Tree Game Winner

Alice and Bob are playing a game on a tree. The tree consists of n vertices and n-1 edges, forming a connected acyclic graph. The players take turns removing an edge from the tree. The game starts with Alice, and they continue alternating turns.

The game ends when only one vertex remains (i.e. after the last edge is removed). The player who is unable to make a move (because there are no more edges left) loses the game.

It can be shown that if the number of vertices is odd, Alice will win under optimal play; otherwise, Bob wins. In mathematical terms, if \(n \mod 2 = 1\), then Alice wins, and if \(n \mod 2 = 0\), then Bob wins.

Your task is to determine the winner given the initial configuration of the tree.

inputFormat

The input is given via standard input (stdin) and has the following format:

The first line contains a single integer n (the number of vertices).
Each of the next n-1 lines contains two integers u and v, representing an edge between vertices u and v in the tree.

outputFormat

Output a single line to standard output (stdout) containing the winner of the game. Print Alice if Alice wins, or Bob if Bob wins.

## sample

3
1 2
2 3

Alice

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