<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 {
    const int max_n = 1e5+1;

    class DSU {
        vector<int> link, size_;
        public:
        DSU(int n) {
            link.resize(n);
            size_.resize(n);

            for (int i = 0 ; i < n ; i++) {
                link[i] = i;
                size_[i] = 1;
            }
        }

        int find(int x) {
            if (x == link[x]) return x;
            return link[x] = find(link[x]);
        }

        bool same(int x , int y) {
            return find(x) == find(y);
        }

        void unite(int x , int y) {
            x = find(x);
            y = find(y);

            if (size_[x] < size_[y])
                swap(x, y);
            
            link[y] = x;
            size_[x] += size_[y];
        }

        int getSize(int x) {
            // cout <<x << " " << find(x) << " " << size_[find(x)] << "\n";
            return size_[find(x)];
        }
    };

public:
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        vector<vector<int>> a(max_n);

        for (int i = 0 ; i < nums.size() ; i++) {
            int n1 = nums[i];
            for (int j = 2 ; 1ll * j * j <= n1 ; j++) {
                if (n1%j) continue;
                a[j].push_back(i);
                while (n1%j == 0) n1 /= j;
            }

            if (n1 > 1) a[n1].push_back(i);
        }

        DSU d(n);
        for (int i = 0 ; i < max_n ; i++) {
            for (int j = 0 ; j+1 < a[i].size() ; j++) {
                if (!d.same(a[i][j], a[i][j+1]))
                    d.unite(a[i][j], a[i][j+1]);
            }
        }

        int ans = 1;
        for (int i = 0 ; i < n ; i++) {
            // cout << d.find(i) << " " << d.getSize(d.find(i)) << "\n";
            ans = max(ans , d.getSize(i));
        }

        return ans;
    }
};
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