<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: 
    int find(vector<int>& parent,int v){
        if(v!=parent[v]){
            parent[v]=find(parent,parent[v]);
        }
        return parent[v];
    }
    void unionFind(vector<int>& parent,vector<int>& rank, int a,int b){
        int x=find(parent,a);
        int y=find(parent,b);
        if(x!=y){
            if(rank[y]>=rank[x]){
                parent[x]=y;
                rank[y]+=rank[x];
            }else{
                parent[y]=x;
                rank[x]+=rank[y];
            }
        }

    }
    int largestComponentSize(vector<int>& nums) {
        int n=1e5+1;
        vector<int> parent(n),rank(n,1);
        for(int i=0;i<n;i++){
            parent[i]=i;
        }
        for(auto it:nums){
            for(int i=2;i<=sqrt(it);i++){
                if(it%i==0){
                    unionFind(parent,rank,i,it);
                    unionFind(parent,rank,it/i,it);
                }
            }
        }
        int count=0;
        unordered_map<int,int>mp;
        for(auto it:nums){
            mp[find(parent,it)]++;
            count=max(count,mp[find(parent,it)]);
        }
        return count;
    }
};
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