"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;
typedef long long int64;
typedef unsigned long long uint64;
const double pi = acos(-1.0);
const double eps = 1e-11;
template <class T>
inline void checkmin(T &a, T b) {
  if (b < a) a = b;
}
template <class T>
inline void checkmax(T &a, T b) {
  if (b > a) a = b;
}
template <class T>
inline T sqr(T x) {
  return x * x;
}
typedef pair<int, int> ipair;
template <class T>
inline T lowbit(T n) {
  return (n ^ (n - 1)) & n;
}
template <class T>
inline int countbit(T n) {
  return (n == 0) ? 0 : (1 + countbit(n & (n - 1)));
}
template <class T>
inline T gcd(T a, T b) {
  if (a < 0) return gcd(-a, b);
  if (b < 0) return gcd(a, -b);
  return (b == 0) ? a : gcd(b, a % b);
}
template <class T>
inline T lcm(T a, T b) {
  if (a < 0) return lcm(-a, b);
  if (b < 0) return lcm(a, -b);
  return a * (b / gcd(a, b));
}
template <class T>
inline T euclide(T a, T b, T &x, T &y) {
  if (a < 0) {
    T d = euclide(-a, b, x, y);
    x = -x;
    return d;
  }
  if (b < 0) {
    T d = euclide(a, -b, x, y);
    y = -y;
    return d;
  }
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  } else {
    T d = euclide(b, a % b, x, y);
    T t = x;
    x = y;
    y = t - (a / b) * y;
    return d;
  }
}
template <class T>
inline vector<pair<T, int> > factorize(T n) {
  vector<pair<T, int> > R;
  for (T i = 2; n > 1;) {
    if (n % i == 0) {
      int C = 0;
      for (; n % i == 0; C++, n /= i)
        ;
      R.push_back(make_pair(i, C));
    }
    i++;
    if (i > n / i) i = n;
  }
  if (n > 1) R.push_back(make_pair(n, 1));
  return R;
}
template <class T>
inline bool isPrimeNumber(T n) {
  if (n <= 1) return false;
  for (T i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return true;
}
template <class T>
inline T eularFunction(T n) {
  vector<pair<T, int> > R = factorize(n);
  T r = n;
  for (int i = 0; i < R.size(); i++) r = r / R[i].first * (R[i].first - 1);
  return r;
}
const int MaxMatrixSize = 40;
template <class T>
inline void showMatrix(int n, T A[MaxMatrixSize][MaxMatrixSize]) {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) cout << A[i][j];
    cout << endl;
  }
}
template <class T>
inline T checkMod(T n, T m) {
  return (n % m + m) % m;
}
template <class T>
inline void identityMatrix(int n, T A[MaxMatrixSize][MaxMatrixSize]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) A[i][j] = (i == j) ? 1 : 0;
}
template <class T>
inline void addMatrix(int n, T C[MaxMatrixSize][MaxMatrixSize],
                      T A[MaxMatrixSize][MaxMatrixSize],
                      T B[MaxMatrixSize][MaxMatrixSize]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = A[i][j] + B[i][j];
}
template <class T>
inline void subMatrix(int n, T C[MaxMatrixSize][MaxMatrixSize],
                      T A[MaxMatrixSize][MaxMatrixSize],
                      T B[MaxMatrixSize][MaxMatrixSize]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = A[i][j] - B[i][j];
}
template <class T>
inline void mulMatrix(int n, T C[MaxMatrixSize][MaxMatrixSize],
                      T _A[MaxMatrixSize][MaxMatrixSize],
                      T _B[MaxMatrixSize][MaxMatrixSize]) {
  T A[MaxMatrixSize][MaxMatrixSize], B[MaxMatrixSize][MaxMatrixSize];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      A[i][j] = _A[i][j], B[i][j] = _B[i][j], C[i][j] = 0;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      for (int k = 0; k < n; k++) C[i][j] += A[i][k] * B[k][j];
}
template <class T>
inline void addModMatrix(int n, T m, T C[MaxMatrixSize][MaxMatrixSize],
