<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 {

private:
    struct DSU {
        vector<int> e;
        DSU() : e(2e5, -1) {}
        int get(int x) { return e[x] < 0 ? x : get(e[x]); }
        int sz(int x) { return -e[get(x)]; }
        void unite(int x, int y) {
            x = get(x), y = get(y);
            if(x == y) return;
            if(e[x] > e[y]) swap(x, y);
            e[x] += e[y];
            e[y] = x;
        }
    };

public:
    int largestComponentSize(vector<int>& nums) {
        vector<int> pset(2e5, -1);
        DSU dsu;
        int ans = 0;
        for(auto a : nums) {
            vector<int> p;
            int tmp = a;
            for(int i = 2; i * i <= tmp; i++) {
                if(tmp % i == 0) {
                    p.push_back(i);
                    while(tmp % i == 0) {
                        tmp /= i;
                    }
                }
            }
            if(tmp > 1) {
                p.push_back(tmp);
            }
            for(auto pr : p) {
                if(pset[pr] != -1) {
                    dsu.unite(a, pset[pr]);
                }
                pset[pr] = a;
            }
            ans = max(ans, dsu.sz(a));
        }
        return ans;
    }
};
235901