"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 = 1000000009;
int num(char c) {
  if (c == 'A') return 0;
  if (c == 'G') return 1;
  if (c == 'C')
    return 2;
  else
    return 3;
}
const int N = 1010;
const int M = 110;
int n, m, ch[M][4], fail[M], val[M], tail = 0;
long long dp[N][M][15], ans = 0;
char s[20];
queue<int> Q;
void insert() {
  int len = strlen(s);
  int tmp = 0;
  for (int i = 0; i < len; i++) {
    int c = num(s[i]);
    if (!ch[tmp][c]) ch[tmp][c] = ++tail;
    tmp = ch[tmp][c];
  }
  val[tmp] = len;
}
void getfail() {
  for (int i = 0; i < 4; i++)
    if (ch[0][i]) {
      Q.push(ch[0][i]);
      fail[ch[0][i]] = 0;
    }
  while (!Q.empty()) {
    int top = Q.front();
    Q.pop();
    for (int i = 0; i < 4; i++) {
      if (!ch[top][i]) {
        ch[top][i] = ch[fail[top]][i];
        continue;
      }
      int u = ch[top][i];
      fail[u] = ch[fail[top]][i];
      val[u] = max(val[u], val[fail[u]]);
      Q.push(u);
    }
  }
}
void getans() {
  memset(dp, 0, sizeof(dp));
  dp[0][0][0] = 1;
  for (int i = 0; i < n; i++) {
    for (int u = 0; u <= tail; u++) {
      for (int j = 0; j <= 10; j++) {
        for (int c = 0; c < 4; c++) {
          int v = ch[u][c];
          if (val[v] >= j + 1)
            dp[i + 1][v][0] = (dp[i + 1][v][0] + dp[i][u][j]) % mod;
          else
            dp[i + 1][v][j + 1] = (dp[i][u][j] + dp[i + 1][v][j + 1]) % mod;
        }
      }
    }
  }
  long long ans = 0;
  for (int i = 1; i <= tail; i++) {
    ans = (ans + dp[n][i][0]) % mod;
  }
  printf("%I64d\n", ans);
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= m; i++) {
    scanf("%s", s);
    insert();
  }
  getfail();
  getans();
  return 0;
}
