<p>You are given an integer array of unique positive integers <code>nums</code>. Consider the following graph:</p>

<ul>
	<li>There are <code>nums.length</code> nodes, labeled <code>nums[0]</code> to <code>nums[nums.length - 1]</code>,</li>
	<li>There is an undirected edge between <code>nums[i]</code> and <code>nums[j]</code> if <code>nums[i]</code> and <code>nums[j]</code> share a common factor greater than <code>1</code>.</li>
</ul>

<p>Return <em>the size of the largest connected component in the graph</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/01/ex1.png" style="width: 500px; height: 97px;" />
<pre>
<strong>Input:</strong> nums = [4,6,15,35]
<strong>Output:</strong> 4
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/01/ex2.png" style="width: 500px; height: 85px;" />
<pre>
<strong>Input:</strong> nums = [20,50,9,63]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/01/ex3.png" style="width: 500px; height: 260px;" />
<pre>
<strong>Input:</strong> nums = [2,3,6,7,4,12,21,39]
<strong>Output:</strong> 8
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
	<li>All the values of <code>nums</code> are <strong>unique</strong>.</li>
</ul>

class DSU
{
    vector<int> parent;
    vector<int> rank;

    public:
    DSU(int n)
    {
        parent.resize(n+1);
        rank.resize(n+1,0);

        for(int i=1;i<=n;i++)
        parent[i]=i;
    }

    int find(int x)
    {
        if(parent[x]==x)
        return x;

        return parent[x] = find(parent[x]); 
    }

    void Union(int x, int y)
    {
        int px = find(x);
        int py = find(y);

        if(px==py)
        return;

        if(rank[px]<rank[py])
        parent[px] = py;
        else if(rank[py]<rank[px])
        parent[py] = px;
        else
        {
            parent[py] = px;
            rank[px]++;
        } 
    }
};

class Solution {
public:
    int largestComponentSize(vector<int>& nums) {
        
        int largest = -1;
        for(auto x:nums)
        largest= max(largest,x);

        DSU unit(largest);

        for(auto x : nums)
        {
            for(int i=2;i*i<=x;i++)
            {
                if(x%i==0){
                unit.Union(i,x);
                unit.Union(x/i,x);
                }
            }
        }

        vector<int> connects(largest+1,0);
        int ans=-1;

        for(auto x:nums)
        {
            connects[unit.find(x)]++;
            ans = max(ans,connects[unit.find(x)]);
        }

        return ans;
    }
};
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