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:

1. The number at the ith position is divisible by i.
2. i is divisible by the number at the ith position.

Now given N, how many beautiful arrangements can you construct?

Example 1:

Input: 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.

Note:

1. N is a positive integer and will not exceed 15.

public class Solution {
    private int count = 0;
    
    public int countArrangement(int N) {
        helper(N, 1, new boolean[N]);
        return count;
    }
    
    private void helper(int N, int level, boolean[] visited) {
        if (level > N) {
            count++;
            return;
        }
        
        for (int i = 1; i <= N; i++) {
            if ( !visited[i - 1] && (level % i == 0 || i % level == 0) ) {
                visited[i - 1] = true;
                helper(N, level + 1, visited); 
                visited[i - 1] = false;
            }
        }
    }
}