<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:
        mx = max(nums)
        fact = [[] for _ in range(mx + 1)]
        prime = [True for _ in range(mx + 1)]
        prime[0] = prime[1] = False
        for i in range(2, mx + 1):
            if not prime[i]: continue
            for j in range(i, mx + 1, i):
                fact[j].append(i)
                prime[j] = False
        
        p = {n: n for n in range(2, mx + 1)}
        s = {n: 1 for n in range(2, mx + 1)}

        def find(u):
            if p[u] == u: return u
            p[u] = find(p[u])
            return p[u]

        def merge(u, v):
            u, v = find(u), find(v)
            if u == v: return
            if s[u] > s[v]:
                p[v] = u
                s[u] += s[v]
            else:
                p[u] = v
                s[v] += s[u]
        
        for n in nums:
            if len(fact[n]) < 2: continue
            u = fact[n][0]
            for v in fact[n][1:]:
                merge(u, v)
        
        ans = 0
        t = {n: 0 for n in range(mx + 1)}
        for n in nums:
            if len(fact[n]) == 0: continue
            idx = find(fact[n][0])
            t[idx] += 1
            ans = max(ans, t[idx])
        return ans

                        
        
52468