Count of Labeled Edge‐Biconnected Graphs

Given an integer n, count the number of labeled edge‐biconnected graphs on n vertices. A graph is an undirected simple graph that is edge‐biconnected (i.e. 2‐edge‐connected) if it is connected and remains connected after the removal of any single edge. The answer should be given modulo \(998244353\).

Note: For n = 2, the only connected graph (a single edge) contains a bridge, so the answer is 0.

inputFormat

The input consists of a single integer n on one line, representing the number of vertices.

Constraints: The value of n is small (for example, 2 ≤ n ≤ 5) so that a brute force enumeration is feasible.

outputFormat

Output a single integer: the number of labeled edge‐biconnected graphs on n vertices modulo \(998244353\).

sample

2

0