<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:
        f={x:x for x in nums}
        size = {x:1 for x in nums}
        ftoi = {n:n for n in nums} # factor -> one of its representative numbers
        def find(x):
            if x!=f[x]: f[x]=find(f[x])
            return f[x]
        def uni(x,y):
            x,y = find(x),find(y)
            if x==y: return x
            if size[x]<size[y]: x,y=y,x
            f[y]=x
            size[x]+=size[y]
            return x
        
        for n in nums:
            for i in range(2,n):
                if i**2>n:break 
                if n%i==0: 
                    if i not in ftoi: ftoi[i]=n
                    else: ftoi[i] = uni(n,ftoi[i])
                    
                    j = n//i
                    if j not in ftoi: ftoi[j]=n
                    else: ftoi[j] = uni(n,ftoi[j])

        return max(size.values())
                

        

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