<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:
        gr = {} 
        dth = {}
        def find(n):
            if n not in gr:
                gr[n] = n
                dth[n] = 1
                return n
            else:
                if gr[n] == n:
                    return n
                else:
                    gr[n] = find(gr[n])
                    return gr[n] 
        def union(i,j):
            ri = find(i)
            rj = find(j)
            if ri == rj:
                return 
            else:
                if dth[ri] > dth[rj]:
                    gr[rj] = ri
                elif dth[ri] < dth[rj]:
                    gr[ri] = rj
                else:
                    gr[ri] = rj
                    dth[rj] += 1

        def prime_factor(n):
            factor = 2
            ret = set()
            while factor ** 2 <= n:
                if n % factor == 0:
                    n /= factor
                    ret.add(factor)
                else:
                    factor += 1
            if n > 1:
                ret.add(n)
            return ret
        
        for n in nums:
            for p in list(prime_factor(n)):        
                union(p, n)
        
        cnt = {}
        for n in nums:
            m = find(n)
            if m not in cnt:
                cnt[m] = 1
            else:
                cnt[m] += 1
        return max(cnt.values())
        


        



            

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