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C. Genetic engineering

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard output"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).

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).

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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