"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 inf = 0x3f3f3f3f;
const int maxn = 105;
const int maxm = 305;
const int mod = 1e9 + 9;
int n, m;
int id[55];
int dp[1005][maxn][12];
struct AC {
  int cnt;
  int tr[maxn][30], fail[maxn];
  int val[maxn];
  queue<int> q;
  void init() {
    cnt = 0;
    memset(tr, 0, sizeof(tr));
    memset(fail, 0, sizeof(fail));
    memset(val, 0, sizeof(val));
    while (!q.empty()) q.pop();
  }
  void insert(char *s) {
    int u = 0;
    int len = strlen(s);
    for (int i = 0; i <= len - 1; i++) {
      int x = id[s[i] - 'A'];
      if (!tr[u][x]) tr[u][x] = ++cnt;
      u = tr[u][x];
    }
    val[u] = len;
  }
  void build() {
    for (int i = 0; i <= 3; i++)
      if (tr[0][i]) q.push(tr[0][i]);
    while (q.size()) {
      int u = q.front();
      q.pop();
      val[u] = max(val[u], val[fail[u]]);
      for (int i = 0; i <= 3; i++) {
        if (tr[u][i])
          fail[tr[u][i]] = tr[fail[u]][i], q.push(tr[u][i]);
        else
          tr[u][i] = tr[fail[u]][i];
      }
    }
  }
  void solve() {
    dp[0][0][0] = 1;
    for (int i = 0; i <= n - 1; i++)
      for (int j = 0; j <= cnt; j++)
        for (int p = 0; p <= 10; p++)
          for (int k = 0; k <= 3; k++) {
            int nxt = tr[j][k];
            if (val[nxt] >= p + 1)
              dp[i + 1][nxt][0] += dp[i][j][p], dp[i + 1][nxt][0] %= mod;
            else
              dp[i + 1][nxt][p + 1] += dp[i][j][p],
                  dp[i + 1][nxt][p + 1] %= mod;
          }
    int ans = 0;
    for (int j = 0; j <= cnt; j++) ans += dp[n][j][0], ans %= mod;
    printf("%d\n", ans);
  }
} ac;
char s[15];
int main() {
  id['A' - 'A'] = 0;
  id['C' - 'A'] = 1;
  id['G' - 'A'] = 2;
  id['T' - 'A'] = 3;
  scanf("%d%d", &n, &m);
  ac.init();
  for (int i = 1; i <= m; i++) scanf("%s", s), ac.insert(s);
  ac.build();
  ac.solve();
  return 0;
}
