**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Medium)
time_limit_ms: 1000
memory_limit_mb: 256
Description: This afternoon, you decided to enjoy the first days of Spring by taking a walk outside. As you come near the Quidditch field, you hear screams. Once again, there is a conflict about the score: the two teams are convinced that they won the game! To prevent this problem from happening one more time, you decide to get involved in the refereeing of the matches.

Now, you will stay in the stadium to watch the game and count the score. At the end of the game, you will decide the winner.

Today, two teams are competing: the red Gryffindor (R) and the blue Ravenclaw (B) team. Each team is composed of $$$P$$$ players ($$$1 \leq P \leq 10$$$).

The field is a rectangle of $$$N$$$ lines and $$$M$$$ columns ($$$3 \leq N, M \leq 99$$$, $$$N$$$ and $$$M$$$ are odd). All the positions are integers, and several entities are allowed to be at the same position in the field. At the beginning of the game, the field contains goals for the two teams (each team can own between one and five goals), the players, and exactly one Quaffle. In this version of the problem, one Bludger can be present. An other type of ball will be available in the harder version of the problem.

A game is composed of $$$T$$$ steps ($$$0 \leq T \leq 10000$$$). At each step, one entity on the field (a player or a ball) performs one action. All entities can move. A player can also catch a ball or throw the Quaffle that it is carrying. To catch a ball, a player must be located on the same cell as it. The Quaffle does not perform any action while it is being carried; it only follows the movements of the player. If a player carrying the Quaffle decides to throw it, the Quaffle is simply put at the current position of the player. If a player is on the same cell as a Bludger (either after a movement from the player or the Bludger), the player is eliminated. If the player is eliminated while it is carrying the Quaffle, the Quaffle remains on the cell containing both the player and the Bludger after the move. It is guaranteed that this never occurs while the player is in a cell containing a goal.

To win a point, a player must leave the Quaffle at a goal of the other team. When it does, the team of the player wins one point, and the Quaffle instantly moves to the middle of the field (the cell at the $$$(M+1)/2$$$-th column of the $$$(N+1)/2$$$-th line of the field, starting from 1). There is no goal in the middle of the field. If a player puts the ball in its own goal, the other team wins the point.

Input: On the first line, the integers $$$N$$$ and $$$M$$$.

The description of the field follows: $$$N$$$ lines of $$$M$$$ pairs of characters separated by spaces. Each pair of characters represents a position on the field. It can be either:

- .. to represent an empty cell
- R0, ..., R9, B0, ..., B9 to represent a player. The first character is the team of the player, and the second is the number of the player in the team. Each pair of characters is unique, but it is not guaranteed that all the pairs appear in the grid.
- RG or BG to represent a goal. The blue team tries to put the ball in a red goal (RG) while the red team tries to put the ball in a blue goal (BG).
- .Q to represent the Quaffle, which is the ball that the players use to score goals.
- .B to represent a Bludger.

The next line contains $$$T$$$, the number of steps that compose the game. $$$T$$$ lines follow, each describing one action. It contains several pieces of information separated by a space. First, a pair of characters representing the entity that must perform the action. Second, the description of the action:

- U, D, L, R indicate that the entity moves on the grid. It can move to the top of the grid (U), to the bottom (D), to the left (L), or to the right (R). Each entity moves by only one cell at a time.
- C indicates that the player catches the ball (only a player can catch a ball). Then, there is a space followed by a pair of characters: the description of the ball caught by the player. This information is needed since several balls can be in the same cell.
- T indicates that the player throws the Quaffle that it is carrying.

All the actions performed by the entities are guaranteed to be valid: the players stay in the field, don't catch a ball if they are not in the same cell, don't release the Quaffle if they are not carrying it, ...

Output: You must output the description of the main events of the game, one event per line. More precisely:

- Each time a team scores, you must print t RED GOAL or t BLUE GOAL, depending on the team who scored, where t is the current time (the position of the action in the list of actions, starting from 0). In the case where a player scores in the wrong goal (a red player scores in the red goal, or a blue player scores in the blue goal), you must print the name of the team who wins one point, that is, the other team.
- Each time a player is eliminated, you must print t p ELIMINATED, where t is the current time and p is the player who is eliminated. The format to print the player is the same as in the input.

The events must be printed in ascending order of t. If several players are eliminated at the same time, the events must be written in alphabetical order: B0, ..., B9, R0, ... R9.

At the end of the game, you must print the final score as: FINAL SCORE: r b, where r is the score of the red team and b is the score of the blue team.

Examples:
input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
12
R0 D
R0 C .Q
R0 R
R0 T
R0 D
B0 R
B0 U
B0 C .Q
B0 L
B0 L
B0 L
B0 T
output:
11 BLUE GOAL
FINAL SCORE: 0 1

input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
5
R0 D
R0 C .Q
R0 L
R0 L
R0 T
output:
4 BLUE GOAL
FINAL SCORE: 0 1

input:
5 5
.. .. .. .. ..
.. .. .. .. ..
RG R0 .Q B0 BG
.. .. .. .. ..
.. .. .B .. ..
5
.B L
.B U
.B U
B0 L
B0 L
output:
2 R0 ELIMINATED
4 B0 ELIMINATED
FINAL SCORE: 0 0

Note: In the first example, the red player takes the Quaffle, move it and throw it. The blue player catches the ball, goes to the red goal and scores.

In the second example, the red player takes the ball and scores in the goal of their own team: the blue team wins a point.

In the third example, the Bludger goes at the position of R0: R0 is eliminated. Then, B0 moves to the position of the Bludger: B0 is eliminated too.

You can find one more example in the easy version of the problem

Buggy Code:
def main():
    import sys
    input = sys.stdin.read
    data = input().split('\n')

    MOD = 10**9 + 7

    # Read dimensions of the field
    N, M = map(int, data[0].split())

    # Read the field configuration
    field = [data[i + 1].split() for i in range(N)]

    # Read number of steps
    T = int(data[N + 1])

    # Read each action
    actions = [data[N + 2 + i] for i in range(T)]

    # Initialize positions and states
    players = {}
    goals = {'RG': [], 'BG': []}
    quaffle = None
    bludger = None

    for i in range(N):
        for j in range(M):
            cell = field[i][j]
            if cell in ('RG', 'BG'):
                goals[cell].append((i, j))
            elif cell == '.Q':
                quaffle = (i, j)
            elif cell == '.B':
                bludger = (i, j)
            elif cell != '..':
                players[cell] = {'pos': (i, j), 'has_quaffle': False}

    # To track scores
    red_score, blue_score = 0, 0
    events = []

    # Process each action
    for t in range(T):
        action = actions[t].split()
        entity = action[0]
        command = action[1]

        if entity in players:
            x, y = players[entity]['pos']
            if command == 'U':
                x -= 1
            elif command == 'D':
                x += 1
            elif command == 'L':
                y -= 1
            elif command == 'R':
                y += 1
            elif command == 'C':
                # Catching the Quaffle
                if (x, y) == quaffle:
                    players[entity]['has_quaffle'] = True
            elif command == 'T':
                # Throwing the Quaffle
                if players[entity]['has_quaffle']:
                    quaffle = (x, y)
                    players[entity]['has_quaffle'] = False
                    # Check if it's a goal
                    for goal_type in goals:
                        if quaffle in goals[goal_type]:
                            if (goal_type == 'RG' and entity[0] == 'B') or (goal_type == 'BG' and entity[0] == 'R'):
                                if entity[0] == 'R':
                                    red_score += 1
                                    events.append(f"{t} RED GOAL")
                                else:
                                    blue_score += 1
                                    events.append(f"{t} BLUE GOAL")
                            quaffle = (N // 2, M // 2)  # Reset to middle
                            break

            # Update position after move
            if command in 'UDLR':
                players[entity]['pos'] = (x, y)
                # Check for Bludger collision
                if (x, y) == bludger:
                    events.append(f"{t} {entity} ELIMINATED")
                    del players[entity]  # Player is eliminated

    # Output all events
    for event in sorted(events):
        print(event)

    # Output final score
    print(f"FINAL SCORE: {red_score} {blue_score}")

if __name__ == "__main__":
    main()

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3 3
.. .. R0
RG .. ..
.. .Q B0
6
R0 D
R0 C .Q
R0 L
R0 T
B0 D
B0 T
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Medium)
time_limit_ms: 1000
memory_limit_mb: 256
Description: This afternoon, you decided to enjoy the first days of Spring by taking a walk outside. As you come near the Quidditch field, you hear screams. Once again, there is a conflict about the score: the two teams are convinced that they won the game! To prevent this problem from happening one more time, you decide to get involved in the refereeing of the matches.

Now, you will stay in the stadium to watch the game and count the score. At the end of the game, you will decide the winner.

Today, two teams are competing: the red Gryffindor (R) and the blue Ravenclaw (B) team. Each team is composed of $$$P$$$ players ($$$1 \leq P \leq 10$$$).

The field is a rectangle of $$$N$$$ lines and $$$M$$$ columns ($$$3 \leq N, M \leq 99$$$, $$$N$$$ and $$$M$$$ are odd). All the positions are integers, and several entities are allowed to be at the same position in the field. At the beginning of the game, the field contains goals for the two teams (each team can own between one and five goals), the players, and exactly one Quaffle. In this version of the problem, one Bludger can be present. An other type of ball will be available in the harder version of the problem.

A game is composed of $$$T$$$ steps ($$$0 \leq T \leq 10000$$$). At each step, one entity on the field (a player or a ball) performs one action. All entities can move. A player can also catch a ball or throw the Quaffle that it is carrying. To catch a ball, a player must be located on the same cell as it. The Quaffle does not perform any action while it is being carried; it only follows the movements of the player. If a player carrying the Quaffle decides to throw it, the Quaffle is simply put at the current position of the player. If a player is on the same cell as a Bludger (either after a movement from the player or the Bludger), the player is eliminated. If the player is eliminated while it is carrying the Quaffle, the Quaffle remains on the cell containing both the player and the Bludger after the move. It is guaranteed that this never occurs while the player is in a cell containing a goal.

To win a point, a player must leave the Quaffle at a goal of the other team. When it does, the team of the player wins one point, and the Quaffle instantly moves to the middle of the field (the cell at the $$$(M+1)/2$$$-th column of the $$$(N+1)/2$$$-th line of the field, starting from 1). There is no goal in the middle of the field. If a player puts the ball in its own goal, the other team wins the point.

Input: On the first line, the integers $$$N$$$ and $$$M$$$.

