<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 UnionFind:
    def __init__(self, n):
        self.parent = list(range(n))
        self.rank = [0] * n

    def find(self, p):
        if p != self.parent[p]:
            self.parent[p] = self.find(self.parent[p])
        return self.parent[p]

    def union(self, p, q):
        prt, qrt = self.find(p), self.find(q)
        if prt == qrt:
            return False
        if self.rank[prt] > self.rank[qrt]:
            prt, qrt = qrt, prt
        self.parent[prt] = qrt
        if self.rank[prt] == self.rank[qrt]:
            self.rank[qrt] += 1
        return True


class Solution:
    def largestComponentSize(self, nums):
        def factorize(n):
            for p in range(2, int(n**0.5) + 1):
                if n % p == 0:
                    result = {p, n // p}
                    result.update(factorize(n // p))
                    return result
            return {n}

        n = len(nums)
        uf = UnionFind(n)
        factors = [factorize(num) for num in nums]
        factor_to_index = {}

        for i, fact in enumerate(factors):
            for f in fact:
                if f in factor_to_index:
                    uf.union(i, factor_to_index[f])
                factor_to_index[f] = i

        group_count = [0] * n
        for i in range(n):
            group_count[uf.find(i)] += 1

        return max(group_count)
31065