<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, size;
    int find(int child){
        if(parent[child]==child)return child;
        return parent[child]=find(parent[child]);
    }
    void unionDsu(int x,int y){
        int x_par = find(x);
        int y_par = find(y);
        if(x_par==y_par)return;
        if(size[x_par]<size[y_par]){
            parent[x_par]=y_par;
            size[y_par]+=size[x_par];
        }
        else{
            parent[y_par]=x_par;
            size[x_par]+=size[y_par];
        }
    }
    vector<int> findFactors(int num) {
        vector<int> factors;
        for (int i = 2; i * i <= num; i++) {
            while (num % i == 0) {
                factors.push_back(i);
                num /= i;
            }
        }
        if (num > 1) factors.push_back(num);
        return factors;
    }
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        int maxi = *max_element(nums.begin(), nums.end());
        size.resize(maxi+1,1);
        parent.resize(maxi+1);
        for(int i=0;i<maxi;i++){
            parent[i]=i;
        }
        for(auto x: nums){
            vector<int> fact = findFactors(x);
            
            int x_parent = find(x);
            for(auto factor : fact){
                // int fact_par = find(factor);
                unionDsu(factor,x);
            }
        }
        int ans=0;
        map<int,int>mp;
        for(auto x: nums){
            int par=find(x);
            mp[par]++;
        }
        for(auto [ele, cnt]:mp){
            ans= max(ans, cnt);
        }
        return ans;
    }
};
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