Betris (Large)

Problem

Betris is a strategic game where players compete in betting to acquire polyomino blocks on a $5 \times 5$ board and efficiently place the acquired blocks to fill the board.

1. Board and Components

Each player starts the game with one empty board and $24$ chips to be used for betting.

The board consists of $7$ rows and $7$ columns. Rows are numbered $1$ to $7$ from top to bottom, and columns are numbered $1$ to $7$ from left to right. A cell at the $x$-th row and $y$-th column is denoted as $(x, y)$. Chips can be used during the betting phase later in the game.

$21$ types of polyomino blocks are used in the game. The shapes and names of each block are shown above.

2. Game Progression

The game proceeds for a total of $12$ rounds. Each round is divided into a Betting Phase and a Placement Phase.

Phase 1: Betting Phase

• The judge selects one of the $21$ types of blocks with equal probability and designates it as $A$. Then, it selects one of the remaining $20$ types of blocks with equal probability and designates it as $B$.
• Each player submits their choice of block (either $A$ or $B$) and the number of chips they wish to bet to the judge. The number of chips bet must be between $0$ and $5$ inclusive, and cannot exceed the number of chips the player currently possesses.
• Once both players have decided on their block and chip amount, the judge determines the success of the bet according to the following rules:
  • If the two players chose different blocks, both players succeed in their bets.
  • If the two players chose the same block and the number of chips bet is different, the player who bet more chips succeeds.
  • If the two players chose the same block and the number of chips bet is the same, the judge randomly selects one player to succeed.
• The player who succeeds in the bet acquires their chosen block and pays the number of chips they bet.
• The player who fails in the bet acquires the block they did not choose and does not pay any chips.

Phase 2: Placement Phase

• Each player can rotate their acquired block clockwise by $90^\circ$ as many times as they want.
• Each player can flip their acquired block horizontally/vertically as many times as they want.
• Afterward, the player can either place the block on the board or choose to PASS.
• If a player chooses to place the block, it must be placed within the board boundaries and on cells that are not already occupied by other blocks.
• If a player decides that it is disadvantageous to place a block even if there is space, they may select PASS.

3. Scoring

After all rounds are completed, each player's score is calculated as follows:

• $1$ point is awarded for each cell occupied by a block on the board.
• $1$ point is awarded for each cell within the largest square that can be formed using only the filled cells on the board.
• $0.5$ points are awarded for each remaining chip.

For example, in the following case, the player's score is $42 + 25 + 3 \times 0.5 = 68.5$ points.

The final winner is the player with the higher score. If the scores are equal, the game ends in a draw.

Input

The judge program communicates with the player using single-line text commands as follows:

• The READY command is given once before the $1$st round starts, and the FINISH command is given once after the $12$th round ends.
• The PHASE1, PHASE2, and OPP commands are given once per round in order.

For the PHASE1 command:

• Input A, B will be one of: I1, I2, I3, L3, I4, L4, S4, T4, O4, I5, L5, F5, N5, P5, T5, U5, V5, W5, X5, Y5, Z5.
• Input A and B are always different.
• Output C must be either A or B.
• Output x must be an integer between $0$ and $5$ inclusive and cannot exceed your current chip count.

For the PHASE2 command:

• Input C is the block you acquired (one of the A or B from the previous PHASE1).
• Output k x1 y1 ... xk yk must be $2k + 1$ space-separated integers.
• If $k > 0$, $k$ must equal the number of cells in block C.
• If $k > 0$, the following $2k$ integers represent the coordinates $(x_1, y_1), \cdots, (x_k, y_k)$ of the cells where the block is placed, which must be valid according to the rules.

General I/O Rules:

• my_chip, opp_chip, my_time, opp_time, and time are all integers.
• All times are in milliseconds.
• After every output, you must print a newline character and flush the buffer.
• Failure to output within the time limit results in a Time Limit Exceeded (TLE) verdict.
• Outputting an invalid format results in a Runtime Error (RE) verdict.

Example

Sample Code

• C20 : sample.c
• CPP20 : sample.cpp
• PYTHON3, PYPY3 : sample.py

Limit

• Time: For the first PHASE1 command given to each player, my_time is $10\,000$ ms.
• Memory: 1024MB
• Judging Environment: HELP > Judging Environment