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.

static int countArrangements(int n,int[] data){
    if(n<=0){
      return 1;
    }
    int count = 0;
    for(int i=0;i<n;++i){

      // Just check if any number can be placed at n index.
      if(data[i]%n == 0 || n%data[i] ==0){
        swap(data,i,n-1);
        count += countArrangements(n-1,data);
        swap(data,i,n-1);
      }
    }
    return count;
  }

  static void swap(int[] data,int i,int j){
    int temp = data[i];
    data[i] = data[j];
    data[j] = temp;
  }

  static int arrangements(int n) {
    int[] data = new int[n];
    for(int i=0;i<n;++i){
      data[i] = i+1;
    }
    return countArrangements(n,data);
  }