<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()
        d = dict()
        def f(x, last):
            n = len(x)-1
            if len(x)==0:
                return [last]
            if len(x)==1 and last == None:
                return x
            if d.get((n,last))!=None:
                return d.get((n,last))
            ans = []
            if not last:
                ans =  max(f(x[:n],x[-1]), f(x[:n-1], x[-1]), f(x[:n], None), key = lambda t:len(t)) 
                d[(n, last)] = ans
                return ans

                       
            if last%x[-1]==0:
                ans =  max(f(x[:n], x[-1])+[last], f(x[:n], last), key = lambda t:len(t)) 
            else:
                ans = f(x[:n], last)
            d[(n, last)] = ans
            return ans
    
        return f(nums, None)
56009