<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 UnionFind:
    def __init__(self,n):
        self.parent = []
        self.rank = [1] * (n + 1)
        for i in range(n+1):
            self.parent.append(i)
    
    def find_parent(self, x):
        if self.parent[x] != x:
            self.parent[x] = self.find_parent(self.parent[x])
        return self.parent[x]
    
    def union(self, v1, v2):
        p1,p2 = self.find_parent(v1), self.find_parent(v2)

        if p1 == p2:
            return
        
        if self.rank[p1] > self.rank[p2]:
            self.parent[p2] = p1
            self.rank[p1] += 1
        else:
            self.parent[p1] = p2
            self.rank[p2] += 1

class Solution:
    def possibleBipartition(self, n: int, dislikes: List[List[int]]) -> bool:
        adj = collections.defaultdict(list)

        for i,j in dislikes:
            adj[i].append(j)
            adj[j].append(i)
        
        dsu = UnionFind(n)

        for node in range(1, n+ 1):
            for neighbor in adj[node]:
                if dsu.find_parent(node) == dsu.find_parent(neighbor): return False
            
                dsu.union(adj[node][0], neighbor)
        return True
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