AT_arc218_b.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.

黑板上写着 $N$ 个非负整数 $A_1,A_2,\dots,A_N$。

爱丽丝（Alice）和鲍勃（Bob）进行一场游戏。游戏由爱丽丝先手，双方轮流执行以下操作；将黑板上的数字个数减至 $0$ 的玩家获胜。

• 设 $m$ 为当前黑板上所有数字中最小的非负整数。
  • 若 $m > 0$，则选择一个介于 $1$ 到 $m$（含端点）之间的正整数 $x$，并将黑板上每个数字均替换为它当前值减去 $x$；
  • 若 $m = 0$，则擦除黑板上一个或多个 $0$。

当双方均以最优策略进行游戏时，判断谁将获胜。

共给出 $T$ 组测试用例，请对每组用例求解。

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:

$N$
$A_1$ $A_2$ $\dots$ $A_N$

输入从标准输入给出，格式如下：

$T$
$\mathrm{case}_1$
$\mathrm{case}_2$
$\vdots$
$\mathrm{case}_T$

每个测试用例的格式如下：

$N$
$A_1$ $A_2$ $\dots$ $A_N$

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

输出 $T$ 行。第 $i$ 行应包含 Alice（若 Alice 在 $\mathrm{case}_i$ 中获胜）或 Bob（若 Bob 在 $\mathrm{case}_i$ 中获胜）。

Sample 1 Explanation:
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.

样例 1 解释：
对于第一个测试用例，一种可能的游戏过程如下：

• 初始时，黑板上写着数字 $2$。
• 爱丽丝选择 $x = 1$，此时黑板上变为 $1$。
• 鲍勃选择 $x = 1$，此时黑板上变为 $0$。
• 爱丽丝选择并擦除一个 $0$，此时黑板上为空。

当双方均以最优策略进行游戏以争取获胜时，爱丽丝获胜。

对于第二个测试用例，一种可能的游戏过程如下：

• 初始时，黑板上写着 $1,1,1$。
• 爱丽丝选择 $x = 1$，此时黑板上变为 $0,0,0$。
• 鲍勃选择并擦除一个 $0$，此时黑板上变为 $0,0$。
• 爱丽丝选择并擦除一个 $0$，此时黑板上变为 $0$。
• 鲍勃选择并擦除一个 $0$，此时黑板上为空。

当双方均以最优策略进行游戏以争取获胜时，鲍勃获胜。

约束条件

• $1 \le T \le 2 \times 10^5$
• $1 \le N \le 2 \times 10^5$
• $0 \le A_i \le 10^9$
• 所有测试用例的 $N$ 之和不超过 $2 \times 10^5$。
• 所有输入值均为整数。