<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:
        MAX_INT = 10 ** 5
        IsPrime = [True] * (MAX_INT + 1)
        for i in range(2, MAX_INT + 1):
            if IsPrime[i]:
                j = i + i
                while j <= MAX_INT:
                    IsPrime[j] = False
                    j += i
        p = [i for i in range(2, MAX_INT + 1) if IsPrime[i]]
        graph = {}
        for v in p:
            graph[-v] = []
        for v in nums:
            graph[v] = []
            x, i = v, 0
            while x >= p[i] * p[i]:
                conn = False
                while x % p[i] == 0:
                    conn = True
                    x //= p[i]
                if conn:
                    graph[v].append(-p[i])
                    graph[-p[i]].append(v)
                i += 1
            if x > 1:
                graph[v].append(-x)
                graph[-x].append(v)
        # print(graph)
        visited, ans = set(), 0
        for v in graph:
            if v < 0 or v in visited:
                continue
            visited.add(v)
            cnt, stack = 0, [v]
            while stack:
                i = stack.pop()
                if i > 0:
                    cnt += 1
                for j in graph[i]:
                    if j not in visited:
                        visited.add(j)
                        stack.append(j)
            ans = max(ans, cnt)
        return ans
28008