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 3×3 Tic-tac-toe boards with both players marking the board with X. Alice always makes the first move. A game ends when all the boards contain three consecutive 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 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.

You are given an integer t (1 <= t <= 100), the number of games.

For each game, you are given n, (1 <= n <= 10⁴), the number of boards.

For each board, you are given a 3×3 grid. Each grid cell is empty (denoted by a dot), or occupied by a cross (denoted by an X).

For each game, print the winner of that game, in the format “Game #x: winner”. Here, x is the game number.