<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>

int max_val = 1e5;

class DisjointSet {
  public:
    vector<int> num, parent;
    int max_num = 1;

    DisjointSet(vector<int>& nums) {
        num.resize(max_val+1, 0);
        parent.resize(max_val+1);
        for (int i = 0; i <= max_val; i++) {
            parent[i] = i;
        }
        for (int x : nums) {
            num[x] = 1;
        }
    }

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

    void Union(int x, int y) {
        x = Find(x);
        y = Find(y);
        if (x == y) return;
        if (num[y] > num[x]) swap(x, y);
        num[x] += num[y];
        parent[y] = x;
        if (num[x] > max_num) {
            max_num = num[x];
        }
    }
};


class Solution {
public:
    int largestComponentSize(vector<int>& nums) {
        DisjointSet djs(nums);

        for (int x : nums) {
            for (int p = 2; p * p <= x; p++) {
                if (x % p == 0) {
                    djs.Union(x, p);
                    djs.Union(x, x / p);
                }
            }
        }
        return djs.max_num;
    }
};
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