**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Easy)
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. Other types of balls will be available in the harder versions 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.

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.

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 in the next versions of the problem, several balls may 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.

The events must be printed in ascending order of t.

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:
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
13
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 C .Q
R0 D
R0 R
R0 R
R0 T
output:
6 BLUE GOAL
12 RED GOAL
FINAL SCORE: 1 1

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

Note: In the first example, a blue player goes to the middle of the grid, at the position of the Quaffle. He takes it, goes to the goal of the red team, and lets the ball there. He scores! The ball gets back to the middle of the field, a red player takes it and scores too.

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

Buggy Code:
// LUOGU_RID: 164066388
#include<bits/stdc++.h>
using namespace std;
int n,m,t,tim,blue,red,rs,bs;
struct node{
    int x,y;
    char ball;
}b[15],r[15],gf,yz,fz;
int qm[105][105];
void end()
{
	cout<<"FINAL SCORE: "<<rs<<" "<<bs;
	exit(0);
}
void died(int l,int num)
{
	if(l==1)
	{
		blue--;
		b[num].x=b[num].y=0;
		cout<<tim<<" B"<<num<<" ELIMINATED"<<'\n';
	}
	if(l==2)
	{
		red--;
		r[num].x=r[num].y=0;
		cout<<tim<<" R"<<num<<" ELIMINATED"<<'\n';
	}
}
void zb(node &mb,int x,int y){mb.x=x;mb.y=y;}
void ballcz(node &mb,char c,bool isgf)
{
	if(c=='U')mb.x--;
	if(c=='D')mb.x++;
	if(c=='L')mb.y--;
	if(c=='R')mb.y++;
	if(isgf)
	{
		for(int i=0;i<=9;i++)
		{
			if(b[i].x==0&&b[i].y==0)continue;
			if(yz.x==b[i].x&&yz.y==b[i].y)
			died(1,i);
		}
		for(int i=0;i<=9;i++)
		{
			if(r[i].x==0&&r[i].y==0)continue;
			if(yz.x==r[i].x&&yz.y==r[i].y)
			died(2,i);
		}
	}
}
void cz(string s,char c)
{
	int num;
	if(s[0]!='.')num=s[1]-'0';
	else
	{
		if(s==".B")ballcz(yz,c,true);
		if(s==".Q")ballcz(gf,c,false);
		if(s==".S")ballcz(fz,c,false);
		return;
	}
	if(c=='U')
	{
		if(s[0]=='B')b[num].x--;
		else r[num].x--;
	}
	if(c=='D')
	{
		if(s[0]=='B')b[num].x++;
		else r[num].x++;
	}
	if(c=='L')
	{
		if(s[0]=='B')b[num].y--;
		else r[num].y--;
	}
	if(c=='R')
	{
		if(s[0]=='B')b[num].y++;
		else r[num].y++;
	}
	if(c=='C')
	{
		string ball;cin>>ball;
		if(ball==".Q")
		{
			if(s[0]=='R')gf=r[num];
			else gf=b[num];
		}
		if(ball==".S")
		{
			cout<<tim;
			if(s[0]=='R')rs+=10,cout<<" RED";
			else bs+=10,cout<<" BLUE";
			cout<<" CATCH GOLDEN SNITCH"<<'\n';
			end();
		}
	}
	if(c=='T')
	{
		if(s[0]=='R')
		{
			if(qm[r[num].x][r[num].y]==1)
			{
				cout<<tim<<" BLUE GOAL"<<'\n';
				bs++;gf.x=(n+1)/2;gf.y=(m+1)/2;
			}
			if(qm[r[num].x][r[num].y]==2)
			{
				cout<<tim<<" RED GOAL"<<'\n';
				rs++;gf.x=(n+1)/2;gf.y=(m+1)/2;
			}
		}
		if(s[0]=='B')
		{
			if(qm[b[num].x][b[num].y]==1)
			{
				cout<<tim<<" BLUE GOAL"<<'\n';
				bs++;gf.x=(n+1)/2;gf.y=(m+1)/2;
			}
			if(qm[r[num].x][r[num].y]==2)
			{
				cout<<tim<<" RED GOAL"<<'\n';
				rs++;gf.x=(n+1)/2;gf.y=(m+1)/2;
			}
		}
	}
	ballcz(gf,'N',true);
}
int main()
{
