<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 DisjointSet{
public:
    int components;
    vector<int>parent;
    vector<int>size;

    DisjointSet(int n){
        components = n;
        parent.resize(n);
        size.resize(n,1);
        for(int i=0;i<n;i++){
            parent[i]=i;
        }
    }
    int findParent(int u){
        if(u==parent[u]){
            return u;
        }
        return parent[u]=findParent(parent[u]);
    }
    void unionbysize(int u,int v){
        int uP=findParent(u);
        int vP=findParent(v);

        if(uP==vP){
            return;
        }

        if(size[uP]>=size[vP]){
            parent[vP]=uP;
            size[uP]+=size[vP];
            components--;
        }
        else{
            parent[uP]=vP;
            size[vP]+=size[uP];
            components--;
        }
        return;
    }
};

class Solution {
public:
    int largestComponentSize(vector<int>& nums) {
       map<int,vector<int>>factor; 
       int n = nums.size();
       for(int i=0;i<n;i++){
           for(int j=2;j*j<=nums[i];j++){
               if(nums[i]%j==0){
                   factor[j].push_back(i);
                   while(nums[i]%j==0) nums[i]/=j; 
               }
           }
          
           if(nums[i]>1) factor[nums[i]].push_back(i) ; 
       }
       
       DisjointSet ds(n);
       for(auto&it:factor){
           vector<int>prime_pos=it.second;
          
           for(int i=1;i<prime_pos.size();i++){
               ds.unionbysize(prime_pos[i-1],prime_pos[i]);
           }
       }

       
       int mx  = 0 ;
       for(int i=0;i<n;i++){
           mx=max(mx,ds.size[i]);
       }
       return mx;
    }
};
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