Biological Software Utilities

You are developing a software kit named Biological Software Utilities (BSU). The kit includes a program that is dedicated to tree recognition. Recall that a tree is a connected undirected graph without cycles.

In nature, when a tree grows, two neighboring vertices are added at the same time. Thus, you consider a tree to be plausible if, after removing some edges, the resulting graph consists only of connected components with $2$ vertices. In other words, a tree is plausible if and only if it has a perfect matching.

Now you are to implement a new function for BSU to calculate the number of plausible trees that have $n$ vertices numbered with distinct integers between $1$ and $n$. Two trees are considered different if there is an edge $(u, v)$ which is present in exactly one of the trees.

Since the number of plausible trees can be very large, you have to calculate it modulo $998\\,244\\,353$.

The only line contains an integer $n$, the number of vertices in a tree ($1 \le n \le 10^6$).

Print the number of plausible trees with $n$ vertices modulo $998\\,244\\,353$.