	cin.tie(0)->sync_with_stdio(0);
    cin>>n>>m;
    for(int i=1;i<=n;i++)
    for(int j=1;j<=m;j++)
    {
        string s;
        cin>>s;
        if(s=="RG")qm[i][j]=1;
        else if(s=="BG")qm[i][j]=2;
        else if(s[0]=='R')
		{
			red++;
			zb(r[s[1]-'0'],i,j);
		}
        else if(s[0]=='B')
		{
			blue++;
			zb(b[s[1]-'0'],i,j);
		}
        else if(s==".Q")zb(gf,i,j);
        else if(s==".B")zb(yz,i,j);
        else if(s==".S")zb(fz,i,j);
    }
    cin>>t;
    for(int i=1;i<=t;i++)
    {
        string s;char c;
        cin>>s>>c;
        cz(s,c);
        tim++;
    }
    end();
    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:
```plaintext
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
13
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 C .Q
R0 D
R0 R
R0 R
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 (Easy)
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. Other types of balls will be available in the harder versions 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.

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.

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 in the next versions of the problem, several balls may 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.

The events must be printed in ascending order of t.

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:
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
13
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 C .Q
R0 D
R0 R
R0 R
R0 T
output:
6 BLUE GOAL
12 RED GOAL
FINAL SCORE: 1 1

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

Note: In the first example, a blue player goes to the middle of the grid, at the position of the Quaffle. He takes it, goes to the goal of the red team, and lets the ball there. He scores! The ball gets back to the middle of the field, a red player takes it and scores too.

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

Buggy Code:
# /**
#  *     author: brownfox2k6
#  *    created: 05/08/2024 21:39:39 Hanoi, Vietnam
# **/

n, m = map(int, input().split())
rg = []
bg = []
player = dict()
for i in range(n):
  s = input().split()
  for j in range(m):
    if s[j] == 'RG':
      rg.append([i, j])
    elif s[j] == 'BG':
      bg.append([i, j])
    elif s[j] == '.Q':
      ball = [i, j]
    else:
      player[s[j]] = [i, j]

carry = None
bs = rs = 0
for t in range(1, int(input()) + 1):
  p, d = input().split()[:2]
  if d == 'C':
    carry = p
  elif d == 'T':
    carry = None
  elif d == '.Q':
    if d == 'U':
      ball[0] -= 1
    elif d == 'D':
      ball[0] += 1
    elif d == 'L':
      ball[1] -= 1
    elif d == 'R':
      ball[1] += 1
  else:
    if d == 'U':
      player[p][0] -= 1
    elif d == 'D':
      player[p][0] += 1
    elif d == 'L':
      player[p][1] -= 1
    elif d == 'R':
      player[p][1] += 1
    if carry == p:
      ball = player[p]
      if ball in rg:
        bs += 1
        print(t, "BLUE GOAL")
        carry = None
        ball = [n // 2, m // 2]
      elif ball in bg:
        rs += 1
        print(t, "RED GOAL")
        carry = None
        ball = [n // 2, m // 2]
print("FINAL SCORE:", rs, bs)

**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 BG
.. B0 ..
10
R0 D
R0 C .Q
R0 R
R0 R
R0 T
B0 U
B0 C .Q
B0 L
B0 L
B0 T
```

