#P1147C. Thanos Nim
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ID: 4709
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Thanos Nim
No submission language available for this problem.
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.
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).
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).
Samples
2
8 8
Bob
4
3 1 4 1
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.