A10294 | Bear and Compressing

Limak is a little polar bear. Polar bears hate long strings and thus they like to compress them. You should also know that Limak is so young that he knows only first six letters of the English alphabet: 'a', 'b', 'c', 'd', 'e' and 'f'.

You are given a set of $q$ possible operations. Limak can perform them in any order, any operation may be applied any number of times. The $i$ -th operation is described by a string $a_{i}$ of length two and a string $b_{i}$ of length one. No two of $q$ possible operations have the same string $a_{i}$ .

When Limak has a string $s$ he can perform the $i$ -th operation on $s$ if the first two letters of $s$ match a two-letter string $a_{i}$ . Performing the $i$ -th operation removes first two letters of $s$ and inserts there a string $b_{i}$ . See the notes section for further clarification.

You may note that performing an operation decreases the length of a string $s$ exactly by $1$ . Also, for some sets of operations there may be a string that cannot be compressed any further, because the first two letters don't match any $a_{i}$ .

Limak wants to start with a string of length $n$ and perform $n-1$ operations to finally get a one-letter string "a". In how many ways can he choose the starting string to be able to get "a"? Remember that Limak can use only letters he knows.

The first line contains two integers $n$ and $q$ ( $2<=n<=6$ , $1<=q<=36$ ) — the length of the initial string and the number of available operations.

The next $q$ lines describe the possible operations. The $i$ -th of them contains two strings $a_{i}$ and $b_{i}$ ( $|a_{i}|=2,|b_{i}|=1$ ). It's guaranteed that $a_{i}≠a_{j}$ for $i≠j$ and that all $a_{i}$ and $b_{i}$ consist of only first six lowercase English letters.

Print the number of strings of length $n$ that Limak will be able to transform to string "a" by applying only operations given in the input.