<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:
    vector<int> par, sz;
    int find(int u) {
        if (par[u] == u) {
            return u;
        }
        return par[u] = find(par[u]);
    }
    void unite(int u, int v) {
        u = find(u), v = find(v);
        if (u == v) {
            return;
        }
        if (sz[u] > sz[v]) {
            par[v] = u;
            sz[u] += sz[v];
        }
        else {
            par[u] = v;
            sz[v] += sz[u];
        }
    }
    int largestComponentSize(vector<int>& nums) {
        par.resize(1e5 + 1);
        sz.assign(1e5 + 1, 0);
        int n = nums.size();
        for (int i = 0; i < n; i++) {
            sz[nums[i]]++;
        }
        for (int i = 0; i <= 1e5; i++) {
            par[i] = i;
        }
        for (int i = 0; i < n; i++) {
            int t = nums[i];
            for (int j = 2; j * j <= nums[i]; j++) {
                if (t % j == 0) {
                    unite(j, nums[i]);
                }
                while (t % j == 0) {
                    t /= j;
                }
            }
            if (t != 1) {
                unite(t, nums[i]);
            }
        }
        int ans = -1;
        for (int i = 0; i < n; i++) {
            ans = max(ans, sz[find(nums[i])]);
        }
        return ans;
    }
};

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