<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 DSU:
    def __init__(self, n):
        self.father = list(range(n))
        self.size = [1] * n 
        self.max_size = 1
    
    def find(self, x):
        if self.father[x] != x:
            self.father[x] = self.find(self.father[x])
            return self.father[x]
        else:
            return x
    
    def union(self, x, y):
        px = self.find(x)
        py = self.find(y)
        if px == py: return 
        if self.size[px] > self.size[py]:
            self.father[py] = px
            self.size[px] += self.size[py]
        else:
            self.father[px] = py
            self.size[py] += self.size[px]
        self.max_size = max(self.max_size, self.size[py], self.size[px])

class Solution:
    def largestComponentSize(self, nums: List[int]) -> int:
        def factor(a):
            res = set([a])
            for i in range(2, int(sqrt(a)) + 1):
                if a % i == 0:
                    res.add(i)
                    res.add(a // i)
            return res
        
        factor_dict = defaultdict(set)
        for num in nums:
            factor_dict[num] = factor(num)
        
        n = len(nums)
        dsu = DSU(n)
        seen = dict()
        for i, num in enumerate(nums):
            for factor in factor_dict[num]:
                if factor in seen:
                    dsu.union(i, seen[factor])
                else:
                    seen[factor] = i
        return dsu.max_size
        
        


        



        
46353