A tree game

Alice and Bob want to play an interesting game on a tree.
Given is a tree on N vertices, The vertices are numbered from 1 to N. vertex 1 represents the root. There are N-1 edges. Players alternate in making moves, Alice moves first. A move consists of two steps. In the first step the player selects an edge and removes it from the tree. In the second step he/she removes all the edges that are no longer connected to the root. The player who has no edge to remove loses.
You may assume that both Alice and Bob play optimally.

The first line of the input file contains an integer T (T<=100) specifying the number of test cases.
Each test case begins with a line containing an integer N (1<=N<=10^5), the number of vertices,The following N-1 lines each contain two integers I , J, which means I is connected with J. You can assume that there are no loops in the tree.

For each case, output a single line containing the name of the player who will win the game.

3
3
1 2
2 3

3
1 2
1 3 

10
6 2
4 3
8 4
9 5
8 6
2 7
5 8
1 9
6 10

Alice
Bob
Alice

2009 Multi-University Training Contest 18 - Host by ECNU