CF346A.Alice and Bob

It is so boring in the summer holiday, isn't it? So Alice and Bob have invented a new game to play. The rules are as follows. First, they get a set of n distinct integers. And then they take turns to make the following moves. During each move, either Alice or Bob (the player whose turn is the current) can choose two distinct integers x and y from the set, such that the set doesn't contain their absolute difference |x - y|. Then this player adds integer |x - y| to the set (so, the size of the set increases by one).

If the current player has no valid move, he (or she) loses the game. The question is who will finally win the game if both players play optimally. Remember that Alice always moves first.

暑假里真是无聊，不是吗？于是爱丽丝（Alice）和鲍勃（Bob）发明了一种新游戏来玩。规则如下：首先，他们得到一个包含 $n$ 个互不相同的整数的集合。然后，他们轮流进行如下操作：在每次操作中，当前轮到的玩家（即爱丽丝或鲍勃）可以从该集合中选择两个不同的整数 $x$ 和 $y$，使得集合中不包含它们的绝对差 $|x - y|$；然后该玩家将整数 $|x - y|$ 加入集合（因此集合的大小增加 1）。

如果当前玩家无法进行任何合法操作，则他（或她）输掉游戏。问题是：若双方均以最优策略进行游戏，最终谁将获胜？注意，爱丽丝总是先手。

The first line contains an integer n (2 ≤ n ≤ 100) — the initial number of elements in the set. The second line contains n distinct space-separated integers _a_1, _a_2, ..., a__n (1 ≤ a__i ≤ 109) — the elements of the set.

第一行包含一个整数 $n$（$2 \leq n \leq 100$）——集合的初始元素个数。
第二行包含 $n$ 个互不相同的、以空格分隔的整数 $a_1,\,a_2,\,...,\,a_n$（$1 \leq a_i \leq 10^9$）——集合中的元素。

Print a single line with the winner's name. If Alice wins print "Alice", otherwise print "Bob" (without quotes).

输出一行，内容为获胜者的名字。如果 Alice 获胜，则输出 "Alice"，否则输出 "Bob"（不带引号）。

Consider the first test sample. Alice moves first, and the only move she can do is to choose 2 and 3, then to add 1 to the set. Next Bob moves, there is no valid move anymore, so the winner is Alice.

考虑第一个测试样例。Alice 先手，她唯一可行的操作是选择 $2$ 和 $3$，然后将 $1$ 加入集合。接下来轮到 Bob 操作，此时已不存在任何合法操作，因此 Alice 获胜。