Background

You may need:

• Alkyl Counting

• Alkane Counting

Since Luogu does not have the two problems above, this problem is made instead.

Problem Description

Find the number of isomers of alkenes (homologs of ethylene) with chemical formula $\text{C}_n \text{H}_{2n}$.

In this problem, stereoisomerism and cis-trans isomerism are not considered.

The answer should be taken modulo $998244353$.

Input Format

A positive integer $n$.

Output Format

Output a total of $n-1$ lines, where the $i$-th line is the answer for alkenes with $2 \sim n$ carbon atoms.

5

1
1
3
5

Hint

Explanation for Sample 1

• $n=2$: ethylene.
• $n=3$: propylene.
• $n=4$: 1-butene; 2-butene; 2-methyl-1-propene.
• $n=5$: 1-pentene; 2-pentene; 2-methyl-1-butene; 3-methyl-1-butene; 2-methyl-2-butene.

Constraints

For $100\%$ of the testdata, it is guaranteed that $1 \leq n \leq 100000$.

Translated by ChatGPT 5