Thanos Nim

题意翻译

Alice 和 Bob 在玩一个游戏，现在有 $n$（$n$ 是偶数）个石堆，每堆石头有 $A_i$ 个，现在由 Alice 先，两人轮流从任意 $\frac n2$ 个石堆中移出至少一个石头，当谁移完之后堆数小于 $\frac n2$，那么 TA 就赢了。 现在要你求出谁会胜利，输出 TA 的名字（见样例）。 注意：两人都很聪明，用最佳策略。

题目描述

Alice and Bob are playing a game with $ n $ piles of stones. It is guaranteed that $ n $ is an even number. The $ i $ -th pile has $ a_i $ stones. Alice and Bob will play a game alternating turns with Alice going first. On a player's turn, they must choose exactly $ \frac{n}{2} $ nonempty piles and independently remove a positive number of stones from each of the chosen piles. They can remove a different number of stones from the piles in a single turn. The first player unable to make a move loses (when there are less than $ \frac{n}{2} $ nonempty piles). Given the starting configuration, determine who will win the game.

输入输出格式

输入格式

The first line contains one integer $ n $ ( $ 2 \leq n \leq 50 $ ) — the number of piles. It is guaranteed that $ n $ is an even number. The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 50 $ ) — the number of stones in the piles.

输出格式

Print a single string "Alice" if Alice wins; otherwise, print "Bob" (without double quotes).

输入输出样例

输入样例 #1

2
8 8

输出样例 #1

Bob

输入样例 #2

4
3 1 4 1

输出样例 #2

Alice

说明

In the first example, each player can only remove stones from one pile ( $ \frac{2}{2}=1 $ ). Alice loses, since Bob can copy whatever Alice does on the other pile, so Alice will run out of moves first. In the second example, Alice can remove $ 2 $ stones from the first pile and $ 3 $ stones from the third pile on her first move to guarantee a win.

题意翻译

Alice 和 Bob 在玩一个游戏，现在有 $n$（$n$ 是偶数）个石堆，每堆石头有 $A_i$ 个，现在由 Alice 先，两人轮流从任意 $\frac n2$ 个石堆中移出至少一个石头，当谁移完之后堆数小于 $\frac n2$，那么 TA 就赢了。 现在要你求出谁会胜利，输出 TA 的名字（见样例）。 注意：两人都很聪明，用最佳策略。