<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 {
public:
    const static int n = 1e5 + 10;
    using ll = long long;
    struct dsu {
        int r[n];
        int c[n];
        dsu() {
            for (int i = 0; i < n; i++) {
                r[i] = i;
                c[i] = 1;
            }
        }
        int root(int u) {
            int p = u;
            while (p != r[p]) {
                p = r[p];
            }
            while (u != p) {
                int t = r[u];
                r[u] = p;
                u = t;
            }
            return p;
        }
        void join(int u, int v) {
            int ru = root(u), rv = root(v);
            if (ru != rv) {
                r[ru] = rv;
                c[rv] += c[ru];
            }
        }
    } uf;
    int f[n];
    int largestComponentSize(vector<int>& nums) {
        memset(f, 0, sizeof(f));
        for (auto v : nums) {
            f[v] = 1;
        }
        for (ll i = 2; i <= 1e5; i++) {
            ll lst = -1;
            for (ll j = i; j <= 1e5; j += i) {
                if (f[j]) {
                    if (lst != -1) {
                        uf.join(lst, j);
                        lst = j;
                    } else {
                        lst = j;
                    }
                }
            }
        }
        int mx = 0;
        for (auto v : nums) {
            mx = max(mx, uf.c[uf.root(v)]);
        }
        return mx;
    }
};
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