Beautiful Arrangement
<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>
Bit Manipulation; Array; Dynamic Programming; Backtracking; Bitmask
impl Solution {
    fn dfs(i: usize, n: usize, mat: &Vec<Vec<usize>>, vis: &mut Vec<bool>, res: &mut i32) {
        if i == n + 1 {
            *res += 1;
            return;
        }
        for &j in mat[i].iter() {
            if !vis[j] {
                vis[j] = true;
                Self::dfs(i + 1, n, mat, vis, res);
                vis[j] = false;
            }
        }
    }

    pub fn count_arrangement(n: i32) -> i32 {
        let n = n as usize;
        let mut vis = vec![false; n + 1];
        let mut mat = vec![Vec::new(); n + 1];
        for i in 1..=n {
            for j in 1..=n {
                if i % j == 0 || j % i == 0 {
                    mat[i].push(j);
                }
            }
        }

        let mut res = 0;
        Self::dfs(1, n, &mat, &mut vis, &mut res);
        res
    }
}
