"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 N = 105;
const int Q = 1e9 + 9;
int nodecnt;
int u[N][4], f[N], len[N];
queue<int> q;
inline int id(char c) {
  if (c == 'A') return 0;
  if (c == 'C') return 1;
  if (c == 'G') return 2;
  if (c == 'T') return 3;
  return -1;
}
void insert(char str[], int p) {
  int x = 0;
  for (int i = 0; str[i]; ++i) {
    int c = id(str[i]);
    if (!u[x][c]) u[x][c] = nodecnt++;
    x = u[x][c];
  }
  len[x] = p;
}
void getFail() {
  for (int i = 0; i < 4; ++i)
    if (u[0][i]) f[u[0][i]] = 0, q.push(u[0][i]);
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    for (int i = 0; i < 4; ++i) {
      int y = u[x][i];
      if (!y) {
        u[x][i] = u[f[x]][i];
        continue;
      }
      q.push(y);
      int j = f[x];
      while (j && !u[j][i]) j = f[j];
      f[y] = u[j][i], len[y] = max(len[y], len[f[y]]);
    }
  }
}
int n, m;
char s[N];
int F[1005][105][15];
inline void add(int& A, int B) {
  A += B;
  if (A >= Q) A -= Q;
}
void work() {
  int i, j, k, l;
  scanf("%d%d", &n, &m);
  nodecnt = 1;
  for (i = 0; i < m; ++i) {
    scanf("%s", s);
    insert(s, strlen(s));
  }
  getFail();
  F[0][0][0] = 1;
  for (i = 0; i <= n; ++i)
    for (j = 0; j < nodecnt; ++j)
      for (k = 0; k < 10; ++k) {
        if (!F[i][j][k]) continue;
        for (l = 0; l < 4; ++l) {
          int x = u[j][l];
          int y = len[x];
          if (y > k)
            add(F[i + 1][x][0], F[i][j][k]);
          else if (k != 9)
            add(F[i + 1][x][k + 1], F[i][j][k]);
        }
      }
  int res = 0;
  for (i = 0; i < nodecnt; ++i) add(res, F[n][i][0]);
  cout << res << endl;
}
int main() {
  work();
  return 0;
}
