<p>You are given a&nbsp;<strong>0-indexed</strong>&nbsp;integer array&nbsp;<code>nums</code>&nbsp;containing&nbsp;<code>n</code>&nbsp;<strong>distinct</strong> positive integers. A permutation of&nbsp;<code>nums</code>&nbsp;is called special if:</p>

<ul>
	<li>For all indexes&nbsp;<code>0 &lt;= i &lt; n - 1</code>, either&nbsp;<code>nums[i] % nums[i+1] == 0</code>&nbsp;or&nbsp;<code>nums[i+1] % nums[i] == 0</code>.</li>
</ul>

<p>Return&nbsp;<em>the total number of special permutations.&nbsp;</em>As the answer could be large, return it&nbsp;<strong>modulo&nbsp;</strong><code>10<sup>9&nbsp;</sup>+ 7</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [2,3,6]
<strong>Output:</strong> 2
<strong>Explanation:</strong> [3,6,2] and [2,6,3] are the two special permutations of nums.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,4,3]
<strong>Output:</strong> 2
<strong>Explanation:</strong> [3,1,4] and [4,1,3] are the two special permutations of nums.
</pre>

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

<ul>
	<li><code>2 &lt;= nums.length &lt;= 14</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def specialPerm(self, nums: List[int]) -> int:
        n = len(nums)
        g = [[] for _ in nums]
        for u, v in combinations(range(n), 2):
            uVal = nums[u]
            vVal = nums[v]
            if uVal > vVal:
                uVal, vVal = vVal, uVal
            if vVal % uVal == 0:
                g[u].append(v)
                g[v].append(u)
        allTakenMask = (1 << n) - 1
        @cache
        def helper(prevIndex, takenNumMask):
            nonlocal n, allTakenMask, g
            if takenNumMask == allTakenMask:
                return 1
            result = 0
            for index in g[prevIndex]:
                if (1 << index) & takenNumMask == 0:
                    result = (result + helper(index, takenNumMask | (1 << index))) % 1_000_000_007
            return result


        result = 0
        for start in range(n):
            result = (result + helper(start, 1 << start)) % 1_000_000_007
        return result
            
225900