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)

#include <bits/stdc++.h>
using namespace std;

int n;
vector<int> edges[100000];

int solve(int v, int p){
    int ch = edges[v].size();
    if(p >= 0) --ch;
    if(ch == 0) return 0;
    int ret = 0;
    for(int u: edges[v]){
        if(u == p) continue;
        ret ^= solve(u, v) + 1;
    }
    return ret;
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    
    cin >> n;
    for(int i=1;i<n;++i){
        int x, y;
        cin >> x >> y;
        --x; --y;
        edges[x].push_back(y);
        edges[y].push_back(x);
    }
    if(solve(0, -1) == 0) cout << "Bob" << endl;
    else cout << "Alice" << endl;
    
    return 0;
}