4068: Genetic engineering
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
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题目描述
C. Genetic engineering
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
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 s1,s2,...,sm − 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 s1,s2,...,sm 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 {si}.
Answer may appear very large, so output it modulo 1000000009.
Let w be a long DNA sequence and s1,s2,...,sm − 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 s1,s2,...,sm 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 {si}.
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 si, one per line. Each si 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 (109+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).
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