<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=sorted(list(set(nums)))

        n=len(nums)
        dp=[[[-1]]*n for _ in range(n)]
        def sol(ind,pre):
            if(ind==n):
                return []
            if(dp[ind][pre]!=[-1]):
                return dp[ind][pre]
            op1=sol(ind+1,pre)
            # op2=[]
            if(pre==-1 or nums[ind]%nums[pre]==0):
                op2=[nums[ind]]+sol(ind+1,ind)

                if len(op1)>len(op2):
                    dp[ind][pre]=op1
                    return op1 
                else: 
                    dp[ind][pre]=op2
                    return op2
            dp[ind][pre]=op1
            return op1
        return sol(0,-1)


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