<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:
   int n;
   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 fup(int x){
    if(x==par[x])
    return x;
    return par[x]=fup(par[x]);
   }
   void ubs(int u,int v){
    int ulp_u=fup(u);
    int ulp_v=fup(v);
    if(ulp_u==ulp_v) return ;
    if(size[ulp_u]<size[ulp_v]){
      par[ulp_u]=ulp_v;
      size[ulp_v]+=size[ulp_u];
    } 
    else{
     par[ulp_v]=ulp_u;
      size[ulp_u]+=size[ulp_v];
    }
   }
   int getLargestSize(){
    int cnt=0;
    for(int i=0;i<=n;i++)
    cnt=max(cnt,size[i]);
    return cnt;
   }
    int getComp(){
    int cnt=0;
    for(int i=0;i<=n;i++)
    if(par[i]==i) cnt++;
        return cnt;
   }
};
class Solution {
public:
    int largestComponentSize(vector<int>& nums) {
        int n=nums.size();
        dsu ds(n);
        map<int,vector<int>>mp;
        for(auto it:nums){
            mp[it].push_back(it);
            for(int i=2;i<=sqrt(it);i++){
                if(it%i==0){
                    if(it==i*i){
                        mp[i].push_back(it);
                    }
                else{
                mp[i].push_back(it);
                mp[it/i].push_back(it);
                }
                }
            }
        }
        unordered_map<int,int>ind;
        int i=0;
        for(int i=0;i<n;i++)
        ind[nums[i]]=i;
        for(auto it:mp){
            vector<int>v=it.second;
            if(v.size()>1){
                for(int i=0;i<v.size()-1;i++){
                    ds.ubs(ind[v[i]],ind[v[i+1]]);
                }
            }
        }
        int ans=1;
        for(auto it:nums){
            ans=max(ans,ds.size[ds.fup(ind[it])]);
        }
        return ans;
    }
};
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