<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 UnionFind {
    vector<int> root_;
    vector<int> rank_;
public:
    UnionFind(int n): root_(n), rank_(n) {
        for (int i = 0; i < n; ++i) {
            root_[i] = i;
        }
    }

    int Find(int x) {
        if (root_[x] == x) {
            return x;
        }
        return root_[x] = Find(root_[x]);
    }

    void Union(int x, int y) {
        int rx = Find(x), ry = Find(y);
        if (rx != ry) {
            if (rank_[rx] < rank_[ry]) {
                root_[rx] = ry;
            } else if (rank_[ry] < rank_[rx]) {
                root_[ry] = rx;
            } else {
                root_[ry] = rx;
                ++rank_[rx];
            }
        }
    }
};

class Solution {
public:
    int largestComponentSize(vector<int>& nums) {
        int max_num = *max_element(nums.begin(), nums.end());
        int n = nums.size();
        UnionFind uf(max_num + 1);
        for (auto num : nums) {
            for (int i = 2; i <= (int)floor(sqrt(num)); ++i) {
                if (num % i == 0) {
                    uf.Union(num, i);
                    uf.Union(num, num / i);
                }
            }
        }
        int result = 0;
        vector<int> freq(max_num + 1);
        for (auto num: nums) {
            result = max(result, ++freq[uf.Find(num)]);
        }
        return result;
    }
};
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