Description

Alice and Bob are playing Toe-Tac-Tics on $n$ boards with $3$ rows and $3$ columns. Some cells on the boards are initially empty, while the others already contain some marks. Alice moves first, and they take turns to select a board and put their marks into an empty cell on that board. Alice's mark is x and Bob's mark is o.

Each player must make sure that no three same marks are in any row, column, or diagonal on any board after his/her move. The player who cannot make a valid move on their turn loses, and the other player wins.

Given the initial state of the $n$ boards, you need to determine who wins, assuming both players play optimally for victory.

Input Format

There are multiple test cases. The first line of the input contains an integer $T$ indicating the number of test cases. For each test case:

The first line contains an integer $n$ ($1 \le n \le 10^5$), indicating the number of boards in the game.

Then $n$ boards of size $3 \times 3$ follow. For each board:

• There will first be an empty line if it is not the first board.
• For the following three lines, the $i$-th line contains a string $s_{i,1}s_{i,2}s_{i,3}$ of length $3$ consisting of characters x, o, and ., describing a board of size $3 \times 3$. Let $(i, j)$ be the cell on the $i$-th row and the $j$-th column. If $s_{i, j} =$ x then cell $(i, j)$ contains a mark x; if $s_{i, j} =$ o then cell $(i, j)$ contains a mark o; if $s_{i, j} =$ . then cell $(i, j)$ is empty.

It is guaranteed that no three same marks are in any row, column, or diagonal on any board. It is also guaranteed that the sum of $n$ for all test cases does not exceed $10^5$.

Output Format

For each test case, output $\texttt{Alice}$ if Alice wins the game, or $\texttt{Bob}$ if Bob wins the game.

4
1
...
...
...
1
...
oo.
oo.
2
...
oo.
oo.

...
xx.
xx.
2
..x
xo.
...

xo.
o..
.x.

Alice
Alice
Bob
Bob