<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 {
    vector<int> par;
    unordered_set<int> primeFactors(int n) 
    { 
        unordered_set<int> primes;
        while (n % 2 == 0) { 
            primes.insert(2);
            n = n/2; 
        } 
        for (int i = 3; i <= sqrt(n); i = i + 2) { 
            while (n % i == 0) { 
                primes.insert(i);
                n = n/i; 
            } 
        } 
        if (n > 2) primes.insert(n);
        return primes;
    } 

    int find(int x) {
        if(par[x]!=x) {
            par[x] = find(par[x]);
        }
        return par[x];
    }
    void dsuunion(int x, int y) {
        int parX = find(x);
        int parY = find(y);
        par[parX] = parY;
    }

public:
    int largestComponentSize(vector<int>& nums) {
        unordered_map<int, vector<int>> prime;
        int n = nums.size();
        for(int i=0;i<n;i++) {
            unordered_set<int> primes = primeFactors(nums[i]);
            for(auto x:primes) {
                prime[x].push_back(i);
            }
        }

        par.resize(n);
        for(int i=0;i<n;i++) par[i]=i;

        for(auto it=prime.begin();it!=prime.end();it++) {
            vector<int> indexes = it->second;
            for(int i=0;i<indexes.size()-1;i++) {
                dsuunion(indexes[i],indexes[i+1]);
            }
        }

        unordered_map<int,int> counts;
        int p = 0;
        int ans = 0;
        for(int i=0;i<n;i++) {
            int p = find(i);
            counts[p]++;
            ans = max(ans,counts[p]);
        }
        par.clear();
        return ans;
    }
};
139791