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 (109<=+<=9).
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).