<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;
    vector<int> rank;

    int find(int x) {
        if (x == parent[x]) return x;
        return parent[x] = find(parent[x]);
    }

    bool unionn(int x, int y) {
        int rootX = find(x);
        int rootY = find(y);
        if(rootX == rootY) return false;
        if (rank[rootX] < rank[rootY]) {
            parent[rootX] = rootY;
        }
        else {
            parent[rootY] = rootX;
            if (rank[rootX] == rank[rootY]) {
                rank[rootX]++;
            }
        }
        return true;
    }


    int largestComponentSize(vector<int>& nums) {
        for(int i = 0; i < 1e5; i++) {
            parent.push_back(i);
            rank.push_back(0);
        }
        map<int, int> map;

        for(auto &n: nums) {
            merge_prime_factors(n);
        }
        int res = 0;
        for(auto &n: nums) {
            int rootN = find(n);
                map[rootN]++;
            res = max(res, map[rootN]);
            
        }
        return res;
    }

    void merge_prime_factors(int n) {
        int m = n;
        for (int i = 2; i <= sqrt(n); i++) {
            if (n % i == 0) {
                int rootM = find(m);
                int rootI = find(i);
                if (rootI != rootM) {
                    unionn(m, i);
                }
                while(n%i==0) n/=i;
            }
        }
        if (n > 1) {
            int rootM = find(m);
            int rootN = find(n);
            if (rootM != rootN) {
                unionn(rootM, rootN);
            }
        }
    }
};
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