<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;
    vector<bool> vis;
    int cnt;
    int count = 0;

    void dfs(int s) {
        if (vis[s]) return;
        vis[s] = true;
        if (s >= count) cnt++;
        for (auto u: adj[s]) {
            dfs(u);
        }
    }

    int largestComponentSize(vector<int>& nums) {
        int spf[100001];
        for (int i = 1; i <= 100000; i++) spf[i] = i;
        for (int i = 2; i * i <= 100000; i++) {
            if (spf[i] == i) {
                for (int j = i * i; j <= 100000; j+=i) {
                    if (spf[j] == j) spf[j] = i;
                }
            }
        }
        map<int, int> primes;
        for (int i = 2; i <= 100000; i++) {
            if (spf[i] == i) {
                primes[i] = count;
                count++;
            }
        }
        adj.resize(count+nums.size());
        fill(adj.begin(), adj.end(), vector<int>());
        vis.resize(count+nums.size());
        fill(vis.begin(), vis.end(), false);
        for (int i = 0; i < nums.size(); i++) {
            int num = nums[i];
            while (num != 1) {
                adj[primes[spf[num]]].push_back(count+i);
                adj[count+i].push_back(primes[spf[num]]);
                num/=spf[num];
            }
        }
        int ans = 0;
        for (int i = 0; i < nums.size(); i++) {
            cnt = 0;
            dfs(i);
            ans = max(ans, cnt);
        }
        return ans;
    }
};
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