<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:
    def possibleBipartition(self, n: int, dislikes: List[List[int]]) -> bool:

        colors = {}
        seen = set()
        adjList = defaultdict(list)
        nodes = set()
        res = True

        if n <= 2:
            return True

        for u, v in dislikes:
            adjList[u].append(v)
            adjList[v].append(u)
            nodes.add(u)
            nodes.add(v)

        depth = 0
        queue = [ (node, 0) for node in nodes ]
        colors[queue[0][0]] = queue[0][1]

        while queue:
            node, depth = queue.pop(0)
            seen.add(node)
            if node not in colors:
                colors[node] = depth % 2
            #print(f"{node=} {depth=} {adjList[node]=}")
            
            for v in adjList[node]:
                if v not in seen:
                    queue.insert(0, (v, depth+1))

        #print(f"{colors=}")

        for u, v in dislikes:
            #print(f"{u=} color={colors[u]}. {v=} color={colors[v]}")
            if colors[u] == colors[v]:
                res = False
                break

        return res
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