Determine the Winner in the Removal Game

You are given an array of n positive integers. Two players, Alice and Bob, take turns to remove an element from the array. On her turn, Alice always removes the smallest element, while on his turn, Bob always removes the largest element. Alice takes the first turn. The game ends when the array is empty.

The winner is determined by the number of moves made: if Alice makes more moves than Bob, then Alice wins, otherwise Bob wins. In other words, if n is odd (i.e. \(n = 2k+1\)), then Alice wins; if n is even (i.e. \(n = 2k\)), then Bob wins.

Your task is to determine the winner based on the given array.

inputFormat

The first line of the input contains a single integer n representing the number of elements in the array.

The second line contains n positive integers separated by spaces.

outputFormat

Output a single line containing either Alice or Bob, representing the winner of the game.

5
4 5 1 2 3

Alice