<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 int N = 1e5 + 1;

    vector<int> parent, rank, count;
    unordered_map<int, vector<int>> m;

    int find(int u) {
        if (u == parent[u]) return u;

        return parent[u] = find(parent[u]);
    }

    void merge(int u, int v) {
        int rootU = find(u);
        int rootV = find(v);
        if (rootU == rootV) return ;

        if (rank[rootU] < rank[rootV]) {
            parent[rootU] = rootV;
            count[rootV] += count[rootU];
        } else {
            parent[rootV] = rootU;
            count[rootU] += count[rootV];

            if (rank[rootU] == rank[rootV]) {
                rank[rootU]++;
            }
        }
    }

    void factorize(int n) {
        int ans = n;
        for (int i = 2; i * i <= ans; i++) {
            if (ans % i == 0) {
                m[i].push_back(n);
                while (ans % i == 0) ans /= i;
            }
        }

        if (ans != 1) {
            m[ans].push_back(n);
        }
    }

    int largestComponentSize(vector<int>& nums) {
        rank = vector<int>(N, 0);
        parent = vector<int>(N, 0);
        count = vector<int>(N, 1);
        for (int i = 1; i < N; i++) {
            parent[i] = i;
        }

        for (int num : nums) {
            // parent[num] = num;
            // rank[num] = 0;
            // count[num] = 1;
            
            factorize(num);
        }

        for (pair<int, vector<int>> p : m) {
            vector<int> elements = p.second;
            for (int i = 0; i < elements.size() - 1; i++) {
                merge(elements[i], elements[i + 1]);
            }
        }

        int result = 0;
        // for (pair<int, int> p : count) {
        //     result = max(result, p.second);
        // }
        for (int num : nums) {
            result = max(result, count[num]);
        }

        return result;
    }
};
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