<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:
    def largestComponentSize(self, nums: List[int]) -> int:
        def dfs(node):
            nonlocal gnodes

            visited.add(node)
            gnodes |= adj[node][0]

            for nd in adj[node][1]:
                if nd in visited:
                    continue

                dfs(nd)

        snums = set(nums)
        seen = set()
        adj = []
        maxv = max(nums)

        for v in range(2, maxv + 1):
            if v not in seen:
                vals = set()
                curr = v
                while curr <= maxv:
                    seen.add(curr)

                    if curr in snums:
                        vals.add(curr)
                    curr += v

                if len(vals) > 1:
                    links = []

                    for i in range(len(adj)):
                        if not vals.isdisjoint(adj[i][0]):
                            adj[i][1].append(len(adj))
                            links.append(i)

                    adj.append((vals, links))
        
        visited = set()
        gnodes = set()
        res = 1
        for i in range(len(adj)):
            if i in visited:
                continue

            gnodes.clear()
            dfs(i)

            res = max(res, len(gnodes))

        return res



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