<p>Given a set of <strong>distinct</strong> positive integers <code>nums</code>, return the largest subset <code>answer</code> such that every pair <code>(answer[i], answer[j])</code> of elements in this subset satisfies:</p>

<ul>
	<li><code>answer[i] % answer[j] == 0</code>, or</li>
	<li><code>answer[j] % answer[i] == 0</code></li>
</ul>

<p>If there are multiple solutions, return any of them.</p>

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

<pre>
<strong>Input:</strong> nums = [1,2,3]
<strong>Output:</strong> [1,2]
<strong>Explanation:</strong> [1,3] is also accepted.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,4,8]
<strong>Output:</strong> [1,2,4,8]
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 2 * 10<sup>9</sup></code></li>
	<li>All the integers in <code>nums</code> are <strong>unique</strong>.</li>
</ul>

class Solution:
    def __init__(self):
        self.memo = dict()
    def helper(self, prev_idx, idx):
        key = "{},{}".format(prev_idx, idx)
        if key in self.memo:
            return self.memo[key]
        if idx == len(self.nums):
            return []
        notake = self.helper(prev_idx, idx+1)
        if prev_idx == -1 or self.nums[idx] % self.nums[prev_idx] == 0:
            take = [self.nums[idx]] + self.helper(idx, idx+1)
        else:
            take = []
        if len(notake) > len(take):
            self.memo[key] = notake
        else:
            self.memo[key] = take
        return self.memo[key]

    def largestDivisibleSubset(self, nums: List[int]) -> List[int]:
        self.nums = sorted(nums)
        return self.helper(-1, 0)
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