<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 = [1]*n
        
    def find(self, x): 
        # if p != self.parent[p]: 
        #     self.parent[p] = self.find(self.parent[p])
        # return self.parent[p]
        par = x
        while self.parent[par] != par:
            par = self.parent[par]
        return par
        # Point all elements on the path to the rep to make the structure less tall
        curr = x
        while self.parent[curr] != curr:
            tmp = self.parent[curr]
            self.parent[curr] = par
            curr = tmp
        return par
    
    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
        self.rank[qrt] += self.rank[prt]
        return True 


class Solution:
    def largestComponentSize(self, A: List[int]) -> int:
        m = max(A)
        uf = UnionFind(m+1)
        seen = set(A)
        
        # modified sieve of eratosthenes 
        sieve = [1]*(m+1)
        sieve[0] = sieve[1] = 0 
        for k in range(m//2+1): 
            if sieve[k]: 
                prev = k if k in seen else 0
                for x in range(2*k, m+1, k): 
                    sieve[x] = 0
                    if x in seen: 
                        if prev: uf.union(prev, x)
                        else: prev = x
        return max(uf.rank)
26479