A12516. 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.

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.

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

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.