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:
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
Example 2:
Input: n = 1 Output: 1
Constraints:
1 <= n <= 15