21976_Game

Bob and Alice are playing a new game. There are n boxes which have been numbered from 1 to n. Each box is either empty or contains several cards. Bob and Alice move the cards in turn. In each turn the corresponding player should choose a non-empty box A and choose another box B that B<A && (A+B)%2=1 && (A+B)%3=0. Then, take an arbitrary number (but not zero) of cards from box A to box B. The last one who can do a legal move wins. Alice is the first player. Please predict who will win the game.

The first line contains an integer T ( T ≤ 100 ) indicating the number of test cases. The first line of each test case contains an integer n ( 1 ≤ n ≤ 10000 ). The second line has n integers which will not be bigger than 100. The i-th integer indicates the number of cards in the i-th box.

For each test case, print the case number and the winner's name in a single line. Follow the format of the sample output.

2
2
1 2
7
1 3 3 2 2 1 2

Case 1: Alice
Case 2: Bob