<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:
        neighbor = defaultdict(list)
        n = len(nums)
        for i in range(n):
            for j in range(i):
                if nums[i]%nums[j] == 0 or nums[j]%nums[i] == 0:
                    neighbor[i].append(j)
                    neighbor[j].append(i)
        visited = []
        ans = 0

        @cache
        def dfs(idx,mask):

            def checkbit(idx,mask):
                return (mask >> idx)&1

            def setbit(idx,mask):
                return mask | (1 << idx)

            def clearbit(idx,mask):
                return mask & ~( 1<< idx)
            if checkbit(idx,mask): return 0
            mask = setbit(idx,mask)
            if len(visited) == n-1:
                return 1
            ans = 0
            visited.append(idx)
            for nei in neighbor[idx]:
                ans += dfs(nei,mask) 
            mask = clearbit(idx,mask)
            visited.pop()
            return ans%(10**9+7)

        for i in range(n):
            ans += dfs(i,0)
            ans %= (10**9+7)
        return ans

147100