<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 {
public:
    vector<int> largestDivisibleSubset(vector<int>& nums) {
        sort(nums.begin(),nums.end());
        int n=nums.size();
        vector<int>dp(n,1);
        vector<int>in(n);
        int ind=0;
        for(int i=0;i<n;i++)in[i]=i;
        for(int i=1;i<n;i++){
            for(int j=i-1;j>=0;j--){
                if(nums[i]%nums[j]==0 && dp[i]<dp[j]+1){
                    dp[i]=dp[j]+1;
                    in[i]=j;
                }
            }
            if(dp[ind]<dp[i])ind=i;
        }
        vector<int>ans;
        while(in[ind]!=ind){
            ans.push_back(nums[ind]);
            ind=in[ind];
        }
        ans.push_back(nums[ind]);
        return ans;
    }
};
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