Problem:
Score : 1100 points

Problem Statement

There is a tree with N vertices numbered 1, 2, ..., N.
The edges of the tree are denoted by (x_i, y_i).

On this tree, Alice and Bob play a game against each other.
Starting from Alice, they alternately perform the following operation:

Select an existing edge and remove it from the tree, disconnecting it into two separate connected components. Then, remove the component that does not contain Vertex 1.

A player loses the game when he/she is unable to perform the operation.
Determine the winner of the game assuming that both players play optimally.

Constraints

2 \leq N \leq 100000

1 \leq x_i, y_i \leq N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_{N-1} y_{N-1}

Output

Print Alice if Alice wins; print Bob if Bob wins.

Sample Input 1

5
1 2
2 3
2 4
4 5

Sample Output 1

Alice

If Alice first removes the edge connecting Vertices 1 and 2, the tree becomes a single vertex tree containing only Vertex 1.
Since there is no edge anymore, Bob cannot perform the operation and Alice wins.

Sample Input 2

5
1 2
2 3
1 4
4 5

Sample Output 2

Bob

Sample Input 3

6
1 2
2 4
5 1
6 3
3 2

Sample Output 3

Alice

Sample Input 4

7
1 2
3 7
4 6
2 3
2 4
1 5

Sample Output 4

Bob

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>

#define F first
#define S second
#define int long long
#define ll long long
//#define int  unsigned long long
#define pb push_back
//#define double long double

using namespace std;
using namespace __gnu_pbds;
typedef  tree< int , null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
const int mod = 998244353;
const int N = 520005;
const int K = 25;
vector < int > g[N];
int dp[N];
void dfs(int v, int p = -1){
    int c = 0;
    for (auto u: g[v]){
        if (u == p) continue;
        dfs(u, v);
        c ^= (dp[u] + 1);
    }
    dp[v] = c;
}
main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    //freopen("input.txt", "r", stdin);
    int n;
    cin >> n;
    for (int i = 1; i < n; i++){
        int u, v;
        cin >> u >> v;
        g[u].pb(v);
        g[v].pb(u);
    }
    dfs(1);
    if (dp[1] == 0) cout << "Bob"; else cout << "Alice";
}