3 3
.. R0 ..
RG .Q BG
.. B0 ..
10
R0 D
R0 C .Q
R0 R
R0 R
R0 T
B0 U
B0 C .Q
B0 L
B0 L
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 (Easy)
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. Other types of balls will be available in the harder versions 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.

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.

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 in the next versions of the problem, several balls may 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.

The events must be printed in ascending order of t.

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:
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
13
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 C .Q
R0 D
R0 R
R0 R
R0 T
output:
6 BLUE GOAL
12 RED GOAL
FINAL SCORE: 1 1

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

Note: In the first example, a blue player goes to the middle of the grid, at the position of the Quaffle. He takes it, goes to the goal of the red team, and lets the ball there. He scores! The ball gets back to the middle of the field, a red player takes it and scores too.

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

Buggy Code:
# /**
#  *     author: brownfox2k6
#  *    created: 05/08/2024 21:39:39 Hanoi, Vietnam
# **/

n, m = map(int, input().split())
rg = []
bg = []
player = dict()
for i in range(n):
  s = input().split()
  for j in range(m):
    if s[j] == 'RG':
      rg.append([i, j])
    elif s[j] == 'BG':
      bg.append([i, j])
    elif s[j] == '.Q':
      ball = [i, j]
    else:
      player[s[j]] = [i, j]

carry = None
bs = rs = 0
for t in range(1, int(input()) + 1):
  p, d = input().split()[:2]
  if d == 'C':
    carry = p
  elif d == 'T':
    carry = None
  else:
    if d == 'U':
      player[p][0] -= 1
    elif d == 'D':
      player[p][0] += 1
    elif d == 'L':
      player[p][1] -= 1
    elif d == 'R':
      player[p][1] += 1
    if carry == p:
      ball = player[p]
      if ball in rg:
        bs += 1
        print(t, "BLUE GOAL")
        carry = None
        ball = [n // 2, m // 2]
      elif ball in bg:
        rs += 1
        print(t, "RED GOAL")
        carry = None
        ball = [n // 2, m // 2]
print("FINAL SCORE:", rs, bs)

**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 expose the bug in the provided code, we need to create a test case that triggers the logic where a player scores in the wrong goal, and the code incorrectly handles this scenario. The code should correctly award the point to the opposing team, but it might have a flaw in this logic.

Let's consider a small-scale test input with a simple field setup and a sequence of actions that lead to a player scoring in the wrong goal. Here's a step-by-step approach to create the test case:

1. **Field Setup:**
   - Small field size (3x5) to keep the input simple.
   - Place one red goal (RG) and one blue goal (BG) on the field.
   - Place one red player (R0) and one blue player (B0) on the field.
   - Place the Quaffle (.Q) on the field.

2. **Actions:**
   - Red player (R0) moves to the Quaffle and catches it.
   - Red player (R0) moves to the red goal (RG) and throws the Quaffle.
   - The blue team should be awarded the point because the red player scored in the wrong goal.

Here is the test input:

```plaintext
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
5
R0 D
R0 C .Q
R0 R
R0 R
R0 T
```

Explanation of the actions:
1. `R0 D`: Red player moves down to the Quaffle's position.
2. `R0 C .Q`: Red player catches the Quaffle.
3. `R0 R`: Red player moves right.
4. `R0 R`: Red player moves right again, reaching the red goal (RG).
5. `R0 T`: Red player throws the Quaffle into the red goal.

Expected output:
```plaintext
4 BLUE GOAL
FINAL SCORE: 0 1
```

This test case should expose the bug if the code incorrectly handles the scenario where a player scores in the wrong goal.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Easy)
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. Other types of balls will be available in the harder versions 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.

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.

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 in the next versions of the problem, several balls may 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.

The events must be printed in ascending order of t.

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:
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
13
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 C .Q
R0 D
R0 R
R0 R
R0 T
output:
6 BLUE GOAL
12 RED GOAL
FINAL SCORE: 1 1

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

Note: In the first example, a blue player goes to the middle of the grid, at the position of the Quaffle. He takes it, goes to the goal of the red team, and lets the ball there. He scores! The ball gets back to the middle of the field, a red player takes it and scores too.

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

Buggy Code:
line,col = map(int,input().split())
red_pos = [-1,-1]*10
blu_pos = [-1,-1]*10
red_goal_zone = []
blu_goal_zone = []
quidditch_location = [-1,-1]
score_red = 0
score_blue = 0

#fetch location
for i in range(line):
    inp = [x for x in input().split()]
    for b, entity in enumerate(inp):
        if entity == 'RG':
            red_goal_zone.append([b,i])
        elif entity == 'BG':
            blu_goal_zone.append([b,i])
        elif 'R' in entity:
            red_pos[int(entity[1])] = [b,i]
        elif 'B' in entity:
            blu_pos[int(entity[1])] = [b,i]
        elif entity == '.Q':
            quidditch_location = [b,i]

#actually doing something with it

for t in range(int(input())):
    inp = [x for x in input().split()]
    entity = inp[0]
    action = inp[1]
    tie_ball_loc = None
    if entity[0] == 'R':
        if action == 'C':
            tie_ball_loc = entity
        elif action == 'T':
            tie_ball_loc = None
        else:
            if action == 'U':
                red_pos[int(entity[1])][1] -= 1
            elif action == 'D':
                red_pos[int(entity[1])][1] += 1
            elif action == 'R':
                red_pos[int(entity[1])][0] += 1
            elif action == 'L':
                red_pos[int(entity[1])][0] -= 1
    elif entity[0] == 'B':
        if action == 'C':
            tie_ball_loc = entity
        elif action == 'T':
            tie_ball_loc = None
        else:
            if action == 'U':
                blu_pos[int(entity[1])][1] -= 1
            elif action == 'D':
                blu_pos[int(entity[1])][1] += 1
            elif action == 'R':
                blu_pos[int(entity[1])][0] += 1
            elif action == 'L':
                blu_pos[int(entity[1])][0] -= 1
    if tie_ball_loc != None:
        if tie_ball_loc[0] == 'R':
            quidditch_location = red_pos[int(tie_ball_loc[1])]
        else:
            quidditch_location = blu_pos[int(tie_ball_loc[1])]
    else:
        if quidditch_location in red_goal_zone:
            print(t+1, " BLUE GOAL")
            score_blue += 1
            quidditch_location = [(line+1)//2 - 1,(col+1)//2 - 1]
        elif quidditch_location in blu_goal_zone:
            print(t+1, " RED GOAL")
            score_red += 1
            quidditch_location = [(line+1)//2 - 1,(col+1)//2 - 1]
print(f"FINAL SCORE: {score_red} {score_blue}")

