Catch The Mouse

Problem

A fierce confrontation is taking place between a group of mice (R) and Nadori's team (C, N) on a $7 \times 11$ kitchen floor.

The board consists of $7$ rows and $11$ columns. Rows are numbered $1$ to $7$ from top to bottom, and columns are numbered $1$ to $11$ from left to right. A cell at the $x$-th row and $y$-th column is denoted as $(x, y)$.

Delicious cheese is placed at the very bottom of the board. The mice are descending the kitchen floor to eat the cheese, while the cats and Nadori are trying to stop them.

Each cell can be in one of four states: empty ., mouse R, cat C, or Nadori N. Initially, the pieces are placed as follows:

The battle begins with the mice, and Nadori and the mice take turns.

On the mice's turn, the following action is performed:

1. Select a cell $(x_1, y_1)$ containing a mouse R and move it to $(x_1 + 1, y_1)$.

• The destination $(x_1 + 1, y_1)$ must be an empty cell ..
• The starting cell $(x_1, y_1)$ becomes an empty cell ..
• The destination cell $(x_1 + 1, y_1)$ becomes a cell containing a mouse R.

In essence, the mice descend one cell at a time, rushing toward the cheese.

On Nadori's turn, one of the following actions is performed:

1. Select a cell $(x_1, y_1)$ containing a cat C and move it to $(x_2, y_2)$. $(2 \le x_2 \le 6; 1 \le y_2 \le 11)$

• A cat can choose one of the $8$ directions (horizontal, vertical, or diagonal) and move along a straight path as long as there are no other pieces in the way. (i.e., the cat moves like a Queen in chess)
• The destination $(x_2, y_2)$ must be an empty cell ..
• The starting cell $(x_1, y_1)$ becomes an empty cell ..
• The destination cell $(x_2, y_2)$ becomes a cell containing a cat C.

2. Select a cell $(x_1, y_1)$ containing Nadori N and move it to $(x_2, y_2)$. $(2 \le x_2 \le 6; 1 \le y_2 \le 11)$

• $\max(\lvert x_2 - x_1 \rvert, \lvert y_2 - y_1 \rvert) = 1$ (i.e., Nadori moves like a King in chess)
• The destination $(x_2, y_2)$ must be either an empty cell . or a cell containing a mouse R.
• The starting cell $(x_1, y_1)$ becomes an empty cell ..
• The destination cell $(x_2, y_2)$ becomes a cell containing Nadori N.

The battle ends when any of the following conditions are met:

• If any mouse reaches the $7$th row, the mouse swarm wins and obtains the cheese.
• If all mice completely disappear from the board, Nadori's team wins.
• If there are no legal moves available for any mouse on the mice's turn, Nadori's team wins.

Please design an AI to become the ultimate winner of the kitchen floor!

Input

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

• x1, y1, x2, y2 are integers.
• my_time, opp_time, and time are integers representing time 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 or an illegal move during a TURN command 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 TURN command given to each agent, my_time is $10\,000$ ms.
• Memory: 1024MB
• Judging Environment: HELP > Judging Environment