The description of the field follows: $$$N$$$ lines of $$$M$$$ pairs of characters separated by spaces. Each pair of characters represents a position on the field. It can be either:

- .. to represent an empty cell
- R0, ..., R9, B0, ..., B9 to represent a player. The first character is the team of the player, and the second is the number of the player in the team. Each pair of characters is unique, but it is not guaranteed that all the pairs appear in the grid.
- RG or BG to represent a goal. The blue team tries to put the ball in a red goal (RG) while the red team tries to put the ball in a blue goal (BG).
- .Q to represent the Quaffle, which is the ball that the players use to score goals.
- .B to represent a Bludger.

The next line contains $$$T$$$, the number of steps that compose the game. $$$T$$$ lines follow, each describing one action. It contains several pieces of information separated by a space. First, a pair of characters representing the entity that must perform the action. Second, the description of the action:

- U, D, L, R indicate that the entity moves on the grid. It can move to the top of the grid (U), to the bottom (D), to the left (L), or to the right (R). Each entity moves by only one cell at a time.
- C indicates that the player catches the ball (only a player can catch a ball). Then, there is a space followed by a pair of characters: the description of the ball caught by the player. This information is needed since several balls can be in the same cell.
- T indicates that the player throws the Quaffle that it is carrying.

All the actions performed by the entities are guaranteed to be valid: the players stay in the field, don't catch a ball if they are not in the same cell, don't release the Quaffle if they are not carrying it, ...

Output: You must output the description of the main events of the game, one event per line. More precisely:

- Each time a team scores, you must print t RED GOAL or t BLUE GOAL, depending on the team who scored, where t is the current time (the position of the action in the list of actions, starting from 0). In the case where a player scores in the wrong goal (a red player scores in the red goal, or a blue player scores in the blue goal), you must print the name of the team who wins one point, that is, the other team.
- Each time a player is eliminated, you must print t p ELIMINATED, where t is the current time and p is the player who is eliminated. The format to print the player is the same as in the input.

The events must be printed in ascending order of t. If several players are eliminated at the same time, the events must be written in alphabetical order: B0, ..., B9, R0, ... R9.

At the end of the game, you must print the final score as: FINAL SCORE: r b, where r is the score of the red team and b is the score of the blue team.

Examples:
input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
12
R0 D
R0 C .Q
R0 R
R0 T
R0 D
B0 R
B0 U
B0 C .Q
B0 L
B0 L
B0 L
B0 T
output:
11 BLUE GOAL
FINAL SCORE: 0 1

input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
5
R0 D
R0 C .Q
R0 L
R0 L
R0 T
output:
4 BLUE GOAL
FINAL SCORE: 0 1

input:
5 5
.. .. .. .. ..
.. .. .. .. ..
RG R0 .Q B0 BG
.. .. .. .. ..
.. .. .B .. ..
5
.B L
.B U
.B U
B0 L
B0 L
output:
2 R0 ELIMINATED
4 B0 ELIMINATED
FINAL SCORE: 0 0

Note: In the first example, the red player takes the Quaffle, move it and throw it. The blue player catches the ball, goes to the red goal and scores.

In the second example, the red player takes the ball and scores in the goal of their own team: the blue team wins a point.

In the third example, the Bludger goes at the position of R0: R0 is eliminated. Then, B0 moves to the position of the Bludger: B0 is eliminated too.

You can find one more example in the easy version of the problem

Buggy Code:
def main():
    import sys
    input = sys.stdin.read
    data = input().splitlines()

    # Read field dimensions
    N, M = map(int, data[0].split())

    # Read the field
    field = []
    for i in range(1, N+1):
        row = data[i].split()
        field.append(row)

    # Read number of steps
    T = int(data[N+1])

    # Read actions
    actions = []
    for i in range(N+2, N+2+T):
        actions.append(data[i].split())

    # Initialize positions and states
    positions = {}
    quaffle_carrier = None
    quaffle_position = None
    bludger_position = None

    # Parse initial positions
    for i in range(N):
        for j in range(M):
            cell = field[i][j]
            if cell != '..':
                if cell.endswith('G'):  # Goals
                    positions[cell] = (i, j)
                elif cell == '.Q':  # Quaffle
                    quaffle_position = (i, j)
                elif cell == '.B':  # Bludger
                    bludger_position = (i, j)
                else:  # Players
                    positions[cell] = (i, j)

    # Directions mapping
    direction_map = {
        'U': (-1, 0),
        'D': (1, 0),
        'L': (0, -1),
        'R': (0, 1)
    }

    # Scores
    red_score = 0
    blue_score = 0

    # Events
    events = []

    # Process each action
    for t in range(T):
        action = actions[t]
        entity = action[0]
        command = action[1]

        if entity in positions:
            x, y = positions[entity]

        if command in direction_map:
            # Move the entity
            dx, dy = direction_map[command]
            new_x = x + dx
            new_y = y + dy
            positions[entity] = (new_x, new_y)

            # If the entity is the quaffle carrier, move the quaffle
            if entity == quaffle_carrier:
                quaffle_position = (new_x, new_y)

            # Check for bludger collision
            if (new_x, new_y) == bludger_position:
                events.append(f"{t} {entity} ELIMINATED")
                del positions[entity]
                if entity == quaffle_carrier:
                    quaffle_position = (new_x, new_y)
                    quaffle_carrier = None

        elif command == 'C':
            # Catch the ball
            ball = action[2]
            if ball == '.Q':
                quaffle_carrier = entity

        elif command == 'T':
            # Throw the quaffle
            if entity == quaffle_carrier:
                quaffle_carrier = None
                # Check if it's a goal
                for goal, (gx, gy) in positions.items():
                    if (gx, gy) == (x, y):
                        if goal.startswith('RG') and entity.startswith('B'):
                            blue_score += 1
                            events.append(f"{t} BLUE GOAL")
                        elif goal.startswith('BG') and entity.startswith('R'):
                            red_score += 1
                            events.append(f"{t} RED GOAL")
                        elif goal.startswith('RG') and entity.startswith('R'):
                            blue_score += 1
                            events.append(f"{t} BLUE GOAL")
                        elif goal.startswith('BG') and entity.startswith('B'):
                            red_score += 1
                            events.append(f"{t} RED GOAL")
                        # Move quaffle to the center
                        quaffle_position = ((N-1)//2, (M-1)//2)
                        break

    # Output all events
    for event in events:
        print(event)

    # Output final score
    print(f"FINAL SCORE: {red_score} {blue_score}")

if __name__ == "__main__":
    main()

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
5
R0 D
R0 C .Q
R0 L
R0 L
R0 T
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Medium)
time_limit_ms: 1000
memory_limit_mb: 256
Description: This afternoon, you decided to enjoy the first days of Spring by taking a walk outside. As you come near the Quidditch field, you hear screams. Once again, there is a conflict about the score: the two teams are convinced that they won the game! To prevent this problem from happening one more time, you decide to get involved in the refereeing of the matches.

Now, you will stay in the stadium to watch the game and count the score. At the end of the game, you will decide the winner.

Today, two teams are competing: the red Gryffindor (R) and the blue Ravenclaw (B) team. Each team is composed of $$$P$$$ players ($$$1 \leq P \leq 10$$$).

The field is a rectangle of $$$N$$$ lines and $$$M$$$ columns ($$$3 \leq N, M \leq 99$$$, $$$N$$$ and $$$M$$$ are odd). All the positions are integers, and several entities are allowed to be at the same position in the field. At the beginning of the game, the field contains goals for the two teams (each team can own between one and five goals), the players, and exactly one Quaffle. In this version of the problem, one Bludger can be present. An other type of ball will be available in the harder version of the problem.

A game is composed of $$$T$$$ steps ($$$0 \leq T \leq 10000$$$). At each step, one entity on the field (a player or a ball) performs one action. All entities can move. A player can also catch a ball or throw the Quaffle that it is carrying. To catch a ball, a player must be located on the same cell as it. The Quaffle does not perform any action while it is being carried; it only follows the movements of the player. If a player carrying the Quaffle decides to throw it, the Quaffle is simply put at the current position of the player. If a player is on the same cell as a Bludger (either after a movement from the player or the Bludger), the player is eliminated. If the player is eliminated while it is carrying the Quaffle, the Quaffle remains on the cell containing both the player and the Bludger after the move. It is guaranteed that this never occurs while the player is in a cell containing a goal.

To win a point, a player must leave the Quaffle at a goal of the other team. When it does, the team of the player wins one point, and the Quaffle instantly moves to the middle of the field (the cell at the $$$(M+1)/2$$$-th column of the $$$(N+1)/2$$$-th line of the field, starting from 1). There is no goal in the middle of the field. If a player puts the ball in its own goal, the other team wins the point.

Input: On the first line, the integers $$$N$$$ and $$$M$$$.

The description of the field follows: $$$N$$$ lines of $$$M$$$ pairs of characters separated by spaces. Each pair of characters represents a position on the field. It can be either:

- .. to represent an empty cell
- R0, ..., R9, B0, ..., B9 to represent a player. The first character is the team of the player, and the second is the number of the player in the team. Each pair of characters is unique, but it is not guaranteed that all the pairs appear in the grid.
- RG or BG to represent a goal. The blue team tries to put the ball in a red goal (RG) while the red team tries to put the ball in a blue goal (BG).
- .Q to represent the Quaffle, which is the ball that the players use to score goals.
- .B to represent a Bludger.

The next line contains $$$T$$$, the number of steps that compose the game. $$$T$$$ lines follow, each describing one action. It contains several pieces of information separated by a space. First, a pair of characters representing the entity that must perform the action. Second, the description of the action:

- U, D, L, R indicate that the entity moves on the grid. It can move to the top of the grid (U), to the bottom (D), to the left (L), or to the right (R). Each entity moves by only one cell at a time.
- C indicates that the player catches the ball (only a player can catch a ball). Then, there is a space followed by a pair of characters: the description of the ball caught by the player. This information is needed since several balls can be in the same cell.
- T indicates that the player throws the Quaffle that it is carrying.

All the actions performed by the entities are guaranteed to be valid: the players stay in the field, don't catch a ball if they are not in the same cell, don't release the Quaffle if they are not carrying it, ...

Output: You must output the description of the main events of the game, one event per line. More precisely:

- Each time a team scores, you must print t RED GOAL or t BLUE GOAL, depending on the team who scored, where t is the current time (the position of the action in the list of actions, starting from 0). In the case where a player scores in the wrong goal (a red player scores in the red goal, or a blue player scores in the blue goal), you must print the name of the team who wins one point, that is, the other team.
- Each time a player is eliminated, you must print t p ELIMINATED, where t is the current time and p is the player who is eliminated. The format to print the player is the same as in the input.

The events must be printed in ascending order of t. If several players are eliminated at the same time, the events must be written in alphabetical order: B0, ..., B9, R0, ... R9.

At the end of the game, you must print the final score as: FINAL SCORE: r b, where r is the score of the red team and b is the score of the blue team.

