"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 = 1005;
const long long mod = 1e9 + 9;
struct node {
  int son[5];
  int fail, tag;
};
node t1[maxn];
int top;
inline int newn() {
  top++;
  return top;
}
inline int sth(char c) {
  if (c == 'A') return 0;
  if (c == 'T') return 1;
  if (c == 'C') return 2;
  if (c == 'G') return 3;
}
inline void insert(string s) {
  int u = 0;
  for (int i = 0; i < s.size(); i++) {
    int tp = sth(s[i]);
    if (t1[u].son[tp] == 0) t1[u].son[tp] = newn();
    u = t1[u].son[tp];
  }
  t1[u].tag = s.size();
}
inline void build() {
  queue<int> q;
  for (int i = 0; i < 4; i++) {
    if (t1[0].son[i]) {
      q.push(t1[0].son[i]);
    }
  }
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int i = 0; i < 4; i++) {
      int v = t1[u].son[i];
      if (v == 0) {
        t1[u].son[i] = t1[t1[u].fail].son[i];
        continue;
      }
      t1[v].fail = t1[t1[u].fail].son[i];
      t1[v].tag = max(t1[v].tag, t1[t1[v].fail].tag);
      q.push(v);
    }
  }
}
int dp[maxn][105][15], n, m;
int main() {
  cin >> n >> m;
  int maxs = 0;
  for (int i = 1; i <= m; i++) {
    string s;
    cin >> s;
    insert(s);
    maxs = max(maxs, (int)s.size());
  }
  build();
  dp[0][0][0] = 1;
  for (int i = 0; i <= n - 1; i++) {
    for (int j = 0; j <= top; j++) {
      for (int k = 0; k <= maxs; k++) {
        for (int l = 0; l < 4; l++) {
          int j1 = t1[j].son[l];
          if (k + 1 <= t1[j1].tag) {
            dp[i + 1][j1][0] = (dp[i + 1][j1][0] + dp[i][j][k]) % mod;
            continue;
          }
          if (k + 1 <= maxs) {
            dp[i + 1][j1][k + 1] = (dp[i + 1][j1][k + 1] + dp[i][j][k]) % mod;
            continue;
          }
        }
      }
    }
  }
  int ans = 0;
  for (int i = 0; i <= top; i++) {
    ans = (ans + dp[n][i][0]) % mod;
  }
  cout << ans << endl;
}
