Inversions of subsequences

Chef has a permutation $P$ of length $N$. Chef wants to find the number of **non-empty** [subsequences](https://en.wikipedia.org/wiki/Subsequence) of $P$ which have the same number of *inversions* as $P$. Since the answer can be large, output it modulo $998244353$. Note: - A permutation of length $N$ contains all integers from $1$ to $N$ exactly once. - The number of *inversions* in an array $