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526. Beautiful Arrangement

Suppose you have n integers from 1 to n. We define a beautiful arrangement as an array that is constructed by these n numbers successfully if one of the following is true for the ith position (1 <= i <= n) in this array:

  • The number at the ith position is divisible by i.
  • i is divisible by the number at the ith position.

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]:
Number at the 1st position (i=1) is 1, and 1 is divisible by i (i=1).
Number at the 2nd position (i=2) is 2, and 2 is divisible by i (i=2).
The second beautiful arrangement is [2, 1]:
Number at the 1st position (i=1) is 2, and 2 is divisible by i (i=1).
Number at the 2nd position (i=2) is 1, and i (i=2) is divisible by 1.

Example 2:

Input: n = 1
Output: 1

Constraints:

  • 1 <= n <= 15