<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> par;
    vector<int> size;
    int hcf(int a, int b){
        return b==0? a: hcf(b,(a%b));
    }
    int findPar(int node){
        if(node==par[node]){
            return node;
        }
        return par[node]=findPar(par[node]);
    }
    void unionf(int u, int v){
        int pu=findPar(u);
        int pv=findPar(v);

        if(pu==pv) return;
        if(size[pu]<size[pv]){
            par[pu]=pv;
            size[pv]+=size[pu];
        }
        else{
            par[pv]=pu;
            size[pu]+=size[pv];
        }
    }
    
    int largestComponentSize(vector<int>& nums) {
        int n=1e5+1;
        size.resize(n,1);
        par.resize(n);
        for(int i=0; i<n; i++){
            par[i]=i;
        }
        unordered_set<int> s;
        int x=0;
        for(auto it :nums){
            s.insert(it);
            x=max(x,it);
        }
        for(int i=2; i<=x; i++){
            int last=-1;
            for(int j=i; j<=x; j+=i){
                if(s.find(j)!=s.end()){
                    if(last==-1) last=j;
                
                    else{
                        unionf(last,j);
                        last=j;
                    }
                }
            }
        }
        int ans=0;
        for(auto x: size){
            ans=max(ans,x);
        }
        return ans;

    }
};
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