                         T A[MaxMatrixSize][MaxMatrixSize],
                         T B[MaxMatrixSize][MaxMatrixSize]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = checkMod(A[i][j] + B[i][j], m);
}
template <class T>
inline void subModMatrix(int n, T m, T C[MaxMatrixSize][MaxMatrixSize],
                         T A[MaxMatrixSize][MaxMatrixSize],
                         T B[MaxMatrixSize][MaxMatrixSize]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = checkMod(A[i][j] - B[i][j], m);
}
template <class T>
inline T multiplyMod(T a, T b, T m) {
  return (T)((((int64)(a) * (int64)(b) % (int64)(m)) + (int64)(m)) %
             (int64)(m));
}
template <class T>
inline void mulModMatrix(int n, T m, T C[MaxMatrixSize][MaxMatrixSize],
                         T _A[MaxMatrixSize][MaxMatrixSize],
                         T _B[MaxMatrixSize][MaxMatrixSize]) {
  T A[MaxMatrixSize][MaxMatrixSize], B[MaxMatrixSize][MaxMatrixSize];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      A[i][j] = _A[i][j], B[i][j] = _B[i][j], C[i][j] = 0;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      for (int k = 0; k < n; k++)
        C[i][j] = (C[i][j] + multiplyMod(A[i][k], B[k][j], m)) % m;
}
template <class T>
inline T powerMod(T p, int e, T m) {
  if (e == 0)
    return 1 % m;
  else if (e % 2 == 0) {
    T t = powerMod(p, e / 2, m);
    return multiplyMod(t, t, m);
  } else
    return multiplyMod(powerMod(p, e - 1, m), p, m);
}
double dist(double x1, double y1, double x2, double y2) {
  return sqrt(sqr(x1 - x2) + sqr(y1 - y2));
}
double distR(double x1, double y1, double x2, double y2) {
  return sqr(x1 - x2) + sqr(y1 - y2);
}
template <class T>
T cross(T x0, T y0, T x1, T y1, T x2, T y2) {
  return (x1 - x0) * (y2 - y0) - (x2 - x0) * (y1 - y0);
}
int crossOper(double x0, double y0, double x1, double y1, double x2,
              double y2) {
  double t = (x1 - x0) * (y2 - y0) - (x2 - x0) * (y1 - y0);
  if (fabs(t) <= eps) return 0;
  return (t < 0) ? -1 : 1;
}
bool isIntersect(double x1, double y1, double x2, double y2, double x3,
                 double y3, double x4, double y4) {
  return crossOper(x1, y1, x2, y2, x3, y3) * crossOper(x1, y1, x2, y2, x4, y4) <
             0 &&
         crossOper(x3, y3, x4, y4, x1, y1) * crossOper(x3, y3, x4, y4, x2, y2) <
             0;
}
bool isMiddle(double s, double m, double t) {
  return fabs(s - m) <= eps || fabs(t - m) <= eps || (s < m) != (t < m);
}
bool isUpperCase(char c) { return c >= 'A' && c <= 'Z'; }
bool isLowerCase(char c) { return c >= 'a' && c <= 'z'; }
bool isLetter(char c) { return c >= 'A' && c <= 'Z' || c >= 'a' && c <= 'z'; }
bool isDigit(char c) { return c >= '0' && c <= '9'; }
char toLowerCase(char c) { return (isUpperCase(c)) ? (c + 32) : c; }
char toUpperCase(char c) { return (isLowerCase(c)) ? (c - 32) : c; }
template <class T>
string toString(T n) {
  ostringstream ost;
  ost << n;
  ost.flush();
  return ost.str();
}
int toInt(string s) {
  int r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
int64 toInt64(string s) {
  int64 r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
double toDouble(string s) {
  double r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
template <class T>
void stoa(string s, int &n, T A[]) {
  n = 0;
  istringstream sin(s);
  for (T v; sin >> v; A[n++] = v)
    ;
}
template <class T>
void atos(int n, T A[], string &s) {
  ostringstream sout;
  for (int i = 0; i < n; i++) {
    if (i > 0) sout << ' ';
    sout << A[i];
  }
  s = sout.str();
}
template <class T>
void atov(int n, T A[], vector<T> &vi) {
