<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 = defaultdict(lambda : 0)
    
    def find(self, x):
        if self.parent[x] != x:
            self.parent[x] = self.find(self.parent[x])
        return self.parent[x]
    
    def union(self, x, y):
        px = self.find(x)
        py = self.find(y)
        if px == py:
            return False
        if self.rank[px] < self.rank[py]:
            self.parent[px] = py
         
        elif self.rank[py] < self.rank[px]:
            self.parent[py] = px
            
        else:
            self.parent[px] = py
            self.rank[py] += 1

        return True
    

class Solution:
    def get_prime(self, n):
        for i in range(2,int(math.sqrt(n))+1):
            if n % i == 0:
                return self.get_prime(n//i) | set([i])
        return set([n])

    def largestComponentSize(self, nums: List[int]) -> int:
        n = len(nums)
        uf = UnionFind(n)
        prime_map = defaultdict(list)
        for i, num in enumerate(nums):
            pm = self.get_prime(num)
            for p in pm:
                prime_map[p].append(i)

        for p in prime_map:
            for i in range(len(prime_map[p])-1):
                uf.union(prime_map[p][i], prime_map[p][i+1])
        
        counter = defaultdict(int)
        ans = 0
        for i in range(n):
            pi = uf.find(i)
            counter[pi] += 1
        return max(counter.values())


        
        
21893