<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()
        n = len(nums)
        dp={}

        # def dfs(ind,prev_ind):
        #     if ind>len(nums): return []

        #     if (ind,prev_ind) in dp: return dp[(ind,prev_ind)]
        #     not_take = dfs(ind+1,prev_ind)
        #     take = []
        #     if prev_ind==0 or nums[ind-1]%nums[prev_ind-1]==0:
        #         take = [nums[ind-1]] + dfs(ind+1,ind)
        #     dp[(ind,prev_ind)] = max(take,not_take,key=len)
        #     return max(take,not_take,key=len)
        for j in range(n+1):
            dp[(n+1,j)]=[]
        for ind in range(n,-1,-1):
            for prev_ind in range(ind-1,-1,-1):
                not_take = dp[(ind+1,prev_ind)]
                take = []
                if prev_ind==0 or nums[ind-1]%nums[prev_ind-1]==0:
                    take = [nums[ind-1]] + dp[(ind+1,ind)]
                dp[(ind,prev_ind)] = max(take,not_take,key=len)

        return dp[(1,0)]


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