<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 {
public:
    int parent[100005],sz[100005];
    vector<int>prime;
    int find_par(int a){
        if(parent[a]==a)return a;
        return parent[a]=find_par(parent[a]);
    }
    void dsu(int a,int b){
        a=find_par(a);
        b=find_par(b);
        if(b==a)return; 
        parent[b]=a;
        return ;
    }
    vector<int>solve(int a){
        vector<int>ans;
        unordered_map<int,int>cnt;
        while(a!=1){
            cnt[prime[a]]++;
            if(cnt[prime[a]]==1)
            ans.push_back(prime[a]);
            a/=prime[a];
        }
        return ans;
    }
    int largestComponentSize(vector<int>& nums){
        int ans=0;
        prime.resize(100005,0);
        memset(sz,0,sizeof(sz));
        unordered_map<int,int>cnt;
        for(int i=2;i<=100000;i++){
            if(prime[i]==0){
                prime[i]=i;
                for(long long j=1LL*i*i;j<=100000;j+=i)prime[j]=i;
            }
        }
        for(int i=0;i<=100000;i++){
            parent[i]=i;
        }
        for(auto j:nums){
            vector<int>primes=solve(j);
            for(int i=0;i<primes.size();i++){
                dsu(primes[0],primes[i]);
            }
        }
        for(auto j:nums){
            int x=prime[j];
            x=find_par(x);
            cnt[x]++;
            sz[x]++;
        }
        for(int i=2;i<=100000;i++){
            if(prime[i]==i and cnt[i]){
                ans=max(ans,sz[i]);
            }
        }
        return ans;
    }
};
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