402597: GYM100814 L Candy Jars

Alice and Bob love to play the following game, they have N jars and the rules are as follows:

• Each jar has a strictly positive number of candies.
• Alice plays first and the two players alternate.
• In his/her turn, the player selects any jar X, throws away all candies in all the other jars and redistributes the candies in X among all jars in anyway he/she wishes, as long as in the end there is at least one candy in each jar (including X).
• The player who cannot make a move in his/her turn loses the game.

Assuming both players play optimally, you are asked the following question who wins the game? Playing optimally means that both players will have insight into all possible next moves and will play in such a way to maximize their chance of winning without making a mistake. However, if all moves lead to the other player winning, then this player still has to play, and any move would be equivalent.

The first line contains the number of test cases T. Each of the next T lines contains an integer (2 ≤ N ≤ 1, 000) the number of jars, and N integers (1 ≤ a_i ≤ 1000) where a_i is the number of candies in jar i.

Output T lines, one for each test case, containing "Alice" if Alice wins the game, or "Bob" otherwise.

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

Bob
Alice
Bob