Alice and Bob's difference game

Alice and Bob made up a game for two players. The rules are as follows.

1. The game starts from one set of $n$ distinct positive integers.
2. The two players take turns. On your turn you pick two distinct numbers $x$ and $y$ from the set. The pair cannot be picked if $|x - y|$ is already in the set. After picking $x$ and $y$ you put $|x - y|$ into the set, and your turn ends.
3. A player who has no pair $(x, y)$ left to pick loses.

Alice always moves first. Both players play optimally. Print who wins for the given $n$ positive integers.

The first line contains the size $n$ of the starting set. ($2 \le n \le 100$)

The second line contains the elements $c_1, c_2, \dots, c_n$ separated by spaces. ($1 \le c_i \le 10^9$)

All $c_i$ are distinct.

Print "Alice" if Alice wins, or "Bob" if Bob wins.