Alice and Bob have got a lot of chocolates. All the chocolates are rectangles of different shapes as Xi * Yi.They decide to play an interesting game on the chocolates. They take turns choose a chocolate and split it into two pieces. The one who can not take operations lose. Due to the game is too simple, the additional rules apply. Alice is only allowed to split the chocolate vertically, and Bob is only allowed to split the chocolate horizontally.
Specifically, for Alice, a chocolate Xi * Yi, can only split into A * Yi, and B * Yi where A + B = Xi and A, B > 0. And for Bob, a chocolate Xi * Yi, can only split into Xi * A, and Xi * B where A + B = Yi and A, B > 0.
Alice and Bob are clever enough to take the optimal operation, if Alice plays first, your are to decide who will win.
For each test cases, output "Alice" when Alice will win, and "Bob" otherwise. See sample test cases for further details.
Case 1: Bob
Case 2: Alice
Case 3: Alice
Case 4: Bob
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