<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>


unordered_set<int> primeFactors(int n) {
    unordered_set<int> factors;
    for (int i = 2; i * i <= n; ++i) {
        while (n % i == 0) {
            factors.insert(i);
            n /= i;
        }
    }
    if (n > 1) factors.insert(n);
    return factors;
}

class DSU {
public:
    unordered_map<int, int> parent;
    unordered_map<int, int> size;

    DSU(const vector<int>& nums) {
        for (int n : nums) {
            parent[n] = n;
            size[n] = 1;
        }
    }

    int find(int n) {
        if (parent[n] != n) {
            parent[n] = find(parent[n]);
        }
        return parent[n];
    }

    void unionSets(int n, int m) {
        int root_n = find(n);
        int root_m = find(m);
        if (root_n != root_m) {
            parent[root_n] = root_m;
            size[root_m] += size[root_n];
        }
    }
};

class Solution {
public:
    int largestComponentSize(vector<int>& nums) {
        DSU dsu(nums);

        for (int n : nums) {
            unordered_set<int> factors = primeFactors(n);
            for (int p : factors) {
                if (dsu.parent.find(p) == dsu.parent.end()) {
                    dsu.parent[p] = p;
                    dsu.size[p] = 0;
                }
                dsu.unionSets(p, n);
            }
        }

        unordered_map<int, int> root_count;
        int maxSize = 0;
        for (int n : nums) {
            int root = dsu.find(n);
            root_count[root]++;
            maxSize = max(maxSize, root_count[root]);
        }

        return maxSize;
    }
};

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