<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: int):
        self.root = list(range(n))
        self.rank = [1 for _ in range(n)]

    def find(self, x: int) -> int:
        if self.root[x] != x: self.root[x] = self.find(self.root[x])
        return self.root[x]

    def union(self, x: int, y: int) -> None:
        rootx, rooty = self.find(x), self.find(y)
        if rootx == rooty: return
        if self.rank[rootx] > self.rank[rooty]: self.root[rooty] = rootx
        elif self.rank[rootx] < self.rank[rooty]: self.root[rootx] = rooty
        else:
            self.root[rooty] = rootx
            self.rank[rootx] += 1

    def is_connected(self, x: int, y: int) -> bool:
        return self.find(x) == self.find(y)


class Solution:
    def largestComponentSize(self, nums: List[int]) -> int:
        def get_prime_factors(n: int) -> List[int]:
            s = set()
            while n % 2 == 0:
                s.add(2)
                n //= 2
            
            for i in range(3, int(math.sqrt(n)) + 1, 2):
                while n % i == 0:
                    s.add(i)
                    n //= i
            
            if n > 2: s.add(n)
            return list(s)

        uf = UnionFind(len(nums))
        prime = collections.defaultdict(int)
        for i, num in enumerate(nums):
            primes = get_prime_factors(num)
            for p in primes:
                if p in prime: uf.union(prime[p], i)
                prime[p] = i

        c = collections.Counter()
        for i in range(len(nums)): c[uf.find(i)] += 1

        return max(c.values())
20364