# Grundy Number

medium

Two players Alice and Bob are playing a game. They have a pile with n coins in it. They can pick only allowed numbers of coins at a time given in an array picks. Alice goes first and they take alternate turns. The player who picks the last coin is the winner. Can you find out the winner.

## Constraints

1<= n <= 1000

## Format

### Input

The first line contains integer n(no. of coins in the pile). Second line contains size of picks array say l picks[0] picks[1] .... picks[l-1]

### Output

Print the winner (ALICE or BOB).

## Example

Sample Input

8
3
5
1
4

### Sample Output

BOB