"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 $*s*_{1}, *s*_{2}, ..., *s*_{*m*}$ — 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 $*s*_{1}, *s*_{2}, ..., *s*_{*m*}$ 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 ${*s*_{*i*}}$.

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 $*s*_{*i*}$, one per line. Each $*s*_{*i*}$ 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 $1000000009$ ($10^{9} + 9$).

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).