<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:
    int findP(unordered_map<int, int> &P, int n) {
        if (P.count(n) == 0) {
            return P[n] = n;
        }
        if (P[n] == n) return n;

        return P[n] = findP(P, P[n]);
    }

    void sieve(vector<int> &v, int n) {
        for (int i=2; i<=n;i++) {
            if (v[i] == i) {
                for (long long j=1LL* i*i; j<=n; j += i) {
                    v[j] = i;
                }
            }
        }
    }

    int largestComponentSize(vector<int>& A) {
        int mx = 1;
        for (auto it : A) mx = max(it, mx);
        vector<int> P(mx+1, 1);
        for (int i=2; i<=mx; i++) P[i] = i;
        sieve(P, mx);

        unordered_map<int, int> par;
        for (auto it : A) {
            int node = it;
            int p = findP(par, node);
            while (node != 1) {
                int pf = P[node];
                node /= pf;
                par[findP(par, pf)] = p;
            }
        }

        map<int, int> cc;
        for (auto it: A) {
            cc[findP(par, it)]++;
        }

        int ans = 1;
        for (auto &[k, v] : cc) {
            ans = max(ans, v);
        }

        return ans;
    }
};
74573