<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>

MAX = 100001

v = [False] * MAX
sp = [0] * MAX

for i in range(2, MAX, 2):
    sp[i] = 2

for i in range(3, MAX, 2):
    if not v[i]:
        sp[i] = i
        j = i
        while j * i < MAX:
            if not v[j * i]:
                v[j * i] = True
                sp[j * i] = i
            j += 2

class Solution:
    def largestComponentSize(self, nums: List[int]) -> int:
        n = len(nums)
        graph = [set() for _ in range(n)]
        f = {}
        for i in range(n):
            curr = nums[i]
            while curr > 1:
                if sp[curr] in f:
                    graph[f[sp[curr]]].add(i)
                    graph[i].add(f[sp[curr]])
                else:
                    f[sp[curr]] = i
                curr //= sp[curr]
        res = 0
        v = [False] * n
        for i in range(n):
            if not v[i]:
                v[i] = True
                sz = 0
                stack = [i]
                while stack:
                    x = stack.pop()
                    sz += 1
                    for y in graph[x]:
                        if not v[y]:
                            v[y] = True
                            stack.append(y)
                res = max(res, sz)
        return res
29536