While doing dfs, pre-check if it meets the requirement of beautiful arrangements.

Question:

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.

Example:

1 2 3 4 5 6 7 8 9

Input: n = 2 Output: 2 Explanation: The first beautiful arrangement is [1,2]: - perm[1] = 1 is divisible by i = 1 - perm[2] = 2 is divisible by i = 2 The second beautiful arrangement is [2,1]: - perm[1] = 2 is divisible by i = 1 - i = 2 is divisible by perm[2] = 1