A8079 | Genetic engineering

"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 $1000000009$ .

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 should contain a single integer — the number of strings filtered by the collection modulo $1000000009$ ( $10^{9}+9$ ).