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The game named "Same" is a single-person game played on a 10 by 15 board. Each square contains a ball colored red (R), green (G), or blue (B). Two balls belong to the same cluster if they have the same color, and one can be reached from another by following balls of the same color in the four directions up, down, left, and right. At each step of the game, the player chooses a ball whose cluster has at least two balls and removes all balls in the cluster from the board. Then, the board is "compressed" in two steps:
For example, choosing the ball at the bottom left corner in the sub-board causes:
The objective of the game is to remove all balls from the board, and the game is over when all balls are removed or when all clusters have only one ball.
The scoring of each game is as follows. The player starts with a score of 0. When a cluster of size m is removed, the player's score increases by (m-2)^2. A bonus of 1000 is given if all balls are removed at the end of the game.
You suspect that a good strategy may be to choose the ball that gives the largest possible cluster at each step, and you want to test this strategy by writing a program to simulate games played using this strategy. If there are two or more balls to choose from, the program chooses the leftmost ball giving the largest cluster. If there is still a tie, choose the bottommost ball of these leftmost balls.
You will be given a number of games in the input. The first line of input contains a positive integer giving the number of games to follow. The initial arrangement of the balls of each game is given one row at a time, from top to bottom. Each row contains 15 characters, each of which is one of "R", "G", or "B", specifying the colors of the balls in the row from left to right. A blank line precedes each game.
For each game, print the game number, followed by a new line, followed by information about each move, followed by the final score. Each move should be printed in the format:
Move x at (r,c): removed b balls of color C, got s points.
The final score should be reported as follows:
Final score: s, with b balls remaining.
Note: use the plural form of "ball" and "point" even if it is 1.
3 RGGBBGGRBRRGGBG RBGRBGRBGRBGRBG RRRRGBBBRGGRBBB GGRGBGGBRRGGGBG GBGGRRRRRBGGRRR BBBBBBBBBBBBBBB BBBBBBBBBBBBBBB RRRRRRRRRRRRRRR RRRRRRGGGGRRRRR GGGGGGGGGGGGGGG RRRRRRRRRRRRRRR RRRRRRRRRRRRRRR GGGGGGGGGGGGGGG GGGGGGGGGGGGGGG BBBBBBBBBBBBBBB BBBBBBBBBBBBBBB RRRRRRRRRRRRRRR RRRRRRRRRRRRRRR GGGGGGGGGGGGGGG GGGGGGGGGGGGGGG RBGRBGRBGRBGRBG BGRBGRBGRBGRBGR GRBGRBGRBGRBGRB RBGRBGRBGRBGRBG BGRBGRBGRBGRBGR GRBGRBGRBGRBGRB RBGRBGRBGRBGRBG BGRBGRBGRBGRBGR GRBGRBGRBGRBGRB RBGRBGRBGRBGRBG
Game 1: Move 1 at (4,1): removed 32 balls of color B, got 900 points. Move 2 at (2,1): removed 39 balls of color R, got 1369 points. Move 3 at (1,1): removed 37 balls of color G, got 1225 points. Move 4 at (3,4): removed 11 balls of color B, got 81 points. Move 5 at (1,1): removed 8 balls of color R, got 36 points. Move 6 at (2,1): removed 6 balls of color G, got 16 points. Move 7 at (1,6): removed 6 balls of color B, got 16 points. Move 8 at (1,2): removed 5 balls of color R, got 9 points. Move 9 at (1,2): removed 5 balls of color G, got 9 points. Final score: 3661, with 1 balls remaining. Game 2: Move 1 at (1,1): removed 30 balls of color G, got 784 points. Move 2 at (1,1): removed 30 balls of color R, got 784 points. Move 3 at (1,1): removed 30 balls of color B, got 784 points. Move 4 at (1,1): removed 30 balls of color G, got 784 points. Move 5 at (1,1): removed 30 balls of color R, got 784 points. Final score: 4920, with 0 balls remaining. Game 3: Final score: 0, with 150 balls remaining.