<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 arr[(int)(1e5+5)];
    int visit[(int)(1e5+5)]={0};
    int member[(int)(1e5+5)];
    constexpr void build(vector<int>& primes, pair<int,int>* sp, int N){
        if(primes.empty()){
            visit[0] = visit[1] = 1;
            sp[1].first = sp[1].second = 1;
            for(int i=2;i<=1e5;i++){
                if(!visit[i]){
                    primes.push_back(i);
                    sp[i].first=i;
                    sp[i].second = i;
                }for (int j=0; i*primes[j]<=1e5; j++){
                     visit[i*primes[j]] = 1;
                     sp[i*primes[j]].first = primes[j];
                     sp[i*primes[j]].second = sp[i].first == primes[j] ? sp[i].second : i;
                     if(i%primes[j]==0)break;
                 }
            }
        }
        for(int i=0;i<=N;i++){
            arr[i] = i;
        }
    }
    int find(int x){
        while(arr[x]!=x)
            x=arr[x];
        return x;
    }
    void uni(int x, int y){
        x = find(x), y = find(y);
        if(x==y)return;
        member[y]+=member[x];
        member[x]=0;
        arr[x] = y;
    }
    int largestComponentSize(vector<int>& nums) {
        static vector<int> primes;
        static pair<int,int> sp[(int)(1e5+5)];
        build(primes, sp, *max_element(nums.begin(),nums.end()));
        int ans=1;
        for(auto& it:nums){
            int pre=sp[it].first;
            it = sp[it].second;
            while(it!=sp[it].first){
                uni(sp[it].first, pre);
                pre = sp[it].first;
                it = sp[it].second;
            }
            uni(sp[it].first, pre);
            member[find(pre)]++;
            ans = max(member[find(pre)], ans);
        }
        return ans;
    }
};
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