<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 rank[100005], parent[100005], ans, N;
    void union_find(int x, int y){
        int Px = find(x);
        int Py = find(y);
        if(Px != Py){
            if(rank[Px] > rank[Py]){
                parent[Py] = Px;
                rank[Px] += rank[Py];
            }
            else{
                parent[Px] = Py;
                rank[Py] += rank[Px]; 
            }
        }
    }
    int find(int x){
        if(parent[x] == -1) return x;
        return parent[x] = find(parent[x]);
    }
    int largestComponentSize(vector<int>& nums) {
        ans = 0;
        N = nums.size();
        for(int i = 0; i < 1e5 + 3; ++i){
            parent[i] = -1;
            rank[i] = 1;
        }
        for(int i = 0; i < N; ++i){ 
            for(int j = 2; j <= sqrt(nums[i]); ++j){
                if(nums[i] % j == 0){
                    union_find(nums[i], j);
                    union_find(nums[i], nums[i]/j);
                }
            }
        }
        
        // for(int i = 0; i < 40; ++i){
        //     cout << i << " - " << parent[i] << " " << rank[i] << endl;
        // }
        unordered_map<int,int> sameParentCount;
        for(int i = 0; i < N; ++i){
            int par = find(nums[i]);
            sameParentCount[par]++;
            ans = max(ans, sameParentCount[par]);
        }
        return ans;
        
    }
};
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