Suppose you have n integers labeled from $1$ to n. A $1$ indexed permutation of these n integers, perm, is considered a beautiful arrangement if for every index i ($1 \leq$ i $\leq$ n), at least one of the following conditions holds:

• perm[i] is divisible by i

• i is divisible by perm[i]

Given an integer n, return the total number of beautiful arrangements that can be constructed.

Constraints:

• $1 \leq$ n $\leq 15$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.