<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 Solution:
    def largestComponentSize(self, nums: List[int]) -> int:
        
        def find(node):
            if parent[node] == -1: return node
            else:
                parent[node] = find(parent[node])
                return parent[node]
        
        def union(idx1,idx2):
            par1,par2 = find(idx1),find(idx2)
            if par1!=par2:
                if rank[par1] > rank[par2]:
                    parent[par2] = par1
                elif rank[par2] > rank[par1]:
                    parent[par1] = par2
                else:
                    parent[par2] = par1
                    rank[par1] += 1
        
        n = len(nums)
        parent = defaultdict(lambda:-1)
        rank = defaultdict(lambda:0)
        for i in range(n):
            limit = int(nums[i]**0.5)
            for j in range(2,limit+1):
                if nums[i] % j == 0:
                    union(nums[i],j)
                    union(nums[i],nums[i]//j)
        count = defaultdict(lambda:0)
        best = -1
        for num in nums:
            par = find(num)
            tmp = count[par] + 1
            if tmp > best: best = tmp
            count[par] = tmp
        return best
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