Counting Is Fun

You are given a positive integer $N$. Find the number of arrays $A$ of size $N$ such that: - There exist two permutations$^\dag$ $P$ and $Q$, each of length $N$, satisfying $A_i = \max(P_i, Q_i)$ for all $1\le i \le N$. Since the number might be huge, print it modulo $998244353$. $^\dag$A permutation of length $N$ consists of all integers from $1$ to $N$ exactly once. ### Input - The first lin