Score: $700$ points

问题陈述

爱丽丝和鲍勃将进行一场游戏。

最初，爱丽丝和鲍勃各自有N张卡片，爱丽丝的第i张卡片上写着整数A_i，鲍勃的第i张卡片上写着整数B_i。

游戏的进行方式如下：

• 准备一块没有任何字迹的黑板。
• 爱丽丝吃掉她的一张卡片，并将吃掉的卡片上的整数写在黑板上。
• 接下来，鲍勃吃掉他的一张卡片，并将吃掉的卡片上的整数写在黑板上。
• 最后，爱丽丝再吃掉她的一张卡片，并将吃掉的卡片上的整数写在黑板上。

如果用写在黑板上的三个整数作为边长可以形成一个（非退化的）三角形，爱丽丝就赢了；否则，鲍勃赢了。

当两位玩家都采取最优行动时，确定谁赢了。

解决给定的T个测试用例中的每一个。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

Alice and Bob will play a game.

Initially, Alice and Bob each have $N$ cards, with the $i$-th card of Alice having the integer $A_i$ written on it, and the $i$-th card of Bob having the integer $B_i$ written on it.

The game proceeds as follows:

• Prepare a blackboard with nothing written on it.
• Alice eats one of her cards and writes the integer from the eaten card on the blackboard.
• Next, Bob eats one of his cards and writes the integer from the eaten card on the blackboard.
• Finally, Alice eats one more of her cards and writes the integer from the eaten card on the blackboard.

If it is possible to form a (non-degenerate) triangle with the side lengths of the three integers written on the blackboard, Alice wins; otherwise, Bob wins.

Determine who wins when both players act optimally.

Solve each of the $T$ given test cases.

Constraints

• $1 \leq T \leq 10^5$
• $2 \leq N \leq 2 \times 10^5$
• $1 \leq A_i, B_i \leq 10^9$
• All input values are integers.
• The sum of $N$ over all test cases in a single input is at most $2 \times 10^5$.

Input

The input is given from Standard Input in the following format:

$T$

$\mathrm{case}_1$

$\vdots$

$\mathrm{case}_T$

Each case is given in the following format:

$N$

$A_1$ $\ldots$ $A_N$

$B_1$ $\ldots$ $B_N$

Output

Print $T$ lines. The $i$-th line $(1 \leq i \leq T)$ should contain Alice if Alice wins for the $i$-th test case, and Bob if Bob wins.

Sample Input 1

3
3
1 2 3
4 5 6
4
6 1 5 10
2 2 4 5
10
3 1 4 1 5 9 2 6 5 3
2 7 1 8 2 8 1 8 2 8

Sample Output 1

Bob
Alice
Alice

In the first test case, for example, the game could proceed as follows:

• Alice eats the card with $2$ written on it and writes $2$ on the blackboard.
• Bob eats the card with $4$ written on it and writes $4$ on the blackboard.
• Alice eats the card with $1$ written on it and writes $1$ on the blackboard.
• The numbers written on the blackboard are $2, 4, 1$. There is no triangle with side lengths $2, 4, 1$, so Bob wins.

For this test case, the above process is not necessarily optimal for the players, but it can be shown that Bob will win if both players act optimally.