Number Game
hard
Alice and Bob play a game. They start with a number n and play in turns. In each turn, a player can make any one of the following moves: 1. Divide n by any of its odd divisors greater than 1. 2. Subtract 1 from n if n is greater than 1. Divisors of a number include the number itself. The player who is unable to make a move loses the game. Alice moves first. Determine the winner of the game if both of them play optimally.
Constraints
1<= t <= 100 1<= n <= 10^9
Format
Input
The first line contains integer t, no. of test cases. Each of next t lines contain a number n.
Output
Print the winner ALICE or BOB.
Example
Sample Input
7
1
2
3
4
5
6
12
Sample Output
BOB
ALICE
ALICE
BOB
ALICE
BOB
ALICE
