Given an undirected connected graph of $$$n$$$ vertices and $$$n-1$$$ edges, where $$$n$$$ is guaranteed to be odd. You want to divide all the $$$n-1$$$ edges to $$$\frac{n-1}{2}$$$ groups under following constraints:
Determine the number of valid dividing schemes modulo $$$998244353$$$. Two schemes are considered different if there are 2 edges that are in the same group in one scheme but not in the same group in the other scheme.
The first line contains one integer $$$n\,(3\le n \le 10^5)$$$, denoting the number of vertices.
Following $$$n-1$$$ lines each contains two integers $$$u,v\,(1 \le u \lt v \le n)$$$, denoting that vertex $$$u,v$$$ are undirectedly connected by an edge.
It is guaranteed that $$$n$$$ is odd and that the given graph is connected.
Output one line containing one integer, denoting the number of valid dividing schemes modulo $$$998244353$$$.
7 1 2 1 3 1 7 4 7 5 7 6 7
3
The 3 schemes are:
