Suppose you have n integers labeled 1 through n. A permutation of those n integers perm (1-indexed) is considered a beautiful arrangement if for every i (1 <= i <= n), either of the following is true:
perm[i] is divisible by i.
i is divisible by perm[i].
Given an integer n, return the number of the beautiful arrangements that you can construct.
Input: n = 2
The first beautiful arrangement is [1,2]:
- perm = 1 is divisible by i = 1
- perm = 2 is divisible by i = 2
The second beautiful arrangement is [2,1]:
- perm = 2 is divisible by i = 1
- i = 2 is divisible by perm = 1