<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:
    const static int g_size = 1e6;
    int prime_size = 1e5 + 1;

    vector<int> g[g_size];
    bool used[g_size];
    void dfs(int v, int& vertices){
        if(v < prime_size){
            vertices++;
        }
        used[v] = true;
        for(int to : g[v]){
            if(!used[to]) dfs(to, vertices);
        }
    }

    int largestComponentSize(vector<int>& nums) {
        bool is_prime[prime_size];
        unordered_set<int> prime;
        fill(is_prime, is_prime + prime_size, true);
        for(int i = 2; i < prime_size; i++){
            if(!is_prime[i]) continue;
            prime.insert(i);
            for(long long j = (long long)i * (long long)i; j < prime_size; j += i){
                is_prime[(int)j] = false;  
            }
        }
        for(int i = 0; i < nums.size(); i++){
            for(int j = 1; j <= sqrt(nums[i]); j++){
                if(nums[i] % j == 0){
                    if(prime.count(j)){
                    g[nums[i]].push_back(j + prime_size);
                    g[j + prime_size].push_back(nums[i]);
                                        //cout << "Edge: " << nums[i] << " to " << j << endl;

                    }
                    if(prime.count(nums[i] / j)){
                        g[nums[i]].push_back(nums[i] / j + prime_size);
                        g[nums[i] / j + prime_size].push_back(nums[i]);

                        //cout << "Edge: " << nums[i] << " to " << nums[i] / j << endl;

                    }
                }
            }
        }
        int ans = 1;
        for(int i = 0; i < nums.size(); i++){
            int vertices = 0;
            if(!used[nums[i]]){
                dfs(nums[i], vertices);
                ans = max(ans, vertices);
            }
        }
        return ans;
    }
};
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