**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
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
9
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 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 (Easy)
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. Other types of balls will be available in the harder versions 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.

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.

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 in the next versions of the problem, several balls may 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.

The events must be printed in ascending order of t.

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:
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
13
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 C .Q
R0 D
R0 R
R0 R
R0 T
output:
6 BLUE GOAL
12 RED GOAL
FINAL SCORE: 1 1

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

Note: In the first example, a blue player goes to the middle of the grid, at the position of the Quaffle. He takes it, goes to the goal of the red team, and lets the ball there. He scores! The ball gets back to the middle of the field, a red player takes it and scores too.

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

Buggy Code:
#include <iostream>
#include <string>
#define ll long long

using namespace std;

int main(){
    int n, m;
    cin >> n >> m;
    int rx[10], ry[10], bx[10], by[10], rgx[5], rgy[5], bgx[5], bgy[5];
    int qx = m/2, qy = n/2;
    int rc = 0, bc = 0, rgc = 0, bgc = 0;
    ll bm = 0, rm = 0;
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
            string inp;
            cin >> inp;
            if (inp[0] == 'R') {
                if (inp == "RG") {
                    rgx[rgc] = j;
                    rgy[rgc] = i;
                    rgc++;
                } else {
                    rx[rc] = j;
                    ry[rc] = i;
                    rc++;
                }
            } else if (inp[0] == 'B') {
                if (inp == "BG") {
                    bgx[bgc] = j;
                    bgy[bgc] = i;
                    bgc++;
                } else {
                    bx[bc] = j;
                    by[bc] = i;
                    bc++;
                }
            }
        }
    }
    ll T;
    cin >> T;
    for (ll t = 0; t < T; ++t) {
        string p;
        char a;
        cin >> p >> a;
        if (a == 'C') {
            cin >> a;
            cin >> a;
        } else {
            int pi = p[1]-'0';
            if (p[0] == 'B') {
                if (a == 'L') {
                    bx[pi]--;
                } else if (a == 'R') {
                    bx[pi]++;
                } else if (a == 'U') {
                    by[pi]--;
                } else if (a == 'D') {
                    by[pi]++;
                } else if (a == 'T') {
                    qx = bx[pi];
                    qy = by[pi];
                }
            } else {
                if (a == 'L') {
                    rx[pi]--;
                } else if (a == 'R') {
                    rx[pi]++;
                } else if (a == 'U') {
                    ry[pi]--;
                } else if (a == 'D') {
                    ry[pi]++;
                } else if (a == 'T') {
                    qx = rx[pi];
                    qy = ry[pi];
                }
            }
            for (int i = 0; i < 5; ++i) {
                if (rgx[i] == qx && rgy[i] == qy) {
                    bm++;
                    qx = m/2;
                    qy = n/2;
                    cout << t << " BLUE GOAL" << endl;
                    break;
                } else if (bgx[i] == qx && bgy[i] == qy) {
                    rm++;
                    qx = m/2;
                    qy = n/2;
                    cout << t << " RED GOAL" << endl;
                    break;
                }
            }
        }
    }
    cout << "FINAL SCORE: " << rm << ' ' << bm << endl;
    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 provided buggy code, we need to focus on edge cases and scenarios that can potentially cause the code to fail. Here are some considerations:

1. **Initial Position of Entities**: Ensure that the initial positions of players, goals, and the Quaffle are set up in a way that can lead to complex interactions.
2. **Movement and Actions**: Design actions that involve moving the Quaffle to goals and ensuring that the scoring logic is tested.
3. **Scoring in the Wrong Goal**: Test scenarios where a player scores in the wrong goal to ensure the correct team gets the point.
4. **Multiple Goals**: Test scenarios with multiple goals to ensure the code handles them correctly.

