<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 largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        vector<int> par(n) , sz(n);
        map<int,int> mp;
        for(int i=0;i<n;i++){
            par[i]=i;
            sz[i]=1;
            mp[nums[i]]=i;
        }
        function<int(int)> find = [&](int a){
            if(par[a]==a)return a;
            return par[a] = find(par[a]);
        };

        auto unite = [&](int a,int b){
            a = find(a) , b = find(b);
            if(a!=b){
                if(sz[a]<sz[b])swap(a,b);
                sz[a]+=sz[b];
                par[b]=a;
            }
        };
        int mx = *max_element(nums.begin(),nums.end());
        for(int i=2;i<=mx;i++){
            int fst = -1;
            for(int j=i;j<=mx;j+=i){
                if(mp.count(j)==1){
                    if(fst==-1)fst=j;
                    else unite(mp[fst],mp[j]);
                }
            }
        }
        return *max_element(sz.begin(),sz.end());
    }
};
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