Examples:
input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
12
R0 D
R0 C .Q
R0 R
R0 T
R0 D
B0 R
B0 U
B0 C .Q
B0 L
B0 L
B0 L
B0 T
output:
11 BLUE GOAL
FINAL SCORE: 0 1

input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
5
R0 D
R0 C .Q
R0 L
R0 L
R0 T
output:
4 BLUE GOAL
FINAL SCORE: 0 1

input:
5 5
.. .. .. .. ..
.. .. .. .. ..
RG R0 .Q B0 BG
.. .. .. .. ..
.. .. .B .. ..
5
.B L
.B U
.B U
B0 L
B0 L
output:
2 R0 ELIMINATED
4 B0 ELIMINATED
FINAL SCORE: 0 0

Note: In the first example, the red player takes the Quaffle, move it and throw it. The blue player catches the ball, goes to the red goal and scores.

In the second example, the red player takes the ball and scores in the goal of their own team: the blue team wins a point.

In the third example, the Bludger goes at the position of R0: R0 is eliminated. Then, B0 moves to the position of the Bludger: B0 is eliminated too.

You can find one more example in the easy version of the problem

Buggy Code:
#include <bits/stdc++.h>
using i64 = long long;
using namespace std;

signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m;
    cin >> n >> m;
    vector<vector<string>> a(n, vector<string>(m));
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            cin >> a[i][j];
    vector<pair<int, int>> posr(10, {-1, -1}), posb(10, {-1, -1});
    pair<int, int> pb = {-1, -1};
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < m; j++)
        {
            if (a[i][j][1] <= '9' && a[i][j][1] >= '0')
            {
                if (a[i][j][0] == 'R')
                    posr[a[i][j][1] - '0'] = {i, j};
                else
                    posb[a[i][j][1] - '0'] = {i, j};
            }
            if (a[i][j] == ".B")
                pb = {i, j};
        }
    }
    int t;
    cin >> t;
    int ansr = 0, ansb = 0;
    for (int _ = 0; _ < t; _++)
    {
        string d, e, f;
        cin >> d >> e;
        if (e == "C")
            cin >> f;
        else if (e == "T")
        {
            auto [x, y] = d[0] == 'R' ? posr[d[1] - '0'] : posb[d[1] - '0'];
            if (a[x][y] == "RG")
            {
                ansb++;
                cout << _;
                cout << " BLUE GOAL";
                cout << '\n';
            }
            else if (a[x][y] == "BG")
            {
                ansr++;
                cout << _;
                cout << " RED GOAL";
                cout << '\n';
            }
        }
        else
        {
            if (d == ".B")
            {
                auto &t = pb;
                if (e == "U")
                    t.first--;
                else if (e == "D")
                    t.first++;
                else if (e == "L")
                    t.second--;
                else
                    t.second++;
                for (int i = 0; i < 10; i++)
                {
                    if (posb[i] == t)
                    {
                        posb[i] = {-1, -1};
                        cout << _ << " B" << i + 1 << " ELIMINATED\n";
                    }
                }
                for (int i = 0; i < 10; i++)
                {
                    if (posr[i] == t)
                    {
                        posr[i] = {-1, -1};
                        cout << _ << " R" << i + 1 << " ELIMINATED\n";
                    }
                }
            }
            else
            {
                auto &t = (d[0] == 'R' ? posr[d[1] - '0'] : posb[d[1] - '0']);
                if (e == "U")
                    t.first--;
                else if (e == "D")
                    t.first++;
                else if (e == "L")
                    t.second--;
                else
                    t.second++;
                if (t == pb)
                {
                    t = {-1, -1};
                    cout << _ << ' ' << d << " ELIMINATED\n";
                }
            }
        }
    }
    cout << "FINAL SCORE: " << ansr << ' ' << ansb << '\n';
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to consider the following edge cases and scenarios:

1. **Bludger Elimination**: Ensure that the Bludger can eliminate multiple players in a single step.
2. **Scoring in the Wrong Goal**: Ensure that a player can score in their own goal, which should award a point to the opposing team.
3. **Quaffle Handling**: Ensure that the player can catch and throw the Quaffle correctly, and that the Quaffle moves to the center of the field after a goal is scored.
4. **Player Movement**: Ensure that players can move around the field and perform actions correctly.

Given these considerations, let's create a small-scale test input that covers these scenarios.

```plaintext
5 5
.. .. .. .. ..
.. .. R0 .Q ..
RG .. .. .. BG
.. .. B0 .. ..
.. .. .B .. ..
7
R0 D
R0 C .Q
R0 R
R0 T
B0 L
B0 L
.B R
```

### Explanation:
1. **Initial Setup**:
   - The field is a 5x5 grid.
   - Red player (R0) is at (1, 2).
   - Quaffle is at (1, 3).
   - Red goal (RG) is at (2, 0).
   - Blue goal (BG) is at (2, 4).
   - Blue player (B0) is at (3, 2).
   - Bludger is at (4, 2).

2. **Steps**:
   - **Step 0**: R0 moves down to (2, 2).
   - **Step 1**: R0 catches the Quaffle.
   - **Step 2**: R0 moves right to (2, 3).
   - **Step 3**: R0 throws the Quaffle.
   - **Step 4**: B0 moves left to (3, 1).
   - **Step 5**: B0 moves left to (3, 0).
   - **Step 6**: Bludger moves right to (4, 3), eliminating B0.

### Expected Output:
```plaintext
3 BLUE GOAL
6 B0 ELIMINATED
FINAL SCORE: 0 1
```

### Explanation of Expected Output:
1. **Step 3**: R0 throws the Quaffle into the blue goal, scoring a point for the blue team.
2. **Step 6**: The Bludger moves to (4, 3), eliminating B0.
3. **Final Score**: The blue team has 1 point, and the red team has 0 points.

This test input is designed to cover multiple edge cases and ensure that the buggy code fails to handle them correctly, exposing the bugs.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Medium)
time_limit_ms: 1000
memory_limit_mb: 256
Description: This afternoon, you decided to enjoy the first days of Spring by taking a walk outside. As you come near the Quidditch field, you hear screams. Once again, there is a conflict about the score: the two teams are convinced that they won the game! To prevent this problem from happening one more time, you decide to get involved in the refereeing of the matches.

Now, you will stay in the stadium to watch the game and count the score. At the end of the game, you will decide the winner.

Today, two teams are competing: the red Gryffindor (R) and the blue Ravenclaw (B) team. Each team is composed of $$$P$$$ players ($$$1 \leq P \leq 10$$$).

The field is a rectangle of $$$N$$$ lines and $$$M$$$ columns ($$$3 \leq N, M \leq 99$$$, $$$N$$$ and $$$M$$$ are odd). All the positions are integers, and several entities are allowed to be at the same position in the field. At the beginning of the game, the field contains goals for the two teams (each team can own between one and five goals), the players, and exactly one Quaffle. In this version of the problem, one Bludger can be present. An other type of ball will be available in the harder version of the problem.

A game is composed of $$$T$$$ steps ($$$0 \leq T \leq 10000$$$). At each step, one entity on the field (a player or a ball) performs one action. All entities can move. A player can also catch a ball or throw the Quaffle that it is carrying. To catch a ball, a player must be located on the same cell as it. The Quaffle does not perform any action while it is being carried; it only follows the movements of the player. If a player carrying the Quaffle decides to throw it, the Quaffle is simply put at the current position of the player. If a player is on the same cell as a Bludger (either after a movement from the player or the Bludger), the player is eliminated. If the player is eliminated while it is carrying the Quaffle, the Quaffle remains on the cell containing both the player and the Bludger after the move. It is guaranteed that this never occurs while the player is in a cell containing a goal.

To win a point, a player must leave the Quaffle at a goal of the other team. When it does, the team of the player wins one point, and the Quaffle instantly moves to the middle of the field (the cell at the $$$(M+1)/2$$$-th column of the $$$(N+1)/2$$$-th line of the field, starting from 1). There is no goal in the middle of the field. If a player puts the ball in its own goal, the other team wins the point.

Input: On the first line, the integers $$$N$$$ and $$$M$$$.

The description of the field follows: $$$N$$$ lines of $$$M$$$ pairs of characters separated by spaces. Each pair of characters represents a position on the field. It can be either:

- .. to represent an empty cell
- R0, ..., R9, B0, ..., B9 to represent a player. The first character is the team of the player, and the second is the number of the player in the team. Each pair of characters is unique, but it is not guaranteed that all the pairs appear in the grid.
- RG or BG to represent a goal. The blue team tries to put the ball in a red goal (RG) while the red team tries to put the ball in a blue goal (BG).
- .Q to represent the Quaffle, which is the ball that the players use to score goals.
- .B to represent a Bludger.

The next line contains $$$T$$$, the number of steps that compose the game. $$$T$$$ lines follow, each describing one action. It contains several pieces of information separated by a space. First, a pair of characters representing the entity that must perform the action. Second, the description of the action:

- U, D, L, R indicate that the entity moves on the grid. It can move to the top of the grid (U), to the bottom (D), to the left (L), or to the right (R). Each entity moves by only one cell at a time.
- C indicates that the player catches the ball (only a player can catch a ball). Then, there is a space followed by a pair of characters: the description of the ball caught by the player. This information is needed since several balls can be in the same cell.
- T indicates that the player throws the Quaffle that it is carrying.

All the actions performed by the entities are guaranteed to be valid: the players stay in the field, don't catch a ball if they are not in the same cell, don't release the Quaffle if they are not carrying it, ...

Output: You must output the description of the main events of the game, one event per line. More precisely:

- Each time a team scores, you must print t RED GOAL or t BLUE GOAL, depending on the team who scored, where t is the current time (the position of the action in the list of actions, starting from 0). In the case where a player scores in the wrong goal (a red player scores in the red goal, or a blue player scores in the blue goal), you must print the name of the team who wins one point, that is, the other team.
- Each time a player is eliminated, you must print t p ELIMINATED, where t is the current time and p is the player who is eliminated. The format to print the player is the same as in the input.

The events must be printed in ascending order of t. If several players are eliminated at the same time, the events must be written in alphabetical order: B0, ..., B9, R0, ... R9.

At the end of the game, you must print the final score as: FINAL SCORE: r b, where r is the score of the red team and b is the score of the blue team.

