AT_abc458_f.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).

给你 $K$ 个由小写英文字母组成的字符串 $S_i$。
求长度为 $N$、由小写英文字母组成的字符串中，不包含 $S_1, S_2, \dots, S_K$ 中任意一个作为子串（连续子序列）的字符串个数，结果对 $998244353$ 取模。

The input is given from Standard Input in the following format:

$N$ $K$
$S_1$
$S_2$
$\vdots$
$S_K$

输入从标准输入中按以下格式给出：

$N$ $K$
$S_1$
$S_2$
$\vdots$
$S_K$

Output the answer.

输出答案。

Sample 1 Explanation:

• 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 3 Explanation:
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.

样例 1 解释：

• 长度为 $3$、由小写英文字母组成的字符串总数为 $26^3 = 17576$。
• 长度为 $3$、由小写英文字母组成且前两个字符为 aa 的字符串数量为 $26$。
• 长度为 $3$、由小写英文字母组成且后两个字符为 aa 的字符串数量为 $26$。
• 长度为 $3$、由小写英文字母组成且前两个字符为 ab 的字符串数量为 $26$。
• 长度为 $3$、由小写英文字母组成且后两个字符为 ab 的字符串数量为 $26$。
• 长度为 $3$、由小写英文字母组成且整个字符串恰好为 aaa 的字符串数量为 $1$。
• 长度为 $3$、由小写英文字母组成且整个字符串恰好为 aab 的字符串数量为 $1$。
• 综合以上事实，可确认该测试用例的答案为 $17474$。

样例 3 解释：
求结果对 $998244353$ 取模的值。

约束条件

• $N$ 是一个介于 $1$ 和 $10^9$（含）之间的整数。
• $K$ 是一个介于 $1$ 和 $10$（含）之间的整数。
• $S_i$ 是一个由小写英文字母组成的字符串，其长度介于 $1$ 和 $10$（含）之间。