P8106 [Cnoi2021] Math Practice

"Cnoi2021" Cirno's Easy Round II warm-up contest has started.

To make contestants pay attention to regular school subjects, Cirno специально added a math exercise from teacher Kamishirasawa Keine: > Find the number of ways to partition a set $\texttt{U}=\{1,2,3,\cdots,n\}$ into two subsets $S,T$ such that $|S|\notin S,|T|\notin T$. Since the contestants cannot do big-integer arithmetic, you only need to output the answer modulo $998244353$.

One line with one integer $n$.

One line with one integer, representing the answer.

**Sample Explanation.** #1: Two valid partition schemes are $\{1,3\},\{2\}$ and $\{2\},\{1,3\}$. **Constraints.** For $100\%$ of the testdata, it is guaranteed that $1 \le n \le 10^5$. Reprinted from XDUCPC 2021 online contest problem B. Translated by ChatGPT 5