<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:
    def countArrangement(self, N: int) -> int:
        if N == 0:
            return 0
        nums = list(range(1, N + 1))
        used = [False] * N
        p, res = [], []
        self.generatePermutation526(nums, 0, p, res, used)
        return len(res)

    def generatePermutation526(self, nums, index, p, res, used):
        if index == len(nums):
            res.append(p[:])
            return
        for i in range(len(nums)):
            if not used[i]:
                if not self.checkDivisible(nums[i], len(p) + 1) and not self.checkDivisible(len(p) + 1, nums[i]):
                    continue
                used[i] = True
                p.append(nums[i])
                self.generatePermutation526(nums, index + 1, p, res, used)
                p.pop()
                used[i] = False

    def checkDivisible(self, num, d):
        return num % d == 0
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