"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 = 1010, MAXM = 14, MAXS = MAXM * MAXM, MOD = 1e9 + 9;
void setmax(int &x, int y) {
  if (x < y) {
    x = y;
  }
}
void add(int &x, int y) { x = (x + y) % MOD; }
int N, M;
string str[MAXM];
map<string, int> mp;
int ind;
int dp[MAXN][MAXS][MAXM];
int nxt[MAXS][4];
int suff[MAXS];
int main() {
  if (fopen("input.txt", "r")) {
    freopen("input.txt", "r", stdin);
  }
  ios::sync_with_stdio(false);
  cin >> N >> M;
  mp[""] = ind++;
  int maxlen = 0;
  for (int i = 0; i < M; i++) {
    cin >> str[i];
    setmax(maxlen, str[i].length());
    string t;
    for (char c : str[i]) {
      t += c;
      if (!mp.count(t)) {
        mp[t] = ind++;
      }
    }
  }
  for (auto it = (mp).begin(); it != (mp).end(); it++) {
    string s;
    for (int i = 0; i < 4; i++) {
      s = it->first + "ACGT"[i];
      while (!mp.count(s)) {
        s.erase(s.begin());
      }
      nxt[it->second][i] = mp[s];
    }
    s = it->first;
    for (int i = 0; i < M; i++) {
      string t = str[i];
      if (s.length() < t.length()) {
        continue;
      }
      bool match = true;
      for (int i = int(s.length()) - 1, j = int(t.length()) - 1; j >= 0;
           i--, j--) {
        if (s[i] != t[j]) {
          match = false;
          break;
        }
      }
      if (match) {
        setmax(suff[it->second], t.length());
      }
    }
  }
  dp[0][0][0] = 1;
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < ind; j++) {
      for (int k = 0; k < maxlen; k++) {
        for (int c = 0; c < 4; c++) {
          int nj = nxt[j][c], nk = k + 1;
          if (nk <= suff[nj]) {
            nk = 0;
          }
          if (nk >= maxlen) {
            continue;
          }
          add(dp[i + 1][nj][nk], dp[i][j][k]);
        }
      }
    }
  }
  int ans = 0;
  for (int i = 0; i < ind; i++) {
    add(ans, dp[N][i][0]);
  }
  cout << ans << endl;
}
