<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 UF:
    def __init__(self, n) -> None:
        self.parents = list(range(n))
        self.rank = [1] * n

    def find(self, x):
        if self.parents[x] != x:
            self.parents[x] = self.find(self.parents[x])
        return self.parents[x]

    def union(self, child, parent):
        p1, p2 = self.find(child), self.find(parent)
        if p1 != p2:
            if self.rank[p1] > self.rank[p2]:
                self.parents[p2] = p1
            elif self.rank[p2] > self.rank[p1]:
                self.parents[p1] = p2
            else:
                self.parents[p1] = p2
                self.rank[p2] += 1

from collections import Counter
class Solution:
    def largestComponentSize(self, nums: List[int]) -> int:
        uf = UF(len(nums))
        factors = defaultdict(set)

        for k,num in enumerate(nums):
            commons = self.get_commons(num)
            for common in commons:
                factors[common].add(k)
        for k,factor in factors.items():
            l = list(factor)
            for i in range(1,len(l)):
                uf.union(l[0],l[i])
        # print(factors)
        for k,num in enumerate(nums):
            uf.find(k)
        # print(uf.parents)
        return max(Counter(uf.parents).values())

    def get_commons(self, n):
        x = int(n**0.5) + 1
        result = set([n])
        for i in range(2, x):
            if n % i == 0:
                result.add(i)
                result.add(n//i)
        return result

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