4 - Minimum Division Permutations

Given two arrays $A$ and $B$, both of length $N$ and consisting of only positive integers, your task is to find the number of permutations $P$ of length $N$ such that $\sum_{i=1}^{N} A_{i}/B_{P_{i}}$ is minimum. Since the number of such permutations can be large, print the answer modulo $998244353$. The sequence of $N$ integers is called a permutation if it contains all integers from $1$ to $N$