Examples:
input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
12
R0 D
R0 C .Q
R0 R
R0 T
R0 D
B0 R
B0 U
B0 C .Q
B0 L
B0 L
B0 L
B0 T
output:
11 BLUE GOAL
FINAL SCORE: 0 1

input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
5
R0 D
R0 C .Q
R0 L
R0 L
R0 T
output:
4 BLUE GOAL
FINAL SCORE: 0 1

input:
5 5
.. .. .. .. ..
.. .. .. .. ..
RG R0 .Q B0 BG
.. .. .. .. ..
.. .. .B .. ..
5
.B L
.B U
.B U
B0 L
B0 L
output:
2 R0 ELIMINATED
4 B0 ELIMINATED
FINAL SCORE: 0 0

Note: In the first example, the red player takes the Quaffle, move it and throw it. The blue player catches the ball, goes to the red goal and scores.

In the second example, the red player takes the ball and scores in the goal of their own team: the blue team wins a point.

In the third example, the Bludger goes at the position of R0: R0 is eliminated. Then, B0 moves to the position of the Bludger: B0 is eliminated too.

You can find one more example in the easy version of the problem

Buggy Code:
#include <iostream>
#include <vector>
#include <set>
#include <map>
#include <cmath>
#include <numeric>
#include <unordered_map>
#include <unordered_set>
#include <iomanip>
#include <algorithm>
#include <assert.h>

#define int long long
#define all(x) x.begin(), x.end()
#define ff first
#define ss second

using namespace std;

signed main() {
    int n, m, i, j, k;
    cin >> n >> m;
    vector<vector<string>>a(n, vector<string>(m));
    for (i = 0; i < n; i++) {
        for (j = 0; j < m; j++) {
            cin >> a[i][j];
        }
    }
    map<string, pair<int, int>>mp;
    vector<pair<int,int>>rg;
    vector<pair<int,int>>bg;
    for (i = 0; i < n; i++) {
        for (j = 0; j < m; j++) {
            if (a[i][j] == "..")continue;
            mp[a[i][j]] = { i+1,j+1 };
            if(a[i][j] == "RG")rg.push_back({i+1,j+1});
            if(a[i][j] == "BG")bg.push_back({i+1,j+1});
        }
    }
    int t;
    cin >> t;
    int ansb = 0, ansr = 0;
    map<string, string>ball;
    map<string, pair<int, int>>udlr = { {"U",{-1,0}},{"D",{1,0}},{"L",{0,-1}},{"R", {0,1}} };
    int ind = 0;
    if(mp.find(".b") == mp.end())mp[".b"] = {-100,-100};
    set<string>igr = {"B0","B1","B2","B3","B4","B5","B6","B7","B8","B9","R0","R1","R2","R3","R4","R5","R6","R7","R8","R9"};
    while (t--) {
        ind++;
        string s;
        cin >> s;
        auto [x, y] = mp[s];
        string dvig;
        cin >> dvig;
        if (udlr.find(dvig) != udlr.end()) {
            x += udlr[dvig].ff;
            y += udlr[dvig].ss;
            if (ball.find(s) != ball.end()) {
                mp[ball[s]] = { x,y };
            }
            mp[s] = { x,y };
            set<string>el;
            for (auto it2 : mp) {
                if (mp[".B"] == it2.ss && ".B" == it2.ff)continue;
                if (mp[".B"] == it2.ss ) {
                    if(igr.find(it2.ff) != igr.end()) {
                        el.insert(it2.ff);
                    }
                }
            }
            if(el.size() > 0) {
                for(auto it:el)cout <<  ind << " " << it << " ELIMINATED" << "\n";
            }
            for(auto it:el)mp[it] = {-1e8,-1e8};
        }
        else {
            if (dvig == "C") {
                string bl;
                cin >> bl;
                ball.clear();
                ball[s] = bl;
                if (bl == ".S") {
                    if (s[0] == 'R') {
                        cout << ind-1 << " RED CATCH GOLDEN SNITCH" << "\n"; ansr += 10;
                    }
                    else {
                        cout << ind-1 << " BLUE CATCH GOLDEN SNITCH" << "\n"; ansb += 10;
                    }
                    break;
                }
            }
            else {
                assert(dvig == "T");
                for (auto it : rg) {
                    if (it == mp[s]) {
                            ansb += 1;
                            cout << ind-1 << " BLUE GOAL" << "\n";
                            mp[".Q"] = {(n+1)/2,(m+1)/2};
                            break;
                    }
                }
                for (auto it : bg) {
                    if (it == mp[s]) {
                        ansr += 1;
                        cout << ind-1 << " RED GOAL" << "\n";
                        mp[".Q"] = {(n+1)/2,(m+1)/2};
                        break;
                    }
                }
                ball[s].clear();
            }
        }
    }
    cout << "FINAL SCORE: " << ansr << " " << ansb << "\n";
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
```plaintext
3 3
RG .. R0
.. .Q ..
.. .. B0
5
R0 D
R0 C .Q
R0 D
B0 U
B0 C .Q
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Medium)
time_limit_ms: 1000
memory_limit_mb: 256
Description: This afternoon, you decided to enjoy the first days of Spring by taking a walk outside. As you come near the Quidditch field, you hear screams. Once again, there is a conflict about the score: the two teams are convinced that they won the game! To prevent this problem from happening one more time, you decide to get involved in the refereeing of the matches.

Now, you will stay in the stadium to watch the game and count the score. At the end of the game, you will decide the winner.

Today, two teams are competing: the red Gryffindor (R) and the blue Ravenclaw (B) team. Each team is composed of $$$P$$$ players ($$$1 \leq P \leq 10$$$).

The field is a rectangle of $$$N$$$ lines and $$$M$$$ columns ($$$3 \leq N, M \leq 99$$$, $$$N$$$ and $$$M$$$ are odd). All the positions are integers, and several entities are allowed to be at the same position in the field. At the beginning of the game, the field contains goals for the two teams (each team can own between one and five goals), the players, and exactly one Quaffle. In this version of the problem, one Bludger can be present. An other type of ball will be available in the harder version of the problem.

A game is composed of $$$T$$$ steps ($$$0 \leq T \leq 10000$$$). At each step, one entity on the field (a player or a ball) performs one action. All entities can move. A player can also catch a ball or throw the Quaffle that it is carrying. To catch a ball, a player must be located on the same cell as it. The Quaffle does not perform any action while it is being carried; it only follows the movements of the player. If a player carrying the Quaffle decides to throw it, the Quaffle is simply put at the current position of the player. If a player is on the same cell as a Bludger (either after a movement from the player or the Bludger), the player is eliminated. If the player is eliminated while it is carrying the Quaffle, the Quaffle remains on the cell containing both the player and the Bludger after the move. It is guaranteed that this never occurs while the player is in a cell containing a goal.

To win a point, a player must leave the Quaffle at a goal of the other team. When it does, the team of the player wins one point, and the Quaffle instantly moves to the middle of the field (the cell at the $$$(M+1)/2$$$-th column of the $$$(N+1)/2$$$-th line of the field, starting from 1). There is no goal in the middle of the field. If a player puts the ball in its own goal, the other team wins the point.

Input: On the first line, the integers $$$N$$$ and $$$M$$$.

The description of the field follows: $$$N$$$ lines of $$$M$$$ pairs of characters separated by spaces. Each pair of characters represents a position on the field. It can be either:

- .. to represent an empty cell
- R0, ..., R9, B0, ..., B9 to represent a player. The first character is the team of the player, and the second is the number of the player in the team. Each pair of characters is unique, but it is not guaranteed that all the pairs appear in the grid.
- RG or BG to represent a goal. The blue team tries to put the ball in a red goal (RG) while the red team tries to put the ball in a blue goal (BG).
- .Q to represent the Quaffle, which is the ball that the players use to score goals.
- .B to represent a Bludger.

The next line contains $$$T$$$, the number of steps that compose the game. $$$T$$$ lines follow, each describing one action. It contains several pieces of information separated by a space. First, a pair of characters representing the entity that must perform the action. Second, the description of the action:

- U, D, L, R indicate that the entity moves on the grid. It can move to the top of the grid (U), to the bottom (D), to the left (L), or to the right (R). Each entity moves by only one cell at a time.
- C indicates that the player catches the ball (only a player can catch a ball). Then, there is a space followed by a pair of characters: the description of the ball caught by the player. This information is needed since several balls can be in the same cell.
- T indicates that the player throws the Quaffle that it is carrying.

All the actions performed by the entities are guaranteed to be valid: the players stay in the field, don't catch a ball if they are not in the same cell, don't release the Quaffle if they are not carrying it, ...

Output: You must output the description of the main events of the game, one event per line. More precisely:

- Each time a team scores, you must print t RED GOAL or t BLUE GOAL, depending on the team who scored, where t is the current time (the position of the action in the list of actions, starting from 0). In the case where a player scores in the wrong goal (a red player scores in the red goal, or a blue player scores in the blue goal), you must print the name of the team who wins one point, that is, the other team.
- Each time a player is eliminated, you must print t p ELIMINATED, where t is the current time and p is the player who is eliminated. The format to print the player is the same as in the input.

The events must be printed in ascending order of t. If several players are eliminated at the same time, the events must be written in alphabetical order: B0, ..., B9, R0, ... R9.

At the end of the game, you must print the final score as: FINAL SCORE: r b, where r is the score of the red team and b is the score of the blue team.

Examples:
input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
12
R0 D
R0 C .Q
R0 R
R0 T
R0 D
B0 R
B0 U
B0 C .Q
B0 L
B0 L
B0 L
B0 T
output:
11 BLUE GOAL
FINAL SCORE: 0 1

input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
5
R0 D
R0 C .Q
R0 L
R0 L
R0 T
output:
4 BLUE GOAL
FINAL SCORE: 0 1

input:
5 5
.. .. .. .. ..
.. .. .. .. ..
RG R0 .Q B0 BG
.. .. .. .. ..
.. .. .B .. ..
5
.B L
.B U
.B U
B0 L
B0 L
output:
2 R0 ELIMINATED
4 B0 ELIMINATED
FINAL SCORE: 0 0

Note: In the first example, the red player takes the Quaffle, move it and throw it. The blue player catches the ball, goes to the red goal and scores.

In the second example, the red player takes the ball and scores in the goal of their own team: the blue team wins a point.

In the third example, the Bludger goes at the position of R0: R0 is eliminated. Then, B0 moves to the position of the Bludger: B0 is eliminated too.

You can find one more example in the easy version of the problem

Buggy Code:
#include <bits/stdc++.h>
using namespace std;
bool search(int i,int j,vector<pair<int,int>>goals){
    int n = goals.size();
    for(int k= 0;k<n;k++){
        if(goals[k].first == i && goals[k].second == j){
            return true;
        }
    }
    return false;
}
int search_index(int i,int j,vector<pair<int,int>>players){
    int n = players.size();
    for(int k = 0;k < n;k++){
        if(players[k].first == i && players[k].second == j){
            return k;
        }
    }
    return -1;
}
int main(){

    int m,n;
    cin>>m>>n;
    vector<pair<int,int>> players_R(10);
    vector<pair<int,int>> players_B(10);
    for(int i = 0; i < 10;i++){
        players_R[i].first = -1;
        players_R[i].second = -1;
        players_B[i].first = -1;
        players_B[i].second= -1;
    }
    pair<int,int>location;
    pair<int,int>location_b;
    string in;
    int num_R = 0;
    int num_B = 0;
    int num;
    vector<pair<int,int>>RG(5);
    int RG_num = 0;
    int BG_num = 0;
    vector<pair<int,int>>BG(5);
    for(int i = 0;i < 5;i++){
        RG[i].first = -1;
        RG[i].second = -1;
        BG[i].first = -1;
        BG[i].second = -1;
    }

    for(int i = 0;i<m;i++){
        for(int j = 0;j < n;j++){
            cin>>in;
            if(in == ".."){
                continue;
            }
            else if(in[0] == 'R' && in[1]!='G'){
                num = stoi(in.substr(1));
                players_R[num].first = i;
                players_R[num].second = j;
                num_R++;
            }
            else if(in[0] == 'B' && in[1]!='G'){
                num = stoi(in.substr(1));
                players_B[num].first = i;
                players_B[num].second = j;
                num_B++;
            }
            else if(in[0] == '.' && in[1]=='Q'){
                location.first = i;
                location.second = j;
            }
            else if(in[0] == '.' && in[1]=='B'){
                location_b.first = i;
                location_b.second = j;
            }
            else if(in[0] == 'B' && in[1] =='G'){
                BG[BG_num].first = i;
                BG[BG_num].second = j;
                BG_num++;
            }
            else if(in[0] == 'R' && in[1]=='G'){
                RG[RG_num].first = i;
                RG[RG_num].second = j;
                RG_num++;
            }

        }
    }
    int T;
    cin>>T;
    int r_goal = 0;
    int b_goal = 0;
    string move;
    string move_1;
    string dum;
    int player_num;
    bool ball_B[10];
    bool ball_R[10];
    for(int i = 0;i < 10;i++){
        ball_B[i] = false;
        ball_R[i] = false;
    }
    for(int i = 0;i<T;i++){
        cin>>move;
        cin >> move_1;
        if(move[0] == 'B'){
            player_num = stoi(move.substr(1));
            if(move_1[0] == 'U'){
                players_B[player_num].first -= 1;
                if((players_B[player_num].first == location_b.first) && (players_B[player_num].second == location_b.second)){
                    cout << i << " B"<<player_num<<" ELIMINATED"<<endl;
                }
            }
            else if(move_1[0] == 'D'){
                players_B[player_num].first += 1;
                if((players_B[player_num].first == location_b.first) && (players_B[player_num].second == location_b.second)){
                    cout << i << " B"<<player_num<<" ELIMINATED"<<endl;
                }
            }
            else if(move_1[0] == 'L'){
                players_B[player_num].second -= 1;
                if((players_B[player_num].first == location_b.first) && (players_B[player_num].second == location_b.second)){
                    cout << i << " B"<<player_num<<" ELIMINATED"<<endl;
                }
            }
            else if(move_1[0] == 'R'){
                players_B[player_num].second += 1;
                if((players_B[player_num].first == location_b.first) && (players_B[player_num].second == location_b.second)){
                    cout << i << " B"<<player_num<<" ELIMINATED"<<endl;
                }
            }
            else if(move_1[0] == 'C'){
                ball_B[player_num] = true;
                cin>>dum;
            }
            else{
                ball_B[player_num] = false;
                if(search(players_B[player_num].first,players_B[player_num].second,RG)){
                    cout<< i << " BLUE GOAL"<<endl;
                    b_goal++;
                    location.first = (m-1)/2;
                    location.second = (n-1)/2;
                }
                else if(search(players_B[player_num].first,players_B[player_num].second,BG)){
                    cout<< i << " RED GOAL"<<endl;
                    r_goal++;
                    location.first = (m-1)/2;
                    location.second = (n-1)/2;
                }
                else{
                    location.first = players_B[player_num].first;
                    location.second = players_B[player_num].second;
                }

            }
        }
        else if(move[0] == 'R'){
            player_num = stoi(move.substr(1));
            if(move_1[0] == 'U'){
                players_R[player_num].first -= 1;
                if((players_B[player_num].first == location_b.first) && (players_B[player_num].second == location_b.second)){
                    cout << i << " R"<<player_num<<" ELIMINATED"<<endl;
                }
            }
            else if(move_1[0] == 'D'){
                players_R[player_num].first += 1;
                if((players_B[player_num].first == location_b.first) && (players_B[player_num].second == location_b.second)){
                    cout << i << " R"<<player_num<<" ELIMINATED"<<endl;
                }
            }
            else if(move_1[0] == 'L'){
                players_R[player_num].second -= 1;
                if((players_B[player_num].first == location_b.first) && (players_B[player_num].second == location_b.second)){
                    cout << i << " R"<<player_num<<" ELIMINATED"<<endl;
                }
            }
            else if(move_1[0] == 'R'){
                players_R[player_num].second += 1;
                if((players_B[player_num].first == location_b.first) && (players_B[player_num].second == location_b.second)){
                    cout << i << " R"<<player_num<<" ELIMINATED"<<endl;
                }
            }
            else if(move_1[0] == 'C'){
                ball_R[player_num] = true;
                cin>>dum;
            }
            else{

                ball_R[player_num] = false;
                if(search(players_R[player_num].first,players_R[player_num].second,RG)){
                    cout<< i << " BLUE GOAL"<<endl;
                    b_goal++;
                    location.first = (m-1)/2;
                    location.second = (n-1)/2;
                }
                else if(search(players_R[player_num].first,players_R[player_num].second,BG)){
                    cout<< i << " RED GOAL"<<endl;
                    r_goal++;
                    location.first = (m-1)/2;
                    location.second = (n-1)/2;
                }
                else{
                    location.first = players_B[player_num].first;
                    location.second = players_B[player_num].second;
                }

            }
        }
        else{
            int num;
            if(move_1[0] == 'U'){
                location_b.first -= 1;
                num = search_index(location_b.first,location_b.second,players_B);
                if(num != -1){
                    cout << i << " B"<<num<<" ELIMINATED"<<endl;
                }
                num = search_index(location_b.first,location_b.second,players_R);
                if(num != -1){
                    cout << i << " B"<<num<<" ELIMINATED"<<endl;
                }

            }
            else if(move_1[0] == 'D'){
                location_b.first += 1;
                num = search_index(location_b.first,location_b.second,players_B);
                if(num != -1){
                    cout << i << " B"<<num<<" ELIMINATED"<<endl;
                }
                num = search_index(location_b.first,location_b.second,players_R);
                if(num != -1){
                    cout << i << " B"<<num<<" ELIMINATED"<<endl;
                }
            }
            else if(move_1[0] == 'L'){
                location_b.second -= 1;
                num = search_index(location_b.first,location_b.second,players_B);
                if(num != -1){
                    cout << i << " B"<<num<<" ELIMINATED"<<endl;
                }
                num = search_index(location_b.first,location_b.second,players_R);
                if(num != -1){
                    cout << i << " B"<<num<<" ELIMINATED"<<endl;
                }
            }
            else if(move_1[0] == 'R'){
                location_b.second += 1;
                num = search_index(location_b.first,location_b.second,players_B);
                if(num != -1){
                    cout << i << " B"<<num<<" ELIMINATED"<<endl;
                }
                num = search_index(location_b.first,location_b.second,players_R);
                if(num != -1){
                    cout << i << " B"<<num<<" ELIMINATED"<<endl;
                }
            }
        }
    }
    cout << "FINAL SCORE: "<<r_goal << " "<<b_goal<<endl;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To create a challenging test input that exposes bugs in the given code, we need to consider edge cases and scenarios that can cause issues. Here are the steps to think through:

1. **Field Size and Initial Setup:**
   - Use a small field size to make the test input manageable.
   - Ensure the field has both red and blue goals.
   - Place players and the Quaffle in positions that can lead to interesting interactions.

2. **Player and Ball Movements:**
   - Include movements that can lead to player eliminations.
   - Include movements that can lead to scoring goals.
   - Ensure the Quaffle is moved in a way that can be caught and thrown.

3. **Bludger Movements:**
   - Place the Bludger in a position where it can eliminate players.
   - Ensure the Bludger moves in a way that can cause multiple eliminations in a single step.

4. **Scoring and Elimination:**
   - Create scenarios where players score in the wrong goals.
   - Create scenarios where players are eliminated by the Bludger.

5. **Final Score:**
   - Ensure the final score is correctly calculated based on the events.

Here is a small-scale test input that meets these criteria:

