<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 {
    class DSU {
        vector<int> root;
        vector<int> sz;
    public:
        DSU(int n) {
            root.resize(n);
            sz.resize(n);

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

        int find_root(int v) {
            if (v == root[v]) {
                return v;
            }
            return root[v] = find_root(root[v]);
        }

        void merge(int u, int v) {
            int ru = find_root(u);
            int rv = find_root(v);

            if (ru == rv) {
                return;
            }

            if (sz[ru] > sz[rv]) {
                sz[ru] += sz[rv];
                root[rv] = ru;
            } else {
                sz[rv] += sz[ru];
                root[ru] = rv;
            }
        }

        int largest_component() {
            int max_size = 1;
            for (int i = 0; i < root.size(); i++) {
                if (root[i] == find_root(root[i])) {
                    max_size = max(max_size, sz[i]);
                }
            }
            return max_size;
        }
    };

    static constexpr int kMaxN = 100000;
public:
    int largestComponentSize(vector<int>& nums) {
        DSU dsu(nums.size());
        vector<int> last_element(kMaxN + 1, -1);
        for (int i = 0; i < nums.size(); i++) {
            for (int j = 2; 1LL * j * j <= nums[i]; j++) {
                if (nums[i] % j == 0) {
                    if (last_element[j] != -1) {
                        dsu.merge(last_element[j], i);
                    }

                    if (last_element[nums[i] / j] != -1) {
                        dsu.merge(last_element[nums[i] / j], i);
                    }
                    last_element[j] = i;
                    last_element[nums[i] / j] = i;
                }
            }
            if (last_element[nums[i]] != -1) {
                dsu.merge(last_element[nums[i]], i);
            }
            last_element[nums[i]] = i;
        }

        return dsu.largest_component();
    }
};
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