<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 DisjointSet {
    vector<int> parent, size;
public:
    DisjointSet(int n){
        parent.resize(n+1); size.resize(n+1);
        for (int i=0; i<=n; i++){
            parent[i] = i;
            size[i] = 1;
        }
    }
    int getLeader(int node) {
        if (node == parent[node]) return node;
        return parent[node] = getLeader(parent[node]);
    }
    void merge(int u, int v) {
        int ult_u = getLeader(u), ult_v = getLeader(v);
        if (ult_u == ult_v) return;
        if (size[ult_v] < size[ult_u]) {
            parent[ult_v] = ult_u;
            size[ult_u] += size[ult_v];
        } else {
            parent[ult_u] = ult_v;
            size[ult_v] += size[ult_u];            
        }
    }
    int getSize(int u){
        return size[u];
    }
};
class Solution {
public:
    int largestComponentSize(vector<int>& nums) {
        int n = nums.size();
        int N = 1e5;
        unordered_map<int, int> mpp;
        DisjointSet ds(n+1);
        for (int i=0; i<n; i++){
            mpp[nums[i]] = i;
        }
        for (int i=2; i<=N; i++){
            int u = -1, v = -1;
            for (int j=i; j<=N; j+=i) {
                if (mpp.find(j) != mpp.end()){
                    if (u == -1) u = j;
                    v = j;
                    ds.merge(mpp[u], mpp[v]);
                }
            }
            mpp.erase(i);
        }
        int ans = 0;
        for (int i=0; i<n; i++){
            ans = max(ans, ds.getSize(i));
        }
        return ans;
    }
};
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