```plaintext
5 5
.. .. .. .. ..
.. .. .. .. ..
RG R0 .Q B0 BG
.. .. .. .. ..
.. .. .B .. ..
5
.B L
.B U
.B U
B0 L
B0 L
```

### Explanation:
- **Field Size:** 5x5, which is small and manageable.
- **Initial Setup:**
  - Red goal (RG) and blue goal (BG) are placed on the third row.
  - Red player (R0) and blue player (B0) are placed near the goals.
  - The Quaffle (.Q) is placed next to R0.
  - The Bludger (.B) is placed on the bottom row.
- **Movements:**
  - The Bludger moves left, up, and up, which will eliminate R0 and B0.
  - B0 moves left twice, which will eventually lead to its elimination by the Bludger.

This test input should expose issues in the code related to player elimination and scoring, especially in handling the Bludger's movements and their effects on players.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Medium)
time_limit_ms: 1000
memory_limit_mb: 256
Description: This afternoon, you decided to enjoy the first days of Spring by taking a walk outside. As you come near the Quidditch field, you hear screams. Once again, there is a conflict about the score: the two teams are convinced that they won the game! To prevent this problem from happening one more time, you decide to get involved in the refereeing of the matches.

Now, you will stay in the stadium to watch the game and count the score. At the end of the game, you will decide the winner.

Today, two teams are competing: the red Gryffindor (R) and the blue Ravenclaw (B) team. Each team is composed of $$$P$$$ players ($$$1 \leq P \leq 10$$$).

The field is a rectangle of $$$N$$$ lines and $$$M$$$ columns ($$$3 \leq N, M \leq 99$$$, $$$N$$$ and $$$M$$$ are odd). All the positions are integers, and several entities are allowed to be at the same position in the field. At the beginning of the game, the field contains goals for the two teams (each team can own between one and five goals), the players, and exactly one Quaffle. In this version of the problem, one Bludger can be present. An other type of ball will be available in the harder version of the problem.

A game is composed of $$$T$$$ steps ($$$0 \leq T \leq 10000$$$). At each step, one entity on the field (a player or a ball) performs one action. All entities can move. A player can also catch a ball or throw the Quaffle that it is carrying. To catch a ball, a player must be located on the same cell as it. The Quaffle does not perform any action while it is being carried; it only follows the movements of the player. If a player carrying the Quaffle decides to throw it, the Quaffle is simply put at the current position of the player. If a player is on the same cell as a Bludger (either after a movement from the player or the Bludger), the player is eliminated. If the player is eliminated while it is carrying the Quaffle, the Quaffle remains on the cell containing both the player and the Bludger after the move. It is guaranteed that this never occurs while the player is in a cell containing a goal.

To win a point, a player must leave the Quaffle at a goal of the other team. When it does, the team of the player wins one point, and the Quaffle instantly moves to the middle of the field (the cell at the $$$(M+1)/2$$$-th column of the $$$(N+1)/2$$$-th line of the field, starting from 1). There is no goal in the middle of the field. If a player puts the ball in its own goal, the other team wins the point.

Input: On the first line, the integers $$$N$$$ and $$$M$$$.

The description of the field follows: $$$N$$$ lines of $$$M$$$ pairs of characters separated by spaces. Each pair of characters represents a position on the field. It can be either:

- .. to represent an empty cell
- R0, ..., R9, B0, ..., B9 to represent a player. The first character is the team of the player, and the second is the number of the player in the team. Each pair of characters is unique, but it is not guaranteed that all the pairs appear in the grid.
- RG or BG to represent a goal. The blue team tries to put the ball in a red goal (RG) while the red team tries to put the ball in a blue goal (BG).
- .Q to represent the Quaffle, which is the ball that the players use to score goals.
- .B to represent a Bludger.

The next line contains $$$T$$$, the number of steps that compose the game. $$$T$$$ lines follow, each describing one action. It contains several pieces of information separated by a space. First, a pair of characters representing the entity that must perform the action. Second, the description of the action:

- U, D, L, R indicate that the entity moves on the grid. It can move to the top of the grid (U), to the bottom (D), to the left (L), or to the right (R). Each entity moves by only one cell at a time.
- C indicates that the player catches the ball (only a player can catch a ball). Then, there is a space followed by a pair of characters: the description of the ball caught by the player. This information is needed since several balls can be in the same cell.
- T indicates that the player throws the Quaffle that it is carrying.

All the actions performed by the entities are guaranteed to be valid: the players stay in the field, don't catch a ball if they are not in the same cell, don't release the Quaffle if they are not carrying it, ...

Output: You must output the description of the main events of the game, one event per line. More precisely:

- Each time a team scores, you must print t RED GOAL or t BLUE GOAL, depending on the team who scored, where t is the current time (the position of the action in the list of actions, starting from 0). In the case where a player scores in the wrong goal (a red player scores in the red goal, or a blue player scores in the blue goal), you must print the name of the team who wins one point, that is, the other team.
- Each time a player is eliminated, you must print t p ELIMINATED, where t is the current time and p is the player who is eliminated. The format to print the player is the same as in the input.

The events must be printed in ascending order of t. If several players are eliminated at the same time, the events must be written in alphabetical order: B0, ..., B9, R0, ... R9.

At the end of the game, you must print the final score as: FINAL SCORE: r b, where r is the score of the red team and b is the score of the blue team.

Examples:
input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
12
R0 D
R0 C .Q
R0 R
R0 T
R0 D
B0 R
B0 U
B0 C .Q
B0 L
B0 L
B0 L
B0 T
output:
11 BLUE GOAL
FINAL SCORE: 0 1

input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
5
R0 D
R0 C .Q
R0 L
R0 L
R0 T
output:
4 BLUE GOAL
FINAL SCORE: 0 1

input:
5 5
.. .. .. .. ..
.. .. .. .. ..
RG R0 .Q B0 BG
.. .. .. .. ..
.. .. .B .. ..
5
.B L
.B U
.B U
B0 L
B0 L
output:
2 R0 ELIMINATED
4 B0 ELIMINATED
FINAL SCORE: 0 0

Note: In the first example, the red player takes the Quaffle, move it and throw it. The blue player catches the ball, goes to the red goal and scores.

In the second example, the red player takes the ball and scores in the goal of their own team: the blue team wins a point.

In the third example, the Bludger goes at the position of R0: R0 is eliminated. Then, B0 moves to the position of the Bludger: B0 is eliminated too.

You can find one more example in the easy version of the problem

Buggy Code:
def main():
    import sys
    input = sys.stdin.read
    data = input().split('\n')

    # Read dimensions of the field
    N, M = map(int, data[0].split())

    # Read the field setup
    field = [data[i+1].split() for i in range(N)]

    # Read number of steps
    T = int(data[N+1])

    # Actions
    actions = [data[N+2+i].split() for i in range(T)]

    # Initialize game state
    players = {}
    goals = {}
    quaffle = None
    bludger = None

    # Parse the field
    for i in range(N):
        for j in range(M):
            cell = field[i][j]
            if cell == '..':
                continue
            elif cell == '.Q':
                quaffle = (i, j)
            elif cell == '.B':
                bludger = (i, j)
            elif cell.endswith('G'):
                goals[(i, j)] = cell
            else:  # Players
                players[cell] = (i, j)

    # Scores
    red_score = 0
    blue_score = 0

    # Events
    events = []

    # Process each action
    for step, action in enumerate(actions):
        entity, move = action[0], action[1]
        if move in 'UDLR':
            # Move the entity
            di, dj = {'U': (-1, 0), 'D': (1, 0), 'L': (0, -1), 'R': (0, 1)}[move]
            if entity in players:
                i, j = players[entity]
                new_pos = (i + di, j + dj)
                players[entity] = new_pos
                # Check for bludger collision
                if new_pos == bludger:
                    events.append(f"{step} {entity} ELIMINATED")
                    del players[entity]
                    if entity == quaffle_holder:
                        quaffle = new_pos
                        quaffle_holder = None
            elif entity == '.Q':
                quaffle = (quaffle[0] + di, quaffle[1] + dj)
            elif entity == '.B':
                bludger = (bludger[0] + di, bludger[1] + dj)
        elif move == 'C':
            # Catch the Quaffle
            quaffle_holder = entity
        elif move == 'T':
            # Throw the Quaffle
            if entity in players:
                i, j = players[entity]
                if (i, j) in goals:
                    goal_type = goals[(i, j)]
                    if (entity[0] == 'R' and goal_type == 'BG') or (entity[0] == 'B' and goal_type == 'RG'):
                        if entity[0] == 'R':
                            red_score += 1
                            events.append(f"{step} RED GOAL")
                        else:
                            blue_score += 1
                            events.append(f"{step} BLUE GOAL")
                    else:
                        if entity[0] == 'R':
                            blue_score += 1
                            events.append(f"{step} BLUE GOAL")
                        else:
                            red_score += 1
                            events.append(f"{step} RED GOAL")
                # Move Quaffle to the center
                quaffle = (N // 2, M // 2)

    # Output events
    for event in events:
        print(event)

    # Output final score
    print(f"FINAL SCORE: {red_score} {blue_score}")

if __name__ == "__main__":
    main()

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the buggy code, let's consider the following aspects:

1. **Bludger Collision with Quaffle Holder**: Ensure that a player holding the Quaffle is hit by the Bludger.
2. **Scoring in the Wrong Goal**: Ensure a player scores in the wrong goal, which should increment the opponent's score.
3. **Multiple Events at the Same Step**: Ensure multiple events (e.g., scoring and elimination) happen at the same step.
4. **Initial Setup**: Ensure the initial setup is valid and follows the problem constraints.

Here's a small-scale test input that covers these aspects:

