<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>

class Solution {
public:
    int helper(std::vector<std::vector<int>>& vec, int n, std::vector<bool>& vis, int begin) {
        if (begin >= n) {
            return 1;
        }
        
        int ans = 0;
        for (int i = 0; i < vec[begin].size(); i++) {
            int num = vec[begin][i];
            if (vis[num]) continue;
            vis[num] = true;
            ans += helper(vec, n, vis, begin + 1);
            vis[num] = false;
        }
        return ans;
    }

    int countArrangement(int n) {
        if (n <= 2) return n;
        
        std::vector<std::vector<int>> vec(n);
        
        for (int i = 0; i < n; i++) {
            for (int j = 1; j <= n; j++) {
                if (i + 1 == j) continue;
                if ((i + 1) % j == 0 || j % (i + 1) == 0) {
                    vec[i].push_back(j);
                }
            }
            vec[i].push_back(i + 1);
        }
        
        std::vector<bool> vis(n + 1, false);
        return helper(vec, n, vis, 0);
    }
};

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