B. Removals Game
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Alice got a permutation $$$a_1, a_2, \ldots, a_n$$$ of $$$[1,2,\ldots,n]$$$, and Bob got another permutation $$$b_1, b_2, \ldots, b_n$$$ of $$$[1,2,\ldots,n]$$$. They are going to play a game with these arrays.

In each turn, the following events happen in order:

  • Alice chooses either the first or the last element of her array and removes it from the array;
  • Bob chooses either the first or the last element of his array and removes it from the array.

The game continues for $$$n-1$$$ turns, after which both arrays will have exactly one remaining element: $$$x$$$ in the array $$$a$$$ and $$$y$$$ in the array $$$b$$$.

If $$$x=y$$$, Bob wins; otherwise, Alice wins. Find which player will win if both players play optimally.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1\le t\le10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1\le n\le 3\cdot 10^5$$$).

The next line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1\le a_i\le n$$$, all $$$a_i$$$ are distinct) — the permutation of Alice.

The next line contains $$$n$$$ integers $$$b_1,b_2,\ldots,b_n$$$ ($$$1\le b_i\le n$$$, all $$$b_i$$$ are distinct) — the permutation of Bob.

It is guaranteed that the sum of all $$$n$$$ does not exceed $$$3\cdot 10^5$$$.

Output

For each test case, print a single line with the name of the winner, assuming both players play optimally. If Alice wins, print $$$\texttt{Alice}$$$; otherwise, print $$$\texttt{Bob}$$$.

Example
Input
2
2
1 2
1 2
3
1 2 3
2 3 1
Output
Bob
Alice
Note

In the first test case, Bob can win the game by deleting the same element as Alice did.

In the second test case, Alice can delete $$$3$$$ in the first turn, and then in the second turn, delete the element that is different from the one Bob deleted in the first turn to win the game.