Alice's Game

Alice and Bob have got a lot of chocolates. All the chocolates are rectangles of different shapes as X_i * Y_i.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 X_i * Y_i, can only split into A * Y_i, and B * Y_i where A + B = X_i and A, B > 0. And for Bob, a chocolate X_i * Y_i, can only split into X_i * A, and X_i * B where A + B = Y_i 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.

The input contains multiple test cases. The first line of input contains a single integer denoting the number of test cases.
For each test case, the first line contains an integer N, the number of pieces of chocolates. (1 <= N <= 100)
For the next N lines, each line contains two integers X_i and Y_i, denoting the chocolate sized X_i * Y_i. (1 <= X_i, Y_i <= 1000000000)

For each test cases, output "Alice" when Alice will win, and "Bob" otherwise. See sample test cases for further details.

4
1
1 1
1
2 1
2
2 2
2 1
1
3 2

Case 1: Bob
Case 2: Alice
Case 3: Alice
Case 4: Bob

HyperHexagon

HyperHexagon's Summer Gift (Original tasks)