Problem A. Appropriate names ≡

Statement

A company wants to name a new product. Marketing department determined, that a name for a product is appropriate, if:

1. it consist of exactly N small English letters;
2. it has alternating vowels and consonants;
3. it does not contain any of given M offensive substrings.

Your program must calculate the number of possible appropriate names. Note that English vowels are: 'a', 'e', 'i', 'o', 'u', 'y'.

Input file format

First line of input file contains two integers N M — name length and number of offensive substrings.

Following M lines contain offensive substrings s_i, one per line.

Output file format

Output file must contain a single integer — number of appropriate names modulo 10⁹ + 7.

Constraints

1 ≤ N ≤ 50, 0 ≤ M ≤ 50, 1 ≤ length(s_i) ≤ N.

Sample tests

2 3
b
ca
b

227

5 0

374400