<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<vector<int>> adj;
    unordered_set<int> vis;
    int cnt = 0;

    void dfs(int num, vector<bool>& has) {
        if (has[num]) cnt++;

        for (auto x : adj[num]) {
            if (!vis.count(x)) {
                vis.insert(x);
                dfs(x, has);
            }
        }
    }

    int largestComponentSize(vector<int>& nums) {
        int mx = 0;
        for (auto x : nums) mx = max(x, mx);
        adj.resize(mx + 1);
        vector<bool> inNums(mx + 1);
        for (auto x : nums) inNums[x] = true;
        vector<bool> primes(mx + 1, true);
        for (int i = 2; i * i <= mx; i++) {
            if (primes[i]) {
                for (int j = i * i; j <= mx; j += i) {
                    primes[j] = false;
                }
            }
        }

        vector<int> p;
        for (long long i = 2; i < primes.size(); i++) {
            if (primes[i]) {
                for (long long j = i * 2; j <= mx; j+=i) {
                    if (inNums[j]) {
                        adj[j].push_back(i);
                        adj[i].push_back(j);
                    }
                }
            }
        }

        // for (int i = 0; i < 35; i++) {
        //     cout << "Node: " << i << endl;
        //     for (auto x : adj[i]) cout << x << " ";
        //     cout << endl;
        // }

        int ans = 0;
        for (int i = 0; i < nums.size(); i++) {
            if (!vis.count(nums[i])) {
                cnt = 0;
                vis.insert(nums[i]);
                dfs(nums[i], inNums);
                ans = max(ans, cnt);
            }
        }

        return ans;
    }
};
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