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.