<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>

struct DSU{
    vector<int>par;
    vector<int>siz;
    DSU(int n){
        for(int i=0; i<n; i++){
            par.push_back(i);
            siz.push_back(1);
        }
    }

    int root(int u){
        if(par[u] != u)par[u] = root(par[u]);
        return par[u];
    }

    void merge(int u, int v){
        u = root(u); 
        v = root(v);
        if(u == v)return;
        if(siz[u] < siz[v])swap(u, v);
        par[v] = u;
        siz[u] += siz[v];
    }

    int sizz(int u){
        u = root(u);
        return siz[u];
    }
};

class Solution {
    vector<int>smallestPrime;
    void init(){
        smallestPrime.assign(100005, -1);
        smallestPrime[0] = 1;
        smallestPrime[1] = 1;
        for(int i=2; i<100005; i++){
            if(smallestPrime[i] != -1)continue;
            smallestPrime[i] = i;
            for(int j=i*2; j<100005; j+=i){
                if(smallestPrime[j] == -1){
                    smallestPrime[j] = i;
                }
            }
        }
    }
public:
    int largestComponentSize(vector<int>& nums) {
        init();
        vector<vector<int>>where(100005);
        int total = nums.size();
        DSU dsu = DSU(total);
        for(int i=0; i<total; i++){
            int tmp = nums[i];
            while(tmp > 1){
                int prime = smallestPrime[tmp];
                if(!(!where[prime].empty() && where[prime].back() == i)){
                    if(!where[prime].empty()){
                        dsu.merge(where[prime].back(), i);
                    }
                    where[prime].push_back(i);
                }
                tmp /= prime;
            }
        }
        int best = 0;
        for(int i=0; i<total; i++){
            best = max(best, dsu.sizz(i));
        }
        return best;
    }
};
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