<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:
class dsu{
public:
    vector<int>parent,rank;
    dsu(int n){
        parent.resize(n+1);
        rank.resize(n+1);
        for(int i=0;i<n+1;i++){
            parent[i]=i;
            rank[i]=1;
        }
    }
    int find(int n){
        if(parent[n]==n)return n;
        return parent[n]=find(parent[n]);
    }
    void join(int u,int v){
        int pu=find(u),pv=find(v);
        if(pv==pu)return;
        if(rank[pv]==rank[pu]){
            rank[pv]++;
            parent[pu]=pv;
        }
        if(rank[pu]>rank[pv])parent[pv]=pu;
        if(rank[pu]<rank[pv])parent[pu]=pv;
    }
    bool is(int u,int v){
        int pu=find(u),pv=find(v);
        return parent[pu]==parent[pv];
        
    }
};
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        dsu d(2*n);
        for(auto v:dislikes){
            if(d.is(v[0],v[1]))return 0;
            d.join(v[0],n+v[1]);
            d.join(v[1],n+v[0]);
        }
        return 1;
    }
};
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