```plaintext
5 5
.. .. .. .. ..
.. .. .. .. ..
RG R0 .Q B0 BG
.. .. .. .. ..
.. .B .. .. ..
5
R0 D
R0 C .Q
R0 L
.B U
B0 C .Q
```

### Explanation:
1. **Initial Setup**:
   - The field is 5x5.
   - There are goals for both teams (RG at (2, 0) and BG at (2, 4)).
   - R0 and B0 are initially at (2, 2).
   - The Quaffle is at (2, 2).
   - The Bludger is at (4, 1).

2. **Actions**:
   - **Step 0**: R0 moves down (D).
     - R0 moves to (3, 2).
   - **Step 1**: R0 catches the Quaffle (C .Q).
     - R0 is now holding the Quaffle.
   - **Step 2**: R0 moves left (L).
     - R0 moves to (3, 1).
   - **Step 3**: Bludger moves up (U).
     - Bludger moves to (3, 1).
   - **Step 4**: B0 catches the Quaffle (C .Q).
     - B0 should not be able to catch the Quaffle because R0 is holding it, but this will expose the bug if the code allows it.

### Expected Output:
- **Step 2**: R0 moves to (3, 1), which is the same cell as the Bludger.
- **Step 3**: The Bludger moves to (3, 1), and R0 should be eliminated.
- **Step 4**: B0 attempts to catch the Quaffle, which should still be at (3, 1) after R0's elimination.

