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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Globalization;
using System.Diagnostics;
using static System.Console;
using Pair = System.Collections.Generic.KeyValuePair<int, int>;
//using System.Numerics;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().Solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    Random rnd = new Random();
    Stopwatch sw = new Stopwatch();
    readonly int[] dd = { 0, 1, 0, -1, 0 };
    readonly int mod = 1000000007;
    readonly string alfa = "abcdefghijklmnopqrstuvwxyz";


    List<int>[] G;
    int N;
    void Solve()
    {
        N = cin.Nextint;
        G = Enumerable.Range(0, N).Select(i => new List<int>()).ToArray();
        for (int i = 0; i < N - 1; i++)
        {
            int x = cin.Nextint - 1;
            int y = cin.Nextint - 1;
            G[x].Add(y);
            G[y].Add(x);
        }
        var A = new int[N];
        var B = new bool[N];

        var Q = new Queue<int>();
        Q.Enqueue(0);
        var R = new Queue<int>();
        R.Enqueue(0);
        B[0] = true;

        while (Q.Any())
        {
            int u = Q.Dequeue();
            int d = R.Dequeue();
            A[d] += G[u].Count - Math.Min(d, 1);
            foreach (var v in G[u])
            {
                if (B[v]) continue;
                B[v] = true;
                Q.Enqueue(v);
                R.Enqueue(d + 1);
            }
        }

        int t = 0;
        //int s = 0;
        for (int i = 0; i < N; i++)
        {
            //WriteLine(A[i]);
            t ^= A[i];
            if (t % 2 == 1) { WriteLine("Alice"); return; }
        }
        //WriteLine(t);
       //if(t % 2 != 0) WriteLine("Alice");
         WriteLine("Bob");

    }

}

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] Scan { get { return ReadLine().Split(); } }
    public int[] Scanint { get { return Array.ConvertAll(Scan, int.Parse); } }
    public long[] Scanlong { get { return Array.ConvertAll(Scan, long.Parse); } }
    public double[] Scandouble { get { return Array.ConvertAll(Scan, double.Parse); } }
    public string Next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return Next;
        }
    }
    public int Nextint { get { return int.Parse(Next); } }
    public long Nextlong { get { return long.Parse(Next); } }
    public double Nextdouble { get { return double.Parse(Next); } }
}