AT_abc419_f [ABC419F] All Included

You are given $ N $ lowercase English strings $ S_1,S_2,\ldots,S_N $ , and an integer $ L $ . Find the number, modulo $ 998244353 $ , of length- $ L $ lowercase English strings that contain all of $ S_1,S_2,\ldots,S_N $ as substrings. What is a substring?A **substring** of $ S $ is a string obtained by deleting zero or more characters from the beginning and zero or more characters from the end of $ S $ . For example, `ab`, `bc`, and `bcd` are substrings of `abcd`, while `ac`, `dc`, and `e` are not substrings of `abcd`.

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

Output the answer.

### Sample Explanation 1 Some of the strings that satisfy the condition are `abcz` and `cabc`. `acbd` does not contain `ab` as a substring, so it does not satisfy the condition. ### Constraints - $ 1\leq N\leq 8 $ - $ 1\leq L\leq 100 $ - $ N $ and $ L $ are integers. - Each $ S_i $ is a string of length $ 1 $ and $ 10 $ , inclusive, consisting of lowercase English letters. - $ S_i\neq S_j\ (i\neq j) $