```plaintext
3 R0 ELIMINATED
4 B0 ELIMINATED
FINAL SCORE: 0 0
```

This test input should expose the bug in the code where the Quaffle is not correctly handled after a player is eliminated and where a player can incorrectly catch the Quaffle.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Medium)
time_limit_ms: 1000
memory_limit_mb: 256
Description: This afternoon, you decided to enjoy the first days of Spring by taking a walk outside. As you come near the Quidditch field, you hear screams. Once again, there is a conflict about the score: the two teams are convinced that they won the game! To prevent this problem from happening one more time, you decide to get involved in the refereeing of the matches.

Now, you will stay in the stadium to watch the game and count the score. At the end of the game, you will decide the winner.

Today, two teams are competing: the red Gryffindor (R) and the blue Ravenclaw (B) team. Each team is composed of $$$P$$$ players ($$$1 \leq P \leq 10$$$).

The field is a rectangle of $$$N$$$ lines and $$$M$$$ columns ($$$3 \leq N, M \leq 99$$$, $$$N$$$ and $$$M$$$ are odd). All the positions are integers, and several entities are allowed to be at the same position in the field. At the beginning of the game, the field contains goals for the two teams (each team can own between one and five goals), the players, and exactly one Quaffle. In this version of the problem, one Bludger can be present. An other type of ball will be available in the harder version of the problem.

A game is composed of $$$T$$$ steps ($$$0 \leq T \leq 10000$$$). At each step, one entity on the field (a player or a ball) performs one action. All entities can move. A player can also catch a ball or throw the Quaffle that it is carrying. To catch a ball, a player must be located on the same cell as it. The Quaffle does not perform any action while it is being carried; it only follows the movements of the player. If a player carrying the Quaffle decides to throw it, the Quaffle is simply put at the current position of the player. If a player is on the same cell as a Bludger (either after a movement from the player or the Bludger), the player is eliminated. If the player is eliminated while it is carrying the Quaffle, the Quaffle remains on the cell containing both the player and the Bludger after the move. It is guaranteed that this never occurs while the player is in a cell containing a goal.

To win a point, a player must leave the Quaffle at a goal of the other team. When it does, the team of the player wins one point, and the Quaffle instantly moves to the middle of the field (the cell at the $$$(M+1)/2$$$-th column of the $$$(N+1)/2$$$-th line of the field, starting from 1). There is no goal in the middle of the field. If a player puts the ball in its own goal, the other team wins the point.

Input: On the first line, the integers $$$N$$$ and $$$M$$$.

The description of the field follows: $$$N$$$ lines of $$$M$$$ pairs of characters separated by spaces. Each pair of characters represents a position on the field. It can be either:

- .. to represent an empty cell
- R0, ..., R9, B0, ..., B9 to represent a player. The first character is the team of the player, and the second is the number of the player in the team. Each pair of characters is unique, but it is not guaranteed that all the pairs appear in the grid.
- RG or BG to represent a goal. The blue team tries to put the ball in a red goal (RG) while the red team tries to put the ball in a blue goal (BG).
- .Q to represent the Quaffle, which is the ball that the players use to score goals.
- .B to represent a Bludger.

The next line contains $$$T$$$, the number of steps that compose the game. $$$T$$$ lines follow, each describing one action. It contains several pieces of information separated by a space. First, a pair of characters representing the entity that must perform the action. Second, the description of the action:

- U, D, L, R indicate that the entity moves on the grid. It can move to the top of the grid (U), to the bottom (D), to the left (L), or to the right (R). Each entity moves by only one cell at a time.
- C indicates that the player catches the ball (only a player can catch a ball). Then, there is a space followed by a pair of characters: the description of the ball caught by the player. This information is needed since several balls can be in the same cell.
- T indicates that the player throws the Quaffle that it is carrying.

All the actions performed by the entities are guaranteed to be valid: the players stay in the field, don't catch a ball if they are not in the same cell, don't release the Quaffle if they are not carrying it, ...

Output: You must output the description of the main events of the game, one event per line. More precisely:

- Each time a team scores, you must print t RED GOAL or t BLUE GOAL, depending on the team who scored, where t is the current time (the position of the action in the list of actions, starting from 0). In the case where a player scores in the wrong goal (a red player scores in the red goal, or a blue player scores in the blue goal), you must print the name of the team who wins one point, that is, the other team.
- Each time a player is eliminated, you must print t p ELIMINATED, where t is the current time and p is the player who is eliminated. The format to print the player is the same as in the input.

The events must be printed in ascending order of t. If several players are eliminated at the same time, the events must be written in alphabetical order: B0, ..., B9, R0, ... R9.

At the end of the game, you must print the final score as: FINAL SCORE: r b, where r is the score of the red team and b is the score of the blue team.

Examples:
input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
12
R0 D
R0 C .Q
R0 R
R0 T
R0 D
B0 R
B0 U
B0 C .Q
B0 L
B0 L
B0 L
B0 T
output:
11 BLUE GOAL
FINAL SCORE: 0 1

input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
5
R0 D
R0 C .Q
R0 L
R0 L
R0 T
output:
4 BLUE GOAL
FINAL SCORE: 0 1

input:
5 5
.. .. .. .. ..
.. .. .. .. ..
RG R0 .Q B0 BG
.. .. .. .. ..
.. .. .B .. ..
5
.B L
.B U
.B U
B0 L
B0 L
output:
2 R0 ELIMINATED
4 B0 ELIMINATED
FINAL SCORE: 0 0

Note: In the first example, the red player takes the Quaffle, move it and throw it. The blue player catches the ball, goes to the red goal and scores.

In the second example, the red player takes the ball and scores in the goal of their own team: the blue team wins a point.

In the third example, the Bludger goes at the position of R0: R0 is eliminated. Then, B0 moves to the position of the Bludger: B0 is eliminated too.

You can find one more example in the easy version of the problem

Buggy Code:
#include <bits/stdc++.h>
using namespace std;

typedef pair <int, int> ii;

const int Maxn = 105;
const int Maxd = 4;
const string dirs = "UDLR";
const int dy[Maxd] = {-1, 1, 0, 0};
const int dx[Maxd] = {0, 0, -1, 1};

char tmp[3];
int n, m;
int G[Maxn][Maxn];
int res[2];
map <string, ii> M;

string Read()
{
    scanf("%s", tmp);
    return tmp;
}

int main()
{
    scanf("%d %d", &n, &m);
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++) {
            string s = Read();
            if (s[1] == 'G')
                G[i][j] = s[0] == 'B'? 1: 2;
            else if (s[0] == 'R' || s[0] == 'B')
                M[s] = ii(i, j);
        }
    int T;
    scanf("%d", &T);
    for (int i = 0; i < T; i++) {
        string s = Read();
        char typ; scanf(" %c", &typ);
        if ((s[0] == 'R' || s[0] == 'B') && isdigit(s[1])) {
            int p = dirs.find(typ);
            if (p != string::npos) {
                M[s].first += dy[p];
                M[s].second += dx[p];
            } else if (typ == 'T') {
                int goal = G[M[s].first][M[s].second];
                if (goal > 0) {
                    printf("%d %s GOAL\n", i, goal == 1? "RED": "BLUE");
                    res[goal - 1]++;
                }
            } else {
                string ball = Read();
            }
        }
    }
    printf("FINAL SCORE: %d %d\n", res[0], res[1]);
    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To create a challenging test input that exposes the bug in the provided buggy code, we need to focus on edge cases and scenarios that the code might handle incorrectly. Here are the key points to consider:

1. **Player Elimination by Bludger**: Ensure that the code correctly handles the elimination of players by the Bludger.
2. **Scoring in the Wrong Goal**: Ensure that the code correctly handles a player scoring in the wrong goal.
3. **Movement and Actions**: Ensure that the code correctly handles movements and actions, especially when players are carrying the Quaffle.
4. **Initial Positioning**: Ensure that the initial positions of players, goals, and the Quaffle are set up in a way that can lead to edge cases.

Given these points, let's create a small-scale test input that includes these scenarios:

