<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:

    long long findUltParent(vector<long long> &ultParent, long long node){
        if (ultParent[node] == node){
            return node;
        }
        return (ultParent[node] = findUltParent(ultParent, ultParent[node]));
    }

    void combine(vector<long long> &ultParent, vector<long long> &rank, long long nodeX, long long nodeY){
        if (rank[findUltParent(ultParent, nodeX)] < rank[findUltParent(ultParent, nodeY)]){
            swap(nodeX, nodeY);
        }
        rank[findUltParent(ultParent, nodeX)] ++;
        rank[findUltParent(ultParent, nodeY)] = 0;
        ultParent[findUltParent(ultParent, nodeY)] = findUltParent(ultParent, nodeX);
    }

    int largestComponentSize(vector<int>& nums) {
        vector<long long> ultParent(100005, 0), rank(100005, 0);
        for (long long i=0; i<nums.size(); i++){
            rank[nums[i]] = 1;
        }
        for (long long i=0; i<100005; i++){
            ultParent[i] = i;
        }
        for (long long i=0; i<nums.size(); i++){
            for (long long j=2; j<=sqrt(nums[i]); j++){
                if (nums[i]%j == 0){
                    combine(ultParent, rank, nums[i], j);
                    combine(ultParent, rank, nums[i], nums[i]/j);
                }
            }
        }
        unordered_map<long long, long long> M;
        for (long long i=0; i<nums.size(); i++){
            long long par = findUltParent(ultParent, nums[i]);
            if (par == 0){
                continue;
            }
            M[par]++;
            cout<<par<<" ";
        }
        long long ans = 0;
        for (auto it=M.begin(); it!=M.end(); it++){
            ans = max(ans, it->second);
        }
        return ans;
    }
};
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