Migrated from Lutece 133 Game

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Description

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 $B<A$ and $A+B\pmod{2}=1$ and $A+B\pmod{3}=0$. 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.

Input

The first line contains an integer $T$ ($T\leq 100$) indicating the number of test cases. The first line of each test case contains an integer $n$ ($1\leq n\leq 10000$). 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.

Output

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

Samples

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

Case 1: Alice 
Case 2: Bob

Resources

The 5th Guangting Cup Central China Invitatio