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1253 - Misere Nim
 PDF (English) Statistics Forum
 Time Limit: 1 second(s) Memory Limit: 32 MB

Alice and Bob are playing game of Misère Nim. Misère Nim is a game playing on k piles of stones, each pile containing one or more stones. The players alternate turns and in each turn a player can select one of the piles and can remove as many stones from that pile unless the pile is empty. In each turn a player must remove at least one stone from any pile. Alice starts first. The player who removes the last stone loses the game.

# Input

Input starts with an integer T (≤ 200), denoting the number of test cases.

Each case starts with a line containing an integer k (1 ≤ k ≤ 100). The next line contains k space separated integers denoting the number of stones in each pile. The number of stones in a pile lies in the range [1, 109].

# Output

For each case, print the case number and 'Alice' if Alice wins otherwise print 'Bob'.

# Output for Sample Input

3

4

2 3 4 5

5

1 1 2 4 10

1

1

Case 1: Bob

Case 2: Alice

Case 3: Bob

Problem Setter: Jane Alam Jan
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