  vi.clear();
  for (int i = 0; i < n; i++) vi.push_back(A[i]);
}
template <class T>
void vtoa(vector<T> vi, int &n, T A[]) {
  n = vi.size();
  for (int i = 0; i < n; i++) A[i] = vi[i];
}
template <class T>
void stov(string s, vector<T> &vi) {
  vi.clear();
  istringstream sin(s);
  for (T v; sin >> v; vi.push_bakc(v))
    ;
}
template <class T>
void vtos(vector<T> vi, string &s) {
  ostringstream sout;
  for (int i = 0; i < vi.size(); i++) {
    if (i > 0) sout << ' ';
    sout << vi[i];
  }
  s = sout.str();
}
template <class T>
struct Fraction {
  T a, b;
  Fraction(T a = 0, T b = 1);
  string toString();
};
template <class T>
Fraction<T>::Fraction(T a, T b) {
  T d = gcd(a, b);
  a /= d;
  b /= d;
  if (b < 0) a = -a, b = -b;
  this->a = a;
  this->b = b;
}
template <class T>
string Fraction<T>::toString() {
  ostringstream sout;
  sout << a << "/" << b;
  return sout.str();
}
template <class T>
Fraction<T> operator+(Fraction<T> p, Fraction<T> q) {
  return Fraction<T>(p.a * q.b + q.a * p.b, p.b * q.b);
}
template <class T>
Fraction<T> operator-(Fraction<T> p, Fraction<T> q) {
  return Fraction<T>(p.a * q.b - q.a * p.b, p.b * q.b);
}
template <class T>
Fraction<T> operator*(Fraction<T> p, Fraction<T> q) {
  return Fraction<T>(p.a * q.a, p.b * q.b);
}
template <class T>
Fraction<T> operator/(Fraction<T> p, Fraction<T> q) {
  return Fraction<T>(p.a * q.b, p.b * q.a);
}
const int MODE = 1000000009;
const int maxsize = 10000;
int size, length, n;
string a[15];
map<pair<string, int>, int> M;
bool good[maxsize];
int deg[maxsize], g[maxsize][50];
int f0[maxsize], f1[maxsize];
void addTo(int &a, int b) {
  a += b;
  if (a >= MODE) a -= MODE;
}
int get_id(string s, int p);
int calc(string s, int p) {
  while (((int)(s.length())) > 0) {
    int L = ((int)(s.length()));
    bool exists = false;
    for (int i = 0; i < n; i++) {
      int L0 = ((int)(a[i].length()));
      if (L0 >= L && s == a[i].substr(0, L)) {
        exists = true;
        break;
      }
    }
    if (exists) break;
    s = s.substr(1);
    if (p > ((int)(s.length()))) return -1;
  }
  return get_id(s, p);
}
int get_id(string s, int p) {
  int L = ((int)(s.length()));
  while (p > 0) {
    int nextp = p;
    for (int i = 0; i < n; i++) {
      int L0 = ((int)(a[i].length()));
      for (int k = 0; k <= L - L0; k++)
        if (k <= L - p && k + L0 - 1 >= L - p && a[i] == s.substr(k, L0))
          checkmin(nextp, L - (k + L0));
    }
    if (nextp == p) break;
    p = nextp;
  }
  if (M.find(make_pair(s, p)) != M.end()) return M[make_pair(s, p)];
  int idx = size++;
  M[make_pair(s, p)] = idx;
  good[idx] = (p == 0);
  deg[idx] = 0;
  for (int i = 0; i < 4; i++) {
    string s2 = s;
    if (i == 0) s2 += 'A';
    if (i == 1) s2 += 'C';
    if (i == 2) s2 += 'G';
    if (i == 3) s2 += 'T';
    int t = calc(s2, p + 1);
    if (t >= 0) {
      g[idx][deg[idx]++] = t;
    }
  }
  return idx;
}
int main() {
  scanf("%d%d", &length, &n);
  for (int i = 0; i < n; i++) {
    char s[1024];
    scanf("%s", s);
    a[i] = s;
  }
  size = 0;
  M.clear();
  int src = get_id("", 0);
  for (int i = 0; i < size; i++) f0[i] = 0;
  f0[src] = 1;
  for (int step = 0; step < length; step++) {
    for (int i = 0; i < size; i++) f1[i] = 0;
    for (int i = 0; i < size; i++)
      if (f0[i])
        for (int j = 0; j < deg[i]; j++) addTo(f1[g[i][j]], f0[i]);
    for (int i = 0; i < size; i++) f0[i] = f1[i];
  }
  int R = 0;
  for (int i = 0; i < size; i++)
    if (good[i]) addTo(R, f0[i]);
  printf("%d\n", R);
  return 0;
}
