<p>Suppose you have <code>n</code> integers labeled <code>1</code> through <code>n</code>. A permutation of those <code>n</code> integers <code>perm</code> (<strong>1-indexed</strong>) is considered a <strong>beautiful arrangement</strong> if for every <code>i</code> (<code>1 &lt;= i &lt;= n</code>), <strong>either</strong> of the following is true:</p>

<ul>
	<li><code>perm[i]</code> is divisible by <code>i</code>.</li>
	<li><code>i</code> is divisible by <code>perm[i]</code>.</li>
</ul>

<p>Given an integer <code>n</code>, return <em>the <strong>number</strong> of the <strong>beautiful arrangements</strong> that you can construct</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 2
<b>Explanation:</b> 
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
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 15</code></li>
</ul>

class Solution {
private:
    void swap( vector<int> & perms, int i ,int  j ){
        int temp = perms[i];
        perms[i] = perms[j];
        perms[j] = temp;
    }
    void getCount(vector<int> & perms,vector<vector<int>> & ans,int pos,int n){
        if(pos >= perms.size()){
            ans.push_back(perms);
            return;
        }

        for( int i = pos ; i <perms.size() ; i++){
            swap(perms,pos, i );
            if((perms[pos])%(pos+1) == 0 || (pos + 1)%perms[pos] ==0)
                getCount(perms,ans,pos+1,n);
            swap(perms,pos,i);
        }
    }
public:
    int countArrangement(int n) {
        vector<int> perms;
        for( int i = 1 ; i <= n ; i++){
            perms.push_back(i);
        }
        vector<vector<int>> ans;
        getCount(perms,ans,0,n);
        

        int count = 0;

        for( auto ele : ans){
            int i ;
            for(  i = 0 ; i < ele.size() ; i++){
                
                if((ele[i])%(i+1) == 0 || (i + 1)%ele[i] ==0 ){
                   continue;
                }
                break;
            }
            if(i == ele.size()){
                count++;
            }
        }
        return count;

    }
};
20997