<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:
     struct DSU
{
    vector<int> par, sz;
    DSU(int n)
    {
        /*
         DSU dsu(n);
         dsu.find(u)
         dsu.Union(u, v);
        */
        par.resize(n + 1), sz.resize(n + 1);
        for (int i = 1; i <= n; i++)
        {
            par[i] = i;
            sz[i] = 1;
        }
    }
    int find(int u)
    {
        if (u == par[u])
            return u;
        return par[u] = find(par[u]);
    }
    void Union(int u, int v)
    {
        int x = find(u);
        int y = find(v);
        if (x != y)
        {
            if (sz[x] < sz[y])
            {
                swap(x, y);
            }
            sz[x] += sz[y];
            par[y] = x;
        }
    }
};
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        int A = *max_element(nums.begin(), nums.end());
        DSU dsu(max(A, n));
         vector<int>PF(A+1);
            for(int i = 1; i <= A; i++){
                  PF[i] = i;
            }
            for(int i = 2; i*i <= A; i++){
                      if(PF[i] != i) continue;
                     for(int j = i*i; j <= A; j += i){
                          if(PF[j] > i) PF[j] = i;
                            
                     }
            }
            auto factors = [&](int x)->vector<int>{
                  vector<int>fact;
                  while(x > 1){
                     fact.push_back(PF[x]);
                     x = x/PF[x];
                  }
                  return fact;

            };

            for(auto x : nums){
                 for(auto y : factors(x)){
                      dsu.Union(x, y);
                 }
            }
            vector<vector<int>>component(max(A, n)+1);
            for(auto x : nums){
                 component[dsu.find(x)].push_back(x);
            }
            int ans = 0;
            for(auto sz : component){
                  ans = max(ans, (int)sz.size());
            }
            return ans;
          
    }
};
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