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

Solution:

```
class Solution {
int count = 0;
public int countArrangement(int n) {
int[] nums = new int[n];
for (int i = 0; i < n; i++)
nums[i] = i + 1;
permute(nums, 0);
return count;
}
private void permute(int[] nums, int k) {
if (k == nums.length)
count++;
for (int i = k; i < nums.length; i++) {
swap(nums, i, k);
if (nums[k] % (k + 1) == 0 || (k + 1) % nums[k] == 0)
permute(nums, k + 1);
swap(nums, i, k);
}
}
private void swap(int[] nums, int i, int j) {
int temp = nums[i];
nums[i] = nums[j];
nums[j] = temp;
}
}
```

Happy Coding!

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