<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 disjointSet
 {
    vector<int> rank,parent,size;
    public :
    disjointSet(int n){
        rank.resize(n+1,0);
        size.resize(n+1);
        parent.resize(n+1);
        for(int i=0;i<n;i++){
            parent[i]=i;
            size[i]=1;
        }
    }
    
  int findul_P(int node){
        if(node==parent[node]){
            return node;
        }
        return parent[node]=findul_P(parent[node]);
    }

    void UnionBySize(int u,int v){
       int ulp_u = findul_P(u);
        int ulp_v = findul_P(v);

        if (ulp_u == ulp_v) return;
        
        if(size[ulp_u]<size[ulp_v]){
            parent[ulp_u]=ulp_v;
            size[ulp_v]+=size[ulp_u];
        }
        else{
            parent[ulp_v]=ulp_u;
             size[ulp_u]+=size[ulp_v];
        }
    }
 };

class Solution {
public:
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        disjointSet ds(2*n+1);
         

        for(auto it: dislikes){
            int u=it[0];
            int v=it[1];
            
            if(ds.findul_P(u)==ds.findul_P(v)) return false;

            ds.UnionBySize(u, ds.findul_P(v + n)); 

            ds.UnionBySize(v, ds.findul_P(u + n));
        }

        return true;
    }
};
62878