```plaintext
5 5
.. .. .. .. ..
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
.. .. .B .. ..
10
R0 D
R0 C .Q
R0 R
R0 T
.B U
B0 U
B0 C .Q
B0 L
B0 T
B0 R
```

### Explanation of the Test Input:
1. **Field Setup**:
   - The field is a 5x5 grid.
   - Red goal (RG) is at (2, 2).
   - Blue goal (BG) is at (2, 4).
   - Red player (R0) starts at (2, 3).
   - Blue player (B0) starts at (2, 3).
   - The Quaffle (.Q) starts at (2, 3).
   - The Bludger (.B) starts at (4, 3).

2. **Actions**:
   - **Step 0**: R0 moves down (D) to (3, 3).
   - **Step 1**: R0 catches the Quaffle (C .Q).
   - **Step 2**: R0 moves right (R) to (3, 4).
   - **Step 3**: R0 throws the Quaffle (T) at the blue goal, scoring a point for the red team.
   - **Step 4**: The Bludger moves up (U) to (3, 3).
   - **Step 5**: B0 moves up (U) to (1, 3).
   - **Step 6**: B0 catches the Quaffle (C .Q).
   - **Step 7**: B0 moves left (L) to (1, 2).
   - **Step 8**: B0 throws the Quaffle (T) at the red goal, scoring a point for the blue team.
   - **Step 9**: B0 moves right (R) to (1, 3).

### Expected Output:
```plaintext
3 RED GOAL
8 BLUE GOAL
4 R0 ELIMINATED
FINAL SCORE: 1 1
```

This test input includes:
- A player scoring in the correct goal.
- A player scoring in the wrong goal.
- A player being eliminated by the Bludger.
- Movements and actions that should be correctly handled by the code.

By using this test input, you can verify if the buggy code correctly handles these scenarios and identify any issues.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Medium)
time_limit_ms: 1000
memory_limit_mb: 256
Description: This afternoon, you decided to enjoy the first days of Spring by taking a walk outside. As you come near the Quidditch field, you hear screams. Once again, there is a conflict about the score: the two teams are convinced that they won the game! To prevent this problem from happening one more time, you decide to get involved in the refereeing of the matches.

Now, you will stay in the stadium to watch the game and count the score. At the end of the game, you will decide the winner.

Today, two teams are competing: the red Gryffindor (R) and the blue Ravenclaw (B) team. Each team is composed of $$$P$$$ players ($$$1 \leq P \leq 10$$$).

The field is a rectangle of $$$N$$$ lines and $$$M$$$ columns ($$$3 \leq N, M \leq 99$$$, $$$N$$$ and $$$M$$$ are odd). All the positions are integers, and several entities are allowed to be at the same position in the field. At the beginning of the game, the field contains goals for the two teams (each team can own between one and five goals), the players, and exactly one Quaffle. In this version of the problem, one Bludger can be present. An other type of ball will be available in the harder version of the problem.

A game is composed of $$$T$$$ steps ($$$0 \leq T \leq 10000$$$). At each step, one entity on the field (a player or a ball) performs one action. All entities can move. A player can also catch a ball or throw the Quaffle that it is carrying. To catch a ball, a player must be located on the same cell as it. The Quaffle does not perform any action while it is being carried; it only follows the movements of the player. If a player carrying the Quaffle decides to throw it, the Quaffle is simply put at the current position of the player. If a player is on the same cell as a Bludger (either after a movement from the player or the Bludger), the player is eliminated. If the player is eliminated while it is carrying the Quaffle, the Quaffle remains on the cell containing both the player and the Bludger after the move. It is guaranteed that this never occurs while the player is in a cell containing a goal.

To win a point, a player must leave the Quaffle at a goal of the other team. When it does, the team of the player wins one point, and the Quaffle instantly moves to the middle of the field (the cell at the $$$(M+1)/2$$$-th column of the $$$(N+1)/2$$$-th line of the field, starting from 1). There is no goal in the middle of the field. If a player puts the ball in its own goal, the other team wins the point.

Input: On the first line, the integers $$$N$$$ and $$$M$$$.

The description of the field follows: $$$N$$$ lines of $$$M$$$ pairs of characters separated by spaces. Each pair of characters represents a position on the field. It can be either:

- .. to represent an empty cell
- R0, ..., R9, B0, ..., B9 to represent a player. The first character is the team of the player, and the second is the number of the player in the team. Each pair of characters is unique, but it is not guaranteed that all the pairs appear in the grid.
- RG or BG to represent a goal. The blue team tries to put the ball in a red goal (RG) while the red team tries to put the ball in a blue goal (BG).
- .Q to represent the Quaffle, which is the ball that the players use to score goals.
- .B to represent a Bludger.

The next line contains $$$T$$$, the number of steps that compose the game. $$$T$$$ lines follow, each describing one action. It contains several pieces of information separated by a space. First, a pair of characters representing the entity that must perform the action. Second, the description of the action:

- U, D, L, R indicate that the entity moves on the grid. It can move to the top of the grid (U), to the bottom (D), to the left (L), or to the right (R). Each entity moves by only one cell at a time.
- C indicates that the player catches the ball (only a player can catch a ball). Then, there is a space followed by a pair of characters: the description of the ball caught by the player. This information is needed since several balls can be in the same cell.
- T indicates that the player throws the Quaffle that it is carrying.

All the actions performed by the entities are guaranteed to be valid: the players stay in the field, don't catch a ball if they are not in the same cell, don't release the Quaffle if they are not carrying it, ...

Output: You must output the description of the main events of the game, one event per line. More precisely:

- Each time a team scores, you must print t RED GOAL or t BLUE GOAL, depending on the team who scored, where t is the current time (the position of the action in the list of actions, starting from 0). In the case where a player scores in the wrong goal (a red player scores in the red goal, or a blue player scores in the blue goal), you must print the name of the team who wins one point, that is, the other team.
- Each time a player is eliminated, you must print t p ELIMINATED, where t is the current time and p is the player who is eliminated. The format to print the player is the same as in the input.

The events must be printed in ascending order of t. If several players are eliminated at the same time, the events must be written in alphabetical order: B0, ..., B9, R0, ... R9.

At the end of the game, you must print the final score as: FINAL SCORE: r b, where r is the score of the red team and b is the score of the blue team.

Examples:
input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
12
R0 D
R0 C .Q
R0 R
R0 T
R0 D
B0 R
B0 U
B0 C .Q
B0 L
B0 L
B0 L
B0 T
output:
11 BLUE GOAL
FINAL SCORE: 0 1

input:
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
5
R0 D
R0 C .Q
R0 L
R0 L
R0 T
output:
4 BLUE GOAL
FINAL SCORE: 0 1

input:
5 5
.. .. .. .. ..
.. .. .. .. ..
RG R0 .Q B0 BG
.. .. .. .. ..
.. .. .B .. ..
5
.B L
.B U
.B U
B0 L
B0 L
output:
2 R0 ELIMINATED
4 B0 ELIMINATED
FINAL SCORE: 0 0

Note: In the first example, the red player takes the Quaffle, move it and throw it. The blue player catches the ball, goes to the red goal and scores.

In the second example, the red player takes the ball and scores in the goal of their own team: the blue team wins a point.

In the third example, the Bludger goes at the position of R0: R0 is eliminated. Then, B0 moves to the position of the Bludger: B0 is eliminated too.

You can find one more example in the easy version of the problem

Buggy Code:
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef std::vector<ll> vll;
typedef std::vector<ld> vld;
typedef std::vector<std::vector<ll> > vvll;
typedef std::vector<std::vector<ld> > vvld;
typedef std::vector<string> vstr;
typedef std::vector<bool> vbl;
typedef std::vector<std::pair<ll,ll> > vpll;
typedef std::pair<ll,ll> pll;
#define fi(x, n) for (ll i = x; i < n; ++i)
#define rfi(x, n) for (ll i = x; i >= n; --i)
#define fj(x, n) for (ll j = x; j < n; ++j)
#define rfj(x, n) for (ll j = x; j >= n; --j)
#define in(n) long long int n;   cin >> n
#define inarr(n, arr)   vector<ll> arr(n); fi(0,n) cin >> arr[i]
#define input(vec,a,b) for(ll i_itr = a;i_itr<b;++i_itr) cin>>vec[i_itr]
#define print(vec,a,b) for(ll i_itr=a;i_itr<b;++i_itr) cout<<vec[i_itr]<<" "; cout<<"\n"
#define ha cout<<"YES"<<endl
#define na cout<<"NO"<<endl
#define pb push_back
#define all(x) (x).begin(), (x).end()
const ll mod = 1000000007;
const long double pi=3.14159265358979323846264338327950288419716939937510582097494459230;

// const ll N=1e6;
// bool isp[N];
// vector<ll> pr;

// void build_primes() // 79000 primes for N=1e6 in O(N)
// {
//     isp[0]=0;
//     isp[1]=0;
//     pr.push_back(1);
//     for(ll i=2;i<N;i++)isp[i]=1;
//     for(ll i=2;i<N;i++)
//     {
//         if(isp[i])
//         {
//             pr.push_back(i);
//             for(ll j=i;j<N;j+=i){
//                 isp[j]=0;
//             }
//         }
//     }
// }

// ll fastPrime(ll a)
// {
//     if (a != 2 && a % 2 == 0 || a < 2)
//         return 0;
//     for(ll i = 3; i * i <= a; i += 2)
//     {
//         if(a % i == 0)
//             return 0;
//     }
//     return 1;
// }

// ll digit_sum(ll n)
// {
//     ll ret = 0;
//     while(n)
//     {
//         ret += n % 10;
//         n /= 10;
//     }
//     return ret;
// }

// stoi(str) string to int conversion
// to_string(num) number to string conversion
// transform(str.begin(), str.end(), str.begin(), ::tolower);
// transform(str.begin(), str.end(), str.begin(), ::toupper;
// str[i]=tolower(str[i]); for single character

// ll binarySearch(ll low,ll high,vector<ll> &v,ll element) // strictly less element
// {
//     ll ans=high+1;
//     while(low<=high)
//     {
//         ll mid=(low+high)/2;
//         if(v[mid]>=element)
//         {
//             ans=mid;
//             high=mid-1;
//         }
//         else
//             low=mid+1;
//     }
//     return ans;
// }

void solve()
{
    in(n);
    in(m);
    map<string,pll> mp;
    mp[".B"]={-1,-1};
    vector<string> ans,ply={"B0","B1","B2","B3","B4","B5","B6","B7","B8","B9","R0","R1","R2","R3","R4","R5","R6","R7","R8","R9"};
    fi(0,20)
        mp[ply[i]]={-1,-1};
    vector<vector<string>> v(n,vector<string>(m));
    fi(0,n)
    {
        fj(0,m)
        {
            cin>>v[i][j];
            if(v[i][j]!="..")
                mp[v[i][j]]={i,j};
        }
    }
    // ha;
    // fi(0,n)
    // {
    //     fj(0,m)
    //         cout<<v[i][j]<<" ";
    //     cout<<endl;
    // }
    in(q);
    ll x=-1,y=-1,wb=0,wr=0;
    char player='#',action;
    fi(0,q)
    {
        string s;
        cin>>s;
        cin>>action;
        // cout<<player<<" "<<action<<endl;
        if(action=='U')
            --mp[s].first;
        else if(action=='D')
            ++mp[s].first;
        else if(action=='L')
            --mp[s].second;
        else if(action=='R')
            ++mp[s].second;
        else if(action=='C')
        {
            string tmp;
            cin>>tmp;
        }
        else if(action=='T')
        {
            string win;
            // cout<<v[mp[s].first][mp[s].second]<<endl;
            if(s[0]=='B')
            {
                if(v[mp[s].first][mp[s].second]=="BG")
                    win=" RED",wr++;
                else if(v[mp[s].first][mp[s].second]=="RG")
                    win=" BLUE",wb++;
                else
                    continue;
            }
            else
            {
                if(v[mp[s].first][mp[s].second]=="BG")
                    win=" RED",wr++;
                else if(v[mp[s].first][mp[s].second]=="RG")
                    win=" BLUE",wb++;
                else
                    continue;
            }
            // cout<<win<<endl;
            ans.pb(to_string(i)+win+" GOAL");
            x=-1;
            y=-1;
        }

        if(mp[".B"].first==-1)
            continue;
        fj(0,20)
        {
            if(mp[ply[j]].first==mp[".B"].first && mp[ply[j]].second==mp[".B"].second)
            {
                ans.pb(to_string(i)+" "+ply[j]+" ELIMINATED");
            }
        }
    }
    ans.pb("FINAL SCORE: "+to_string(wr)+" "+to_string(wb));
    fi(0,ans.size())
        cout<<ans[i]<<endl;
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    // cout << fixed<<setprecision(15); ///activate it if the answers are in decimal.
    ll T=1;
    // cin>>T;
    while(T--)
    {
        solve();
    }
    return 0;
}

**Instructions:**
- Focus on edge cases or scenarios that maximize the failure probability in faulty solutions.
- Due to the output length limit, you should generate a **small-scale** test input that is **complete and valid**.
- Output the test input directly, not code to generate it.

**Output format:**
```plaintext
{test input}
```

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the given code, we need to consider several edge cases and scenarios that can maximize the failure probability. Here are the steps to think through the problem:

1. **Initial Setup:**
   - Ensure the field dimensions and initial positions are valid.
   - Place the goals, players, Quaffle, and Bludger in strategic positions.

2. **Movement and Actions:**
   - Plan a sequence of actions that can lead to scoring, eliminations, and other critical events.
   - Ensure the actions are valid and follow the rules of the game.

3. **Edge Cases:**
   - Test scenarios where players move into the same cell as the Bludger.
   - Test scenarios where players score in their own goals.
   - Test scenarios where the Quaffle is thrown and caught in quick succession.

4. **Output:**
   - Ensure the test input is complete and valid.

Here is a small-scale test input that covers these aspects:

```plaintext
5 5
.. .. .. .. ..
.. .. .. .. ..
RG R0 .Q B0 BG
.. .. .. .. ..
.. .. .B .. ..
5
.B L
.B U
.B U
B0 L
B0 L
```

### Explanation:
1. **Field Setup:**
   - The field is a 5x5 grid.
   - Red goal (RG) and Blue goal (BG) are placed in the center of the field.
   - Red player (R0) and Blue player (B0) are placed next to the goals.
   - The Quaffle (.Q) is placed next to the Red player.
   - The Bludger (.B) is placed in the bottom left corner.

2. **Actions:**
   - The Bludger moves left, up, and up, eventually reaching the position of the Red player (R0), eliminating R0.
   - The Blue player (B0) then moves left twice, reaching the position of the Bludger and getting eliminated.
   - No scoring happens in this sequence, but the eliminations are critical to test the bug.

3. **Expected Output:**
   - The Red player (R0) should be eliminated at time 2.
   - The Blue player (B0) should be eliminated at time 4.
   - The final score should be 0-0.

This test input should help expose any issues in the code related to player eliminations and the order of events.