<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:
        MAXN = 100005
        spf = list(range(MAXN))

        for i in range(4, MAXN, 2):
            spf[i] = 2
        for i in range(3, ceil(sqrt(MAXN))):
            if spf[i] == i:
                for j in range(i * i, MAXN, i):
                    if spf[j] == j:
                        spf[j] = i
        
        def primeFactors2(x):
            pf = []
            while x != 1:
                p = spf[x]
                # print(x, p)
                pf.append(p)
                while x % p == 0:
                    x = x// p
            return pf
        
        # print(primeFactors2(210))

        def primeFactors(x):
            pf = []
            if x % 2 == 0:
                pf.append(2)
                while x % 2 == 0:
                    x = x// 2
            
            for p in range(3, int(sqrt(x)) + 1, 2):
                if x % p == 0:
                    pf.append(p)
                while x % p == 0:
                    x = x // p
                if x == 1:
                    break
            if x != 1:
                pf.append(x)
            return pf
        
        # print(primeFactors(210))

        n = len(nums)
        p = {}
        r = defaultdict(int)

        def union(i, j):
            i = find(i)
            j = find(j)
            if r[i] > r[j]:
                p[j] = i
            elif r[j] > r[i]:
                p[i] = j
            else:
                r[i] += 1
                p[i] = j
            
        
        def find(i):
            if i not in p:
                p[i] = i
            if p[i] != i:
                p[i] = find(p[i])
            return p[i]
           
        for num in nums:
            for pf in primeFactors2(num):
                union(num, pf)
                
        comp = collections.defaultdict(int)
        
        for num in nums:
            comp[find(num)] += 1
        
        # print(comp)
        return max(comp.values())
41766