AT_arc218_b [ARC218B] All Minus

There are $ N $ non-negative integers $ A_1,A_2,\dots,A_N $ written on a blackboard. Alice and Bob play a game. Starting with Alice, they alternately perform the following operation, and the player who reduces the number of integers written on the blackboard to $ 0 $ wins. - Let $ m $ be the minimum non-negative integer currently written on the blackboard. - If $ m > 0 $ , choose a positive integer $ x $ between $ 1 $ and $ m $ , inclusive. Replace every integer written on the blackboard with its current value minus $ x $ . - If $ m = 0 $ , erase one or more of the $ 0 $ s written on the blackboard. Determine who wins when both players play optimally to win. $ T $ test cases are given; solve each of them.

The input is given from Standard Input in the following format: > $ T $ $ \mathrm{case}_1 $ $ \mathrm{case}_2 $ $ \vdots $ $ \mathrm{case}_T $ Each test case is given in the following format: > $ N $ $ A_1 $ $ A_2 $ $ \dots $ $ A_N $

Output $ T $ lines. The $ i $ -th line should contain `Alice` if Alice wins in $ \mathrm{case}_i $ , or `Bob` if Bob wins.

### Sample Explanation 1 For the first test case, one possible game progression is as follows: - Initially, $ 2 $ is written on the blackboard. - Alice chooses $ x = 1 $ . Now $ 1 $ is written on the blackboard. - Bob chooses $ x = 1 $ . Now $ 0 $ is written on the blackboard. - Alice chooses and erases one $ 0 $ . Now nothing is written on the blackboard. When both players play optimally to win, Alice wins. For the second test case, one possible game progression is as follows: - Initially, $ 1,1,1 $ are written on the blackboard. - Alice chooses $ x = 1 $ . Now $ 0,0,0 $ are written on the blackboard. - Bob chooses and erases one $ 0 $ . Now $ 0,0 $ are written on the blackboard. - Alice chooses and erases one $ 0 $ . Now $ 0 $ is written on the blackboard. - Bob chooses and erases one $ 0 $ . Now nothing is written on the blackboard. When both players play optimally to win, Bob wins. ### Constraints - $ 1 \le T \le 2 \times 10^5 $ - $ 1 \le N \le 2 \times 10^5 $ - $ 0 \le A_i \le 10^9 $ - The sum of $ N $ over all test cases is at most $ 2 \times 10^5 $ . - All input values are integers.