<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>

static const int N = 1e5+1;
vector<int> isPrime(N, 1);
class Disjoint {
public: 
    vector<int> par, size;
    Disjoint() {
        par.resize(N);
        size.resize(N);
        for(int i = 1; i < N; i++) {
            par[i] = i;
            size[i] = 1;
        }
    }
    int find(int num) {
        if(num == par[num]) return num;
        return par[num] = find(par[num]);
    }
    void merge(int n1, int n2) {
        int p1 = find(n1), p2 = find(n2);
        if(p1 != p2) {
            if(size[p1] >= size[p2]) {
                par[p2] = p1;
                size[p1] += size[p2];
            } else {
                par[p1] = p2;
                size[p2] += size[p1];
            }
        }
    }
};
class Solution {
    unordered_map<int, vector<int>> mp, mp1;
    void constructPrime() {
        isPrime[0] = isPrime[1] = 0;
        for(int i = 2; i * i <= 1e5; i++) {
            for(int j = i * i; j <= 1e5; j += i) {
                isPrime[j] = 0;
            }
        }
    }
    void constructMap(vector<int>& nums) {
        for(int i = 0; i < nums.size(); i++) {
            for(int j = 2; j * j <= nums[i]; j++) {
                if(nums[i] % j == 0) {
                    mp[j].push_back(nums[i]);
                    mp[nums[i] / j].push_back(nums[i]);
                }
            }
            mp[nums[i]].push_back(nums[i]);
        }
        // for(int i = 2; i <= 1e5; i++) {
        //     if(isPrime[i]) {
        //         for(int j = 0; j < nums.size(); j++) {
        //             if(nums[j] % i == 0) {
        //                 mp1[i].push_back(nums[j]);
        //             }
        //         }
        //     }
        // }
    }
public:
    int largestComponentSize(vector<int>& nums) {
        if(isPrime[0] == 1)
            constructPrime();
        constructMap(nums);
        // for(auto& [x, y]: mp) {
        //     cout<<x<<":";
        //     for(auto& z: y) {
        //         cout<<z<<' ';
        //     }
        //     cout<<endl;
        // }
        // cout<<endl;
        // for(auto& [x, y]: mp1) {
        //     cout<<x<<":";
        //     for(auto& z: y) {
        //         cout<<z<<' ';
        //     }
        //     cout<<endl;
        // }
        Disjoint ds;
        for(auto& [x, y]: mp) {
            int f = 1;
            for(auto& z: y) {
                if(x == z) {
                    f = 0;
                } else {
                    ds.merge(x, z);
                }
            }
            if(f) ds.size[ds.find(x)]--;
        }
        int ans = 0;
        for(int i = 1; i < N; i++) {
            ans = max(ans, ds.size[i]);
        }
        return ans;
    }
};
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