<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>

// prime factorization
int maxn = 1e5 + 2;

vector<int> arr(maxn, -1);
void seivepf()
{
    for (int i = 2; i * i <= maxn; i++)
        if (arr[i] == -1)
            for (int j = i * i; j < maxn; j += i)
            {
                if (arr[j] == -1) arr[j] = i;
                arr[i] = i;
            }
}
void fetch(int no, map<int, int>& mp)
{
    int k = no;
    while (k != 1)
    {
        if (arr[k] == -1)
        {
            mp[k]++;
            break;
        }
        mp[arr[k]]++;
        k /= arr[k];
    }
}

template<typename T>
struct Dsu
{
private:
    vector<T> dsu_par, dsu_sz;
public:
    int m_n;

    Dsu(T n) 
    {
        m_n = n;
        dsu_par = vector<T>(n);
        dsu_sz = vector<T>(n, -1);
        for (int i = 0; i < n; i++)
            dsu_par[i] = i;
    }

    int getPar(int v) 
    {
        while ((v = dsu_par[v]) != dsu_par[v]);
        return v;
    }

    int getSize(int v) { return -dsu_sz[getPar(v)];}

    bool connected(int v, int u) { return getPar(v) == getPar(u); }

    void merge(int v, int u) 
    {
        v = getPar(v);
        u = getPar(u);
        if (v == u) return;
        if (dsu_sz[v] > dsu_sz[u]) swap(u, v);
        dsu_par[u] = v;
        dsu_sz[v] += dsu_sz[u];
    }
};

class Solution {
public:
    int largestComponentSize(vector<int>& nums) {
        seivepf();
        Dsu<int> dd(maxn);
        map<int, int> mp;
        map<int, vector<int>> pp;

        for (int num: nums) {
            mp.clear();
            fetch(num, mp);

            for (auto [k, v] : mp) {
                pp[k].push_back(num);
            }
        } 
        
        for (auto [k, v]: pp) {
            for (int i=0; i<v.size(); i++) {
                dd.merge(v[0], v[i]);
            }
        }
       
        int mx=0;

        for (int i=0; i<maxn; i++) {
            int pp = dd.getSize(i);
            mx = max(mx, pp);
        }
        return mx;
    }
};
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