<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 prime_factors(n):
            r = set()
            if n == 1:
                return r
            it, div, bound = 2, n, int(n**0.5)+1
            while it < bound and it < div: 
                while div % it == 0:
                    r.add(it)
                    div //= it
                it += 1
            if div > 1:
                r.add(div)
            return r

        nums_factors = [prime_factors(n) for n in nums]

        adj_list = defaultdict(list)
        l = len(nums)

        for i, ni in enumerate(nums):
            for f in nums_factors[i]:
                adj_list[ni].append(f)
                adj_list[f].append(ni)

        noc = 0
        max_size = 0
        visited = set()
        aset = set(nums)

        def dfs(n):
            if n in visited:
                return 0
            visited.add(n)
            r = sum(dfs(nei) for nei in adj_list[n] if nei not in visited)
            r += 1 if n in aset else 0
            return r

        for n in nums:
            if n not in visited:
                noc += 1
                max_size = max(max_size, dfs(n))

        return max_size
43295