<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>

#define MAX 100005
class Solution {
    vector<int>tree;
    vector<int>rank;
    vector<int>isPrime;
public:
    
    int findParent(int u){
        if(tree[u] == -1)
            return u;
        tree[u] = findParent(tree[u]);
        return tree[u];
    }
    
    void doUnion(int x, int y){
        int parent_x = findParent(x);
        int parent_y = findParent(y);
        if(parent_x == parent_y)
            return;
        if(rank[parent_x] < rank[parent_y]){
            tree[parent_x] = parent_y;
        } else if(rank[parent_x] > rank[parent_y]){
            tree[parent_y] = parent_x;
        } else {
            tree[parent_x] = parent_y;
            rank[parent_y]++;
        }
    }
    void precompute(){
        tree.resize(MAX + 1, -1);
        rank.resize(MAX + 1);
        isPrime.resize(MAX + 1, true);
        
        for(int i=2;i*i<=MAX;i++){
            for(int j=i*i; j<=MAX && isPrime[i]; j+= i)
                isPrime[j] = false;
        }
    }
    
    void primeFactor(int num){
        vector<int>res;
        int j = 2;
        int val = num;
        while(num > 1){
            if(isPrime[j] && num % j == 0){
                num /= j;
                doUnion(j, val);
            } else {
                j++;
            }
        }
    }
    
    int largestComponentSize(vector<int>& nums) {
        precompute();
        unordered_map<int, int>M;
        for(int i=0;i<nums.size();i++){
           if(!isPrime[nums[i]])
                primeFactor(nums[i]);

        }
        int maxIndex = -1;
        for(int i=0;i<nums.size();i++){
            int p = findParent(nums[i]);
            M[p]++;
            if(M[p] > M[maxIndex])
                maxIndex = p;
        }
        return M[maxIndex];
        
    }
};
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