<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>

#include<vector> 
#include<math.h> 

class Solution {
public:    
    void resolve(int index,std::vector<int>& source,int range
    ,std::vector<bool>& marks,std::vector<std::vector<int>>& nested){
        if(index>range){
            std::vector<int> clone(source) ; 
            nested.push_back(clone) ; 
            return  ; 
        } 
        for( int dx=1;dx<=range;dx++){  
            if(marks[dx-1]==true){continue ;  }
            if(((index>=dx)&& (index%dx==0))||((dx>index)&&(dx%index==0))){  
                marks[dx-1] = true ; 
                 source.push_back(dx) ;  
                resolve(index+1,source,range,marks,nested) ;
               source.erase(--source.end()) ;  
               marks[dx-1] = false ;    } 
                 }  
    }
    int countArrangement(int n) {
        std::vector<int> vectors ;
        std::vector<std::vector<int>> nested ;     
        std::vector<bool> signs(n+1,false) ; 
        resolve(1,vectors,n,signs,nested) ; 
        int width = nested.size() ; 
        return width  ; 
    }
}  ;
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