CF1147C.Thanos Nim

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.

爱丽丝和鲍勃正在玩一个包含 $n$ 堆石子的游戏。已知 $n$ 为偶数。第 $i$ 堆石子有 $a_i$ 颗。

爱丽丝和鲍勃将轮流进行游戏，爱丽丝先手。

在一名玩家的回合中，他必须恰好选择 $\frac{n}{2}$ 个非空石子堆，并且对每个所选堆独立地移除正整数颗石子（即至少移除 1 颗）。同一回合中，不同堆移除的石子数量可以不同。当某位玩家无法进行操作时（即当前非空堆的数量少于 $\frac{n}{2}$），该玩家判负。

给定初始石子堆配置，判断谁将获胜。

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.

第一行包含一个整数 $n$（$2 \leq n \leq 50$）—— 堆的数量。保证 $n$ 为偶数。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \leq a_i \leq 50$）—— 每堆中的石子数量。

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

如果 Alice 获胜，则输出单个字符串 “Alice”；否则，输出 “Bob”（不带双引号）。

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.

在第一个例子中，每位玩家每次只能从一堆石子中取走石子（$\frac{2}{2}=1$）。爱丽丝会输，因为鲍勃总能在另一堆中模仿爱丽丝的操作，因此爱丽丝将首先无步可走。

在第二个例子中，爱丽丝在第一步可以从第一堆中取走 $2$ 颗石子、从第三堆中取走 $3$ 颗石子，从而确保获胜。