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<cstdio>
const int N=400002;
int n,a,b,i,j,k;
int h[N],t[N],v[N],sg[N];
void add(int a,int b){
	t[++k]=h[a];
	h[a]=k;
	v[k]=b;
}
void init(){
	scanf("%d",&n);
	for(i=1;i<n;i++){
		scanf("%d%d",&a,&b);
		add(a,b);
		add(b,a);
	}
}
void dfs(int i,int fa){
	for(int j=h[i];j;j=t[j])
		if(v[j]!=fa){
			dfs(v[j],i);
			sg[i]^=sg[v[j]]+1;
		}
}
int main(){
	init();
	dfs(1,0);
	printf("%s",sg[1]?"Alice":"Bob");
}