Good Permutations

You are given two arrays $A$ and $B$, each of size $N$. Let $P$ denote a permutation length $N$. The permutation $P$ is said to be *good*, if you can make an array $C$ where: - $C_i = A_i + B_{P_i}$ **or** $C_i = A_i - B_{P_i}$, for all $(1\le i \le N)$; - All elements of $C$ are **equal**. Out of the $N!$ possible permutations, find the count of *good* permutations. Since the count can be hu