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A Modified Game Of Nim

Given an array of integers, two players Alice and Bob are playing a game where Alice can remove any element from the array that are multiples of 3. Similarly, Bob can remove multiples of 5. The player who can't remove any element loses the game. The task is to find the winner of the game if Alice starts first and both play optimally.

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A Modified Game Of Nim

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Given an array of integers, two players Alice and Bob are playing a game where Alice can remove any element from the array that are multiples of 3. Similarly, Bob can remove multiples of 5. The player who can't remove any element loses the game. The task is to find the winner of the game if Alice starts first and both play optimally.

Constraints

1<= n <= 10^5 1<= arr[i] <= 10^8

Format

Input

The first line contains integer n, no. of integers. second line contains n integers arr[1],arr[2]...arr[n].

Output

Print the winner (ALICE or BOB).

Example

Sample Input

5 15 6 9 10 20

Sample Output

ALICE

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