AT_abc458_f [ABC458F] Critical Misread

You are given $ K $ strings $ S_i $ consisting of lowercase English letters. Find the number, modulo $ 998244353 $ , of strings of length $ N $ consisting of lowercase English letters that do not contain any of $ S_1, S_2, \dots, S_K $ as a substring (contiguous subsequence).

The input is given from Standard Input in the following format: > $ N $ $ K $ $ S_1 $ $ S_2 $ $ \vdots $ $ S_K $

Output the answer.

### Sample Explanation 1 - The number of strings of length $ 3 $ consisting of lowercase English letters is $ 26^3=17576 $ . - The number of strings of length $ 3 $ consisting of lowercase English letters whose first two characters are `aa` is $ 26 $ . - The number of strings of length $ 3 $ consisting of lowercase English letters whose last two characters are `aa` is $ 26 $ . - The number of strings of length $ 3 $ consisting of lowercase English letters whose first two characters are `ab` is $ 26 $ . - The number of strings of length $ 3 $ consisting of lowercase English letters whose last two characters are `ab` is $ 26 $ . - The number of strings of length $ 3 $ consisting of lowercase English letters whose entirety is `aaa` is $ 1 $ . - The number of strings of length $ 3 $ consisting of lowercase English letters whose entirety is `aab` is $ 1 $ . - Combining the above facts, it can be confirmed that the answer for this test case is $ 17474 $ . ### Sample Explanation 3 Find the count modulo $ 998244353 $ . ### Constraints - $ N $ is an integer between $ 1 $ and $ 10^9 $ , inclusive. - $ K $ is an integer between $ 1 $ and $ 10 $ , inclusive. - $ S_i $ is a string consisting of lowercase English letters with length between $ 1 $ and $ 10 $ , inclusive.