<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 dfs(int node, vector<vector<int>>& graph, vector<int>& vis){
        int ans=1;
        vis[node]=1;
        for(auto& g:graph[node]){
            if(!vis[g]){
                ans+=dfs(g,graph,vis);
            }
        }
        return ans;
    }
    
    int largestComponentSize(vector<int>& nums) {
        int maxi=*max_element(nums.begin(),nums.end()),n=nums.size();
        vector<int> p(maxi+1,1),primes;
        for(long long i=2;i<=maxi;++i){
            if(p[i]==1){
                primes.push_back(i);
                for(long long j=i*i;j<=maxi;j+=i){
                    p[j]=0;
                }
            }
        }
        for(int i=0;i<=maxi;++i) p[i]=-1;
        for(int i=0;i<n;++i){
            p[nums[i]]=i;
        }
        vector<vector<int>> graph(n);
        for(int i=0;i<primes.size();++i){
            int prev=-1;
            for(int j=primes[i];j<=maxi;j+=primes[i]){
                if(p[j]!=-1){
                    if(prev==-1) prev=j;
                    else{
                        graph[p[prev]].push_back(p[j]);
                        graph[p[j]].push_back(p[prev]);
                        prev=j;
                    }
                }
            }
        }
        int ans=0;
        vector<int> vis(n,0);
        for(int i=0;i<n;++i){
            if(!vis[i]){
                ans=max(ans,dfs(i,graph,vis));
            }
        }
        return ans;
    }
};
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