<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 ll long long 
struct DSU{
    vector<ll> par, siz;
    ll n;
    DSU(ll n){
        this->n = n + 4;
        par.assign(n + 5, 0);
        siz.assign(n + 5 ,1);
    }
    void make_set(){
        for(ll i = 0;i<=n;i++){
            par[i] = i; siz[i] = 1;
        }
    }
    ll find_parent(ll x){
        if(par[x] == x) return x;
        return find_parent(par[x]);
    }
    ll get_size(ll x){
        return siz[find_parent(x)];
    }
    void merge(ll x, ll y){
        x = find_parent(x), y = find_parent(y);
        ll szx = siz[x], szy = siz[y];
        if(szx < szy) swap(x, y);
        if(x != y){
            siz[x] += siz[y];
            par[y] = x;
        }
    }
};
class Solution {
public:
    ll sieve[200005], freq[200005];
    int largestComponentSize(vector<int>& nums) {
        for(auto p : nums) freq[p]++;
        DSU d(1e5);
        d.make_set();
        for(ll i = 2;i<=1e5;i++){
            if(sieve[i] == 0){
                ll prev = -1;
                // cout << i << " : ";
                for(ll j = i;j<=1e5;j+=i){
                    if(freq[j] != 0){
                        // cout << j << " ";
                        if(prev != -1) d.merge(prev, j);
                        prev = j;
                    }
                    sieve[j] = 1;
                }
                // cout << endl;
            }
        }
        ll ans = 0;
        for(ll i = 1;i<=1e5;i++){
            ans = max(ans, d.get_size(i));
        }
        return ans;
    }
};
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