<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 Solution {
public:
    vector<int>rank,parent;
    int find(int x){
        return (x == parent[x])?x:parent[x] =find(parent[x]);
    }
    void merge(int x,int y){
        int xroot = find(x);
        int yroot = find(y);

        if(xroot != yroot){
            if(rank[xroot] > rank[yroot]){
                rank[xroot] += rank[yroot];
                parent[yroot] = xroot ;
            }
            else{
                rank[yroot] += rank[xroot];
                parent[xroot] = yroot ;
            }
        }
    }
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        parent.resize(n+1,0);
        rank.resize(n+1,1);
        for(int i =0 ; i<n ;i++){
            parent[i] = i;
        }
        
        vector<int>factors(100100,-1);
        for(int i =0 ;i<n ;i++){
            int x = nums[i];
            for(int j = 2 ; j*j <=x ; j++){
                if(x%j == 0){
                    if(factors[j] != -1 ){
                        // cout<< i <<" "<<j<<endl;
                        merge(factors[j],i);
                    }
                        factors[j] = i ;

                    if(j*j != x){
                      int of = x/j ;
                      if(factors[of] != -1){
                        merge(factors[of],i);
                      }
                        factors[of] = i ;
                    }
                }
            }
            if(factors[x]!=-1)merge(factors[x],i);
            factors[x] = i ;
        }
        
        int sz = 0;
        // for(int i =0 ;i<n ;i++){
        //     cout<<find(i)<<"";
        // }
        // cout<<endl;

        for(int i =0 ;i<n ;i++){
            sz = max(sz,rank[find(i)]);
        }
        return sz ;
    }
};
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