K. Number Deletion Game
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

Alice and Bob are playing a number deletion game.

At the beginning, there are $$$n$$$ integers $$$a_1,a_2, \ldots ,a_n$$$. Alice and Bob take turns to delete numbers, with Alice going first. Each person can delete the largest number $$$x$$$ (if there are multiple largest numbers, delete one of them), choose a non-negative integer $$$y$$$ that is smaller than $$$x$$$, and add the numbers $$$1,2,\ldots, y$$$. In particular, it is possible to choose $$$y=0$$$, in which case no numbers will be added. This means that when deleting $$$1$$$, no numbers can be added. The person who deletes the last number wins.

Both players use the optimal strategy. Determine who wins, Alice or Bob.

Input

The first line contains a positive integer $$$n$$$ ($$$1\le n\le 10^3$$$), indicating the initial number of integers.

The second line contains $$$n$$$ positive integers $$$a_1,a_2\dots a_n$$$ ($$$1\le a_i\le 10^9$$$).

Output

Output one line. If Alice wins, output Alice. Otherwise, output Bob.

Examples
Input
2
3 3
Output
Bob
Input
2
2 3
Output
Alice