<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 (parent[x] == x) return x;
        return parent[x] = find(parent[x]);
    }
    
    void unionDsu(int x, int y) {
        int _x = find(x), _y = find(y);
        if (_x == _y) return;
        if (rank[_x] < rank[_y]) {
            parent[_x] = _y;
        } else if (rank[_x] > rank[_y]) {
            parent[_y] = _x;
        } else {
            parent[_y] = _x;
            rank[_x] += 1;
        }
    }
    int largestComponentSize(vector<int>& nums) {
        vector<int> dp(100005,0);
         parent.resize(100005);
         for(int i=0;i<parent.size();i++) parent[i]=i;
        rank.resize(100005, 1);
        for(int i=1;i<dp.size();i++) {dp[i]=i;}
      //  cout<<dp[15]<<endl;
        for(int i=2;i<100005;i++){
            for(int j=2*i;j<100005;j+=i){
                if(dp[j]==j) dp[j]=i;
            }
        }
     

        for(int i=0;i<nums.size();i++){
             int val=nums[i];
             int prev1=-1;
            while(val!=1){
                  int fac=dp[val];
       //    cout<<prev1<<" "<<fac<<endl;
                  while(val%fac==0){val/=fac;}

                  if(prev1!=-1) unionDsu(prev1,nums[i]);
                  prev1=fac;
                 unionDsu(nums[i],fac);
            }
       
        }
        cout<<find(2)<<endl;
         unordered_map<int, int> componentSize;
        int maxCount = 0;

        for (int num : nums) {
            int root = find(num);
           // cout<<num<<" "<<root<<endl;
            componentSize[root]++;
            maxCount = max(maxCount, componentSize[root]);
        }
        return maxCount;

    }
};
184413