<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:
    vector<int>rank,parent,size;
    disjointset(int n){
        rank.resize(n+1,0);
        parent.resize(n+1,0);
        size.resize(n+1,0);
        for(int i=0;i<=n;i++){
            parent[i]=i;
            size[i]=1;
        }
    }
    
    int findpar(int node){
        if(node==parent[node]) return node;
        return parent[node]=findpar(parent[node]);
    }
    
    void unionbyrank(int u,int v){
        int ulp_u=findpar(u);
        int ulp_v=findpar(v);
        if(ulp_u==ulp_v) return;
        if(rank[ulp_u]<rank[ulp_v]){
            parent[ulp_u]=ulp_v;
        }
        else if(rank[ulp_u]>rank[ulp_v]){
            parent[ulp_v]=ulp_u;
        }
        else{
            parent[ulp_v]=ulp_u;
            rank[ulp_v]++;
        }
    }
    
    void unionbysize(int u,int v){
        int ulp_u=findpar(u);
        int ulp_v=findpar(v);
        if(ulp_u==ulp_v) return;
        if(size[ulp_u]<size[ulp_v]){
            parent[ulp_u]=ulp_v;
            size[ulp_v]+=size[ulp_u];
        }
        else{
            parent[ulp_v]=ulp_u;
            size[ulp_u]+=size[ulp_v];
        }
    }
    
};
class Solution {
public:
    int largestComponentSize(vector<int>& nums) {
        int sz=*max_element(nums.begin(),nums.end());
        disjointset ds(sz+1);
        for(auto it:nums){
            for(int i=2;i*i<=it;i++){
                if(it%i==0){
                    ds.unionbyrank(it,i);
                    ds.unionbyrank(it/i,i);
                }
            }
        }
        map<int,int>mp;
        for(int i=0;i<nums.size();i++){
            int x=ds.findpar(nums[i]);
            mp[x]++;
        }
        int ans=1;
        for(auto it:mp) ans=max(ans,it.second);
        return ans;
    }
};
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