Problem Description

There are $ N $ piles of stones, each pile numbered from $ 1 $ to $ N $. The number of stones in pile $ i $ is $ a_i $. Additionally, $ N $ numbers $ b_i $ are given. Alice and Bob play a game. Alice starts and they alternate turns, with the player who cannot make a move losing the game.

• Choose a pile of stones $ i $. Choose a non-negative integer $ k $ and remove $ b_i^k $ stones from pile $ i $. The number of stones after removal must not be negative.

When both players play optimally, who will win?

Input Format

The input is given from the standard input in the following format:

$ N $ $ a_1 $ $ b_1 $ $ a_2 $ $ b_2 $ $\vdots$ $ a_N $ $ b_N $

Output Format

Output Alice if Alice wins, or Bob if Bob wins, in one line.

Sample Input and Output

Sample Input #1

2
10 3
7 4

Sample Output #1

Bob

Sample Input #2

16
903 5
246 38
884 12
752 10
200 17
483 6
828 27
473 21
983 35
953 36
363 35
101 3
34 23
199 8
134 2
932 28

Sample Output #2

Alice

Sample Input #3

16
35 37
852 17
789 37
848 40
351 27
59 32
271 11
395 20
610 3
631 33
543 14
256 28
48 8
277 24
748 38
109 40

Sample Output #3

Bob

Notes/Hints

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq a_i, b_i \leq 10^9$
• All inputs are integers

见题面 Input 部分

见题面 Output 部分