<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 DSU{
    public:

    vector<int> parent;
    vector<int> size;

    DSU(int n){
        parent.resize(n);
        size.resize(n, 0);

        for(int i = 0; i < n; ++i) parent[i] = i;
    }

    int findPar(int node){
        if(parent[node] == node) return node;

        return parent[node] = findPar(parent[node]);
    }

    void join(int node1, int node2){
        int par1 = findPar(node1);
        int par2 = findPar(node2);

        if(par1 == par2) return;

        if(size[par1] <= size[par2]){
            size[par2] += size[par1];
            parent[par1] = par2;
        }
        else{
            size[par1] += size[par2];
            parent[par2] = par1;
        }
    }

    void resize(int node){
        int par = findPar(node);

        size[par]++;
    }

    int findSize(int node){
        int par = findPar(node);

        return size[par];
    }
};

class Solution {
private:
    vector<int> fact(){
        vector<int> prime(1e5 + 1, 0);

        prime[1] = 1;

        for(int i = 2; i*i <= 1e5; ++i){
            if(prime[i] == 1) continue;
            for(int j = i*i; j <= 1e5; j += i){
                if(prime[j] == 0){
                    prime[j] = i;
                }
            }
        }

        return prime;
    }

    vector<int> split(int num, vector<int> &factor){
        // vector<int> res;
        unordered_set<int> res;

        while(num != 1){
            if(factor[num] != 0){
                res.insert(factor[num]);
                num = num/factor[num];
            }
            else{
                res.insert(num);
                num = num/num;
            }
        }

        vector<int> ans;

        for(auto it: res){
            ans.push_back(it);
        }

        return ans;
    }
public:
    int largestComponentSize(vector<int>& nums) {
        vector<int> factor = fact();

        unordered_map<int, int> indexing;

        int ind = 0;

        for(int i = 1; i <= 1e5; ++i){
            if(factor[i] == 0){
                indexing[i] = ind++;
            }
        }

        DSU dsu(ind);

        int res = 0;

        for(int i = 0; i < nums.size(); ++i){
            if(nums[i] == 1){
                res = 1;
                
                continue;
            }
            vector<int> temp = split(nums[i], factor);

            dsu.resize(indexing[temp[0]]);

            for(int j = 1; j < temp.size(); ++j){
                dsu.join(indexing[temp[0]], indexing[temp[j]]);
            }
        }

        

        for(auto it: indexing){
            res = max(res, dsu.findSize(indexing[it.first]));
        }

        return res;
    }
};


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