<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 dsu{
public:
    vector<int> par,size;
    dsu(int n){
        par.resize(n+1);
        size.resize(n+1,1);
        for(int i=0;i<n;i++)par[i]=i;
    }
    int findpar(int u){
        if(par[u]==u)return u;
        return par[u]=findpar(par[u]);
    }
    void unionbysize(int u,int v){
        int pu=findpar(u),pv=findpar(v);
        if(pu==pv)return ;
        if(size[pu]>=size[pv]){
            par[pv]=pu;
            size[pu]+=size[pv];
        }
        else{
            par[pu]=pv;
            size[pv]+=size[pu];
        }
        return;
    }
};
class Solution {
public:
    void primefactors(int n,int ind,unordered_map<int,vector<int>> &mp){
        if(n%2==0){
            mp[2].push_back(ind);
            while(n%2==0){
                n=n/2;
            }
        }
        for(int i=3;i*i<=n;i++){
            if(n%i==0){
                mp[i].push_back(ind);
                while(n%i==0)n=n/i;
            }
        }
        if(n>2){
            mp[n].push_back(ind);
        }
        return;
    }
    int largestComponentSize(vector<int>& nums) {
        int n=nums.size();
        dsu ds(n+1);
        unordered_map<int,vector<int>> mp;
        for(int i=0;i<n;i++){
            primefactors(nums[i],i,mp);
        }
        for(auto &[a,b]:mp){
            for(int i=0;i<b.size()-1;i++){
                ds.unionbysize(b[i],b[i+1]);
            }
        }
        int maxi=0;
        for(auto it:ds.size)maxi=max(maxi,it);
        return maxi;
    }
};
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