<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 func(self, index, prev_index, nums, dp):
        #base case
        if(index == len(nums)):
            return []
        if(dp[index][prev_index + 1] != None):
            return dp[index][prev_index + 1]
        #pick and not_pick
        not_pick = self.func(index + 1, prev_index, nums, dp)
        pick = []
        if(prev_index == -1 or nums[index] % nums[prev_index] == 0):
            pick = [nums[index]] + self.func(index + 1, index, nums, dp)
        dp[index][prev_index + 1] = pick if len(pick) > len(not_pick) else not_pick
        return dp[index][prev_index + 1] 
    def largestDivisibleSubset(self, nums: List[int]) -> List[int]:
        nums.sort()
        dp = []
        n = len(nums)
        for i in range(n):
            dp.append([None] * (n + 1))
        return self.func(0, -1, nums, dp)
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