<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>siz;
    unordered_map<int,int>mk;
    int find_par(int u)
    {
        return ((par[u]<0)?(u):(par[u]=find_par(par[u])));
    }
    void join_no(int a,int b)
    {
            if(mk.find(b)!=mk.end())
            {
                b = mk[b];
            }
            a = find_par(a);
            b = find_par(b);
            if(a!=b)
            {
                if(siz[a]<siz[b]) {swap(a,b);}
                par[b]=a;
                siz[a]+=siz[b];
            }
            mk[b]=a;
    }
    int largestComponentSize(vector<int>& nums) 
    {
        int n = nums.size(); int maxi = *max_element(nums.begin(),nums.end());
        mk.clear();
        par.resize(maxi+1,-1);
        siz.resize(maxi+1,1);
        // iota(par.begin(),par.end(),0);
        unordered_set<int>s; for(auto it:nums) {s.insert(it);}
        for(int i=2;i<=maxi;i++)
        {
            for(int j=(2*i);j<=maxi;j+=i)
            {
                if(s.find(j)!=s.end()) {
                // cout << i << " " << j << "\n";
                    join_no(i,j);
                }
            }
        }   
        mk.clear();
        // map<int,int>mk1;
        for(auto it:nums)
        {
            // cout << it << " " << find_par(it) << "\n";
            mk[find_par(it)]++;
        }
        // int ans=*max_element(siz.begin(),siz.end());
        int ans=-1;
        for(auto it:mk) {ans = max(ans,it.second);}
        return ans;
    }
};
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