<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 largestDivisibleSubset(self, nums: List[int]) -> List[int]:
        nums.sort()
        dp = [[[]]*(len(nums)+1) for _ in range(len(nums)+1)]


        for ind in range(len(nums)-1,-1,-1):
            for preInd in range(ind-1,-2,-1):
                notTake = [] + dp[ind+1][preInd+1]
                take = []
                if preInd==-1 or nums[ind]%nums[preInd]==0:
                    take = [nums[ind]] + dp[ind+1][ind+1]
                if len(take) >= len(notTake):
                    dp[ind][preInd+1] = take
                else:
                    dp[ind][preInd+1] = notTake
        return dp[0][-1+1]









        def solve(ind,preInd):
            if ind>=len(nums):
                return []
            if dp[ind][preInd+1]:
                return dp[ind][preInd+1]
            notTake = [] + solve(ind+1,preInd)
            take = []
            if preInd==-1 or nums[ind]%nums[preInd]==0:
                take = [nums[ind]] + solve(ind+1,ind)
            if len(take) >= len(notTake):
                dp[ind][preInd+1] = take
            else:
                dp[ind][preInd+1] = notTake
            return dp[ind][preInd+1]
        return solve(0,-1)
35691