<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 Disjointset{
    public:
    vector<int> parent;
    vector<int> rank;

    Disjointset(int n){
        parent.resize(n,0);
        rank.resize(n,0);
        for(int i=0;i<n;i++){
            parent[i] = i;
        }
    }

    int getParent(int node){
        if(node==parent[node]) return node;
        return parent[node] = getParent(parent[node]);
    }

    void unionbyrank(int u, int v){
        int pu = getParent(u);
        int pv = getParent(v);
        if(pu==pv) return;
        if(rank[pu] < rank[pv]){
            parent[pu] = pv;
        }
        else if(rank[pu]>rank[pv]){
            parent[pv] = pu;
        }
        else{
             parent[pv] = pu;
             rank[pu]++;
        }
    }
};

class Solution {
public:

    vector<int> getFactors(int n) {
        vector<int> arr;
        if(n%2 == 0){
            arr.push_back(2);
            while(n%2 == 0){
                n=n/2;
            }
        }

        for(int i=3;i<=sqrt(n);i++){
            if(n%i == 0){
                arr.push_back(i);
                while(n%i == 0){
                    n=n/i;
                }
            }
        }

        if(n>2){
            arr.push_back(n);
        }

        return arr;
    }
    
    int largestComponentSize(vector<int>& nums) {
    
        Disjointset ds(2*1e5);
        for (int i=0;i<nums.size();i++){
            vector<int> factors = getFactors(nums[i]);
            for (auto j : factors){
                ds.unionbyrank(nums[i],j);
            }
        }

        map<int,int> hash;
        for (int i=0;i<nums.size();i++){
            hash[ds.getParent(nums[i])]++;
        }

        int maxi = 0;
        for(auto it: hash){
            maxi = max(maxi, it.second);
        }
        return maxi;
    }
};
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