P6598 Alkane Counting

How many structural isomers (stereoisomers not considered) are there for an alkane with $n$ carbon atoms? Hint: If you do not know what an alkane is, you can consider this problem equivalent to counting the number of unlabelled unrooted trees with $n$ nodes, where the degree of each node is $\le 4$.

An integer $n$ representing the number of carbon atoms.

Output an integer representing the answer, taken modulo $998244353$.

#### Explanation for Sample 1  #### Constraints For all testdata, it is guaranteed that $1 \le n \le 10^5$. Translated by ChatGPT 5