<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:
        _len = len(nums)
        # def dfs(s): # s: start position
        #     nonlocal ans
        #     if s == len(nums):
        #         ans += 1
                        
        #     for i in range(s, len(nums)):
        #         if s > 0:
        #             if nums[i] % nums[s - 1] != 0 and nums[s - 1] % nums[i] != 0:
        #                 continue
        #         nums[i], nums[s] = nums[s], nums[i]
        #         dfs(s + 1)
        #         nums[i], nums[s] = nums[s], nums[i]

        @functools.lru_cache(None)
        def dfs(state, last_position): # state is 000001000, s is the start postion
            if state == (1 << _len) - 1:
                return 1
            ans = 0
            for i in range(_len):
                if state & (1 << i) > 0:
                    continue
                if (last_position == -1 or 
                    nums[i] % nums[last_position] == 0 or
                    nums[last_position] % nums[i] == 0):
                    ans += dfs(state | 1 << i, i)
            return ans
        
        return dfs(0, -1) % (10 ** 9 + 7)
                    
        
2762