k];
              dp[i + 1][nxt[j][f]][k + 1] %= MOD;
            }
          }
      }
    }
    long long ans = 0;
    for (int i = 0; i <= L; i++) {
      ans += dp[n][i][0];
      ans %= MOD;
    }
    cout << ans << endl;
  }
} ac;
char ss[15];
int main() {
  ing['A'] = 0, ing['T'] = 1, ing['C'] = 2, ing['G'] = 3;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= m; i++) {
    scanf("%s", ss);
    ac.inserta(ss);
  }
  ac.getfail();
  ac.work();
  return 0;
}
