<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> parent, rank;
    int find(int a) {
        if(parent[a] == a) return a;
        return parent[a] = find(parent[a]);
    }
    void unite(int a, int b) {
        int pa = find(a);
        int pb = find(b);
        if(rank[pa] > rank[pb]) {
            parent[pb] = pa;
        } else if(rank[pb] > rank[pa]) {
            parent[pa] = pb;
        } else {
            rank[pa] ++;
            parent[pb] = pa;
        }
    }
    int largestComponentSize(vector<int>& nums) {
        int maxx = -1;
        for(auto itr: nums) {
            maxx = max(maxx, itr);
        }

        vector<int> prime;
        for(int i=0;i<maxx+1;i++) {
            prime.push_back(i);
            rank.push_back(0);
            parent.push_back(i);
        }

        prime[1] = 1;
        for(int i=2;i*i<=maxx;i++) {
            if(prime[i] == i) {
                for(int j=i*i;j<=maxx;j+=i) {
                    prime[j] = i;
                }
            }
        }

        for(int i=0;i<nums.size();i++) {
            int temp = nums[i];
            // cout<<nums[i]<<"\n";
            while(temp > 1) {
                int factor = prime[temp];
                // cout<<factor<<" ";
                unite(factor, nums[i]);
                while(temp % factor == 0) {
                    temp /= factor;
                }
            }
            // cout<<"\n";
        }
        // cout<<"Chala"<<"\n";


        unordered_map<int, int> mp;
        int ans = 0;
        for(auto itr: nums) {
            int parent = find(itr);
            mp[parent] ++;
            ans = max(ans, mp[parent]);
        }
        return ans;
    }
};
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