<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 count(self, nums, graph, index, num, mask):
        if mask == ((1 << len(nums)) - 1):
            return 1

        idx = index[num] if num else 0

        if self.dp[mask][idx] != -1:
            return self.dp[mask][nums.index(num)]

        result = 0
        for nex in graph[num]:
            if (1 << index[nex]) & mask == 0:
                result += self.count(nums, graph, index, nex, mask | (1 << index[nex]))
                result = result % (1e9 + 7)

        self.dp[mask][idx] = result
        return result

    def specialPerm(self, nums: List[int]) -> int:
        graph = {num : [] for num in nums}
        for i, num1 in enumerate(nums):
            for j, num2 in enumerate(nums):
                if i > j and (num1 % num2 == 0 or num2 % num1 == 0):
                    graph[num1].append(num2)
                    graph[num2].append(num1)

        index = {num: i for i, num in enumerate(nums)}

        graph[0] = nums
        self.dp = [[-1 for _ in range(20)] for _ in range((1 << 14) + 10)]    
        return int(self.count(nums, graph, index, 0, 0))

24400