"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).

Letwbe 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 lengthnfiltered by the collection $\{s_i\}$.
Answer may appear very large, so output it modulo 1000000009.

First line contains two integer numbers $n,m\ (1≤n≤1000,\ 1≤m≤10)$ − 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.