Problem Statement

You are given $a set S=\lbrace s _ 1,s _ 2,\ldots,s _ M\rbrace$ of non-empty strings of length at most 6 consisting of a and b.
Find the number of strings T of length N consisting of a and b that satisfy the following condition:

• T does not contain s _ i as a consecutive substring for any $s _ i\in$ S.

Since the answer can be enormous, find it modulo 998244353.

Input

The input is given from Standard Input in the following format:
N M
s _ 1
s _ 2
$\vdots$
s _ M

Output

Print the answer modulo 998244353 in a single line.

Constraints

• $1\leq N\leq10^{18}$
• $1\leq M\leq126$
• N and M are integers.
• s _ i is a non-empty string of length at most 6 consisting of a and b.
• $s _ i\neq s _ j$\ $(1\leq i\lt j\leq M)$

Sample Input 1

4 3
aab
bbab
abab

Sample Output 1

10

There are 10 strings of length 4 consisting of a and b that do not contain aab, bbab, or abab as consecutive substrings: aaaa, abaa, abba, abbb, baaa, baba, babb, bbaa, bbba, and bbbb. Thus, you should print 10.

Sample Input 2

20 1
aa

Sample Output 2

17711

Sample Input 3

1000000007 28
bbabba
bbbbaa
aabbab
bbbaba
baaabb
babaab
bbaaba
aabaaa
aaaaaa
aabbaa
bbaaaa
bbaabb
bbabab
aababa
baaaba
ababab
abbaba
aabaab
ababaa
abbbba
baabaa
aabbbb
abbbab
baaaab
baabbb
ababbb
baabba
abaaaa

Sample Output 3

566756841

Print the answer modulo 998244353.

见题面 Input 部分

见题面 Output 部分