Alice and Bob are playing a game of Tic-tac-toe, to be precise a variant of tic-tac-toe called Notakto. In a game of Notakto, there will always be a winner.
Notakto is played across one or several $3 \times 3$ Tic-tac-toe boards with both players marking the board with $\texttt{X}$. Alice always makes the first move. A game ends when all the boards contain three consecutive $\texttt{X}$ in any direction (horizontal/vertical/diagonal), at which point the player to have made the last move loses the game. If there is 3 consecutive $\texttt{X}$ in a board already, then no more moves can be made on that particular board.
Given a configuration of the game, you have to find out the winner.
Input
You are given an integer $t$ ($1 \le t \le 100$), the number of games.
For each game, you are given $n$ ($1 \le n \le 10^4$), the number of boards.
For each board, you are given a $3 \times 3$ grid. Each grid cell is empty (denoted by a dot), or occupied by a cross (denoted by an $\texttt{X}$).
Output
For each game, print the winner of that game, in the format $\texttt{Game \#c: winner}$. Here, $c$ is the game number.
Sample
| Input | Output |
|---|---|
4 1 ... ... ..X 1 XX. X.X .XX 2 XX. X.X .XX XX. X.X .XX 3 XX. X.X .XX XX. X.X .XX XX. X.X .XX | Game #1: Alice Game #2: Bob Game #3: Alice Game #4: Bob |
