<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 Solution {
public:
    vector<int> parent;
    vector<int> size;

    void make(int v){
        parent[v] = v;
        size[v] = 1;
    }

    int find(int v){
        if(v == parent[v]) return v;
        return parent[v] = find(parent[v]);
    }

    void Union(int a, int b){
        a = find(a);
        b = find(b);
        if(a != b){
            if(size[a] < size[b])
                swap(a, b);
            parent[b] = a;
            size[a] += size[b];
        }
    }

    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        parent.resize(2*n+1);
        size.resize(2*n+1);

        for(int i=1;i<=2*n;i++){
            make(i);
        }

        for(auto& edge : dislikes){
            int u = edge[0];
            int v = edge[1];
            if(find(u)==find(v)) return false;
            Union(u, v+n);
            Union(v, u+n);
        }

        return true;
    }
};
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