Theater Ticket Booking Simulation

You are given a theater seating arrangement represented as a grid with rows and columns. All seats are initially available, denoted by the character A. Your task is to implement a ticket booking system that supports three types of operations:

• B r c: Book the seat at row r and column c. If the seat is available (A), mark it as booked (B) and output True; otherwise, output False.
• C r c: Cancel the booking of the seat at row r and column c. If the seat is booked (B), mark it as available (A) and output True; otherwise, output False.
• D: Display the current seating plan. The seating plan should be printed as rows lines of a string with each row represented continuously (i.e. without spaces), where each character is either A (available) or B (booked).

Note that the seat indices are 0-indexed (i.e. the first row/column is numbered 0).

The operations must be processed in the order they appear in the input.

In mathematical notation, let the seat at row i and column j be denoted by \(S_{i,j}\). Initially, \(S_{i,j} = A\) for all valid \(i,j\). A booking operation changes \(S_{r,c}\) from \(A\) to \(B\) if \(S_{r,c} = A\), and a cancellation changes \(S_{r,c}\) from \(B\) to \(A\) if \(S_{r,c} = B\). Invalid indices or operations on seats already in the desired state should produce False as output.

inputFormat

The input is read from stdin and has the following format:

rows cols
Q
op1
op2
...
opQ

Here, rows and cols are the dimensions of the theater, and Q is the number of operations. Each of the next Q lines defines an operation:

• B r c for booking a seat,
• C r c for cancellation, or
• D for displaying the seating arrangement.

Note that r and c are integers.

outputFormat

For each operation, output the following to stdout:

• For a booking (B) or cancellation (C) operation, output True or False on a new line.
• For a display (D) operation, output the current seating arrangement as rows lines. Each line represents a row without spaces.

The outputs for consecutive operations should appear in the order they are processed.

## sample

3 3
5
D
B 1 1
B 1 1
D
C 1 1

AAA
AAA
AAA
True
False
AAA
ABA
AAA
True

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