Thanos Nim

1000ms

262144K

Description:

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.

Input:

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.

Output:

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

Sample Input:

2
8 8

Sample Output:

Bob

Sample Input:

4
3 1 4 1

Sample Output:

Alice

Note:

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.

Informação

Provedor Codeforces

Código CF1147C