<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>

MX = int(1e5)
factors = [[] for _ in range(MX+1)]
for x in range(2, MX+1):
    if not factors[x]:
        for y in range(x, MX+1, x):
            factors[y].append(x)
class DSU:
    def __init__(self, size: int):
        self.parent = list(range(size))
        self.cc_size = [1] * size
    
    def find(self, p: int) -> int:
        if self.parent[p] != p:
            self.parent[p] = self.find(self.parent[p])
        return self.parent[p]
    
    def join(self, p: int, q: int):
        pp, pq = self.find(p), self.find(q)
        if pp != pq:
            if self.cc_size[pq] > self.cc_size[pp]:
                pp, pq = pq, pp
            self.parent[pq] = pp
            self.cc_size[pp] += self.cc_size[pq]

class Solution:
    def largestComponentSize(self, nums: List[int]) -> int:
        fac_seen = {}
        dsu = DSU(len(nums))
        for i, x in enumerate(nums):
            for fac in factors[x]:
                if fac in fac_seen:
                    dsu.join(i, fac_seen[fac])
                else:
                    fac_seen[fac] = i
        return max(dsu.cc_size)
29536