<p>We want to split a group of <code>n</code> people (labeled from <code>1</code> to <code>n</code>) into two groups of <strong>any size</strong>. Each person may dislike some other people, and they should not go into the same group.</p>

<p>Given the integer <code>n</code> and the array <code>dislikes</code> where <code>dislikes[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that the person labeled <code>a<sub>i</sub></code> does not like the person labeled <code>b<sub>i</sub></code>, return <code>true</code> <em>if it is possible to split everyone into two groups in this way</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 4, dislikes = [[1,2],[1,3],[2,4]]
<strong>Output:</strong> true
<strong>Explanation:</strong> The first group has [1,4], and the second group has [2,3].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 3, dislikes = [[1,2],[1,3],[2,3]]
<strong>Output:</strong> false
<strong>Explanation:</strong> We need at least 3 groups to divide them. We cannot put them in two groups.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 2000</code></li>
	<li><code>0 &lt;= dislikes.length &lt;= 10<sup>4</sup></code></li>
	<li><code>dislikes[i].length == 2</code></li>
	<li><code>1 &lt;= a<sub>i</sub> &lt; b<sub>i</sub> &lt;= n</code></li>
	<li>All the pairs of <code>dislikes</code> are <strong>unique</strong>.</li>
</ul>

class DSU{
    public:
    vector<int> sz, id;
    DSU(int n){
        for(int i = 0; i < n; i++){
            sz.push_back(1);
            id.push_back(i);
        }
    }
    
    int findParent(int i){
        if(i == id[i]) return i;
        return id[i] = findParent(id[i]);
    }
    
    void Union(int x, int y){
        int i = findParent(x);
        int j = findParent(y);
        if(i != j){
            if(sz[i] > sz[j]){
                id[j] = i;
                sz[i] += sz[j];
            } else {
                id[i] = j;
                sz[j] += sz[i];
            }
        }
    }
};

class Solution {
public:
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {

        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout.tie(nullptr);

        DSU dsu(2 * n + 1);

        int cnt = n;

        for(auto itr : dislikes){
            if(dsu.findParent(itr[0]) == dsu.findParent(itr[1]))
                return false;
            dsu.Union(itr[0], itr[1] + n);
            dsu.Union(itr[1], itr[0] + n);
        }
        return true;
    }
};
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