<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>

#define f(i, a, b) for(int i = a; i < b; i++)
#define fd(i,a, b) for(int i = a; i >= b; i--)
#define nl  endl
#define all(a) a.begin(), a.end()
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define sz size()
#define oo INT_MAX
#define inf LLONG_MAX
#define ins insert
#define set_bits(x) __builtin_popcountll(x)
typedef long long ll;
typedef long double ld;
typedef pair<int, int>  pii;
typedef pair<ll, ll>  pll;
typedef vector<int> vi;
typedef vector<vector<int> > vvi;
typedef vector<ll> vl;
typedef vector<vector<ll> > vvl;
const int mod = 1e9+7;
const int mod1 = 998244353;
const int N = 2e5+5;
class Solution {
public:
    vector<set<int>> adj;
    vi vis, color;
    bool dfs(int cur, int p, int c) {
        vis[cur] = 1;
        color[cur] = c;
        c ^= 1;
        for (auto child : adj[cur]) {
            if (!vis[child]) {
                if (!dfs(child, cur, c))
                    return false;
            } else {
                if (color[child] == color[cur]) {
                    return false;
                }
            }
        }
        return true;
    }
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        ios::sync_with_stdio(false);    cin.tie(nullptr);
        adj.resize(n+1);
        vis.resize(n+1);
        color.resize(n+1);
        f(i, 0, dislikes.sz) {
            adj[dislikes[i][0]].insert(dislikes[i][1]);
            adj[dislikes[i][1]].insert(dislikes[i][0]);
        }
        for (int i = 0; i < n; i++) {
            if (!vis[i]) {
                if (!dfs(i, -1, 0))
                    return false;
            }
        }
        return true;
    }
};
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