<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:
    void uni(int a, int b, vector<int>& parent, vector<int>& size){
        int pa = find(a, parent);
        int pb = find(b, parent);
        if(pa == pb) return;
        if(size[a] >= size[b]){
            parent[pb] = pa;
            size[pa] += size[pb];
        }
        else{
            parent[pa] = pb;
            size[pb] += size[pa];
        }
    }
    int find(int a, vector<int>& parent){
        if(parent[a] != a){
            return parent[a] = find(parent[a], parent);
        }
        return a;
    }
    int gcd(int a, int b){
        if(b == 0) return a;
        return gcd(b, a % b);
    }
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        int m = *max_element(nums.begin(), nums.end());
        vector<int> parent(m + 1, 0);
        vector<int> size(m + 1, 0);
        for(int i = 0; i < m + 1; i++){
            parent[i] = i;
        }
        for(int num: nums){
            size[num] = 1;
        }

        for(int num: nums){
            for(int i = 2; i <= sqrt(num); i++){
                if(num % i == 0){
                    uni(num, i, parent, size);
                    uni(num, num/i, parent, size);
                }
            }
        }

        int size_max = 0;
        for(int num: nums){
            if(parent[num] == num){
                if(size_max < size[num]) size_max = size[num];
            }
        }
        return size_max;
    }
};
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