Stone Game III

Problem Description

Alice and Bob are playing a game with stones.

There are $n$ piles of stones ($n$ is even), where the $i$-th pile initially contains $a_i$ stones.

They take turns choosing $\frac{n}{2}$ non-empty piles and removing a positive number (possibly different) of stones from each chosen pile, starting with Alice.

The player who cannot make a move loses.

Assuming both Alice and Bob play optimally, who will win the game?

Input Format

The first line contains an integer $n$ ($2 \le n \le 10^6$, $n$ is even).

The second line contains $n$ positive integers $a_1, \dots, a_n$ ($1 \le a_1, \dots, a_n \le 10^9$).

Output Format

Output Alice or Bob, indicating the final winner.

Sample Input

4
1 1 1 1

Sample Output

Bob