<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>

import math
class Solution:
    def largestComponentSize(self, a: List[int]) -> int:
        n=len(a)
        maxi=max(a)
        primes=[1]*(maxi+1)
        parent=list(range(maxi+1))
        def findParent(x):
            if parent[x]!=x:
                parent[x]=findParent(parent[x])
            return parent[x]
        def union(x,y):
            px=findParent(x)
            py=findParent(y)
            if px==py:return
            if primes[px]>primes[py]:
                parent[py]=px
                primes[px]+=primes[py]
            else:
                parent[px]=py
                primes[py]+=primes[px]
        for i in range(n):
            for j in range(2,int(math.sqrt(a[i]))+1):
                if a[i]%j==0:
                    union(j,a[i])
                    union(a[i]//j,j)
        d={findParent(x):0 for x in a}
        for x in a:
            d[findParent(x)]+=1
        return max(d.values())
60111