Given these considerations, let's create a small-scale test input:

```plaintext
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
10
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 C .Q
R0 T
```

### Explanation:
- **Initial Setup**:
  - The field is a 5x5 grid.
  - Red goals (RG) are at (1, 1), (1, 3), and (3, 1).
  - Blue goals (BG) are at (1, 4), (3, 4), and (5, 4).
  - Players: R0 at (3, 2), R1 at (1, 2), R2 at (5, 2), B0 at (3, 3), B1 at (1, 3), B2 at (1, 2).
  - The Quaffle (.Q) is at (3, 2).

- **Actions**:
  - B2 moves up twice, left, catches the Quaffle, moves left twice, and throws it (scores a blue goal).
  - R0 moves right, catches the Quaffle, and throws it (scores in the wrong goal, so the blue team gets the point).

This test input should help expose any issues in the scoring logic and handling of multiple goals and incorrect scoring.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Easy)
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. Other types of balls will be available in the harder versions 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.

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.

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 in the next versions of the problem, several balls may 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.

The events must be printed in ascending order of t.

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:
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
13
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 C .Q
R0 D
R0 R
R0 R
R0 T
output:
6 BLUE GOAL
12 RED GOAL
FINAL SCORE: 1 1

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

Note: In the first example, a blue player goes to the middle of the grid, at the position of the Quaffle. He takes it, goes to the goal of the red team, and lets the ball there. He scores! The ball gets back to the middle of the field, a red player takes it and scores too.

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

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

using namespace std;
int n,m,r,b,q;
int bx[12],by[12],rx[12],ry[12];
bool bg[120][120],rg[120][120];
bool stater[12],stateb[12];
void solve(){
    //The code goes here
    cin >> n >> m;
    for (int i=1;i<=n;i++){
        for (int j=1;j<=m;j++){
            char T,s;
            cin >> T >> s;
            if (T=='B'){
                if (s=='G'){
                    bg[i][j]=true;
                }
                else{
                    bx[s-'0']=i; by[s-'0']=j;
                    stateb[i]=false;
                }
            }
            if (T=='R'){
                if (s=='G'){
                    rg[i][j]=true;
                }
                else{
                    rx[s-'0']=i; ry[s-'0']=j;
                    stater[i]=false;
                }
            }
        }
    }
    cin >> q;
    for (int i=1;i<=q;i++){
        string s;
        char c;
        string s2;
        cin >> s >> c;
        if (s[0]=='B'){
            int num=s[1]-'0';
            if (c=='U'){
                bx[num]--;
            }
            if (c=='D'){
                bx[num]++;
            }
            if (c=='L'){
                by[num]--;
            }
            if (c=='R'){
                by[num]++;
            }
            if (c=='C'){
                cin >> s2;
                stateb[num]=true;
            }
            if (c=='T'){
                stateb[num]=false;
            }
            if (stateb[num] && i!=q){
                if (bg[bx[num]][by[num]]){
                    cout << i << " RED GOAL" << endl;
                    r++;
                    stateb[num]=false;
                }
                if (rg[bx[num]][by[num]]){
                    cout << i << " BLUE GOAL" << endl;
                    b++;
                    stateb[num]=false;
                }
            }
        }
        else{
            int num=s[1]-'0';
            if (c=='U'){
                rx[num]--;
            }
            if (c=='D'){
                rx[num]++;
            }
            if (c=='L'){
                ry[num]--;
            }
            if (c=='R'){
                ry[num]++;
            }
            if (c=='C'){
                cin >> s2;
                stater[num]=true;
            }
            if (c=='T'){
                stater[num]=false;
            }
            if (stater[num] && i!=q){
                if (bg[rx[num]][ry[num]]){
                    cout << i << " RED GOAL" << endl;
                    r++;
                    stater[num]=false;
                }
                if (rg[rx[num]][ry[num]]){
                    cout << i << " BLUE GOAL" << endl;
                    b++;
                    stater[num]=false;
                }
            }
        }
    }
    cout << "FINAL SCORE: " << r << " " << b << endl;
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int 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:
```plaintext
3 3
.. RG ..
.. .Q ..
.. .. BG
5
R0 U
R0 C .Q
R0 D
R0 D
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 (Easy)
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. Other types of balls will be available in the harder versions 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.

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.

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 in the next versions of the problem, several balls may 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.

The events must be printed in ascending order of t.

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:
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
13
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 C .Q
R0 D
R0 R
R0 R
R0 T
output:
6 BLUE GOAL
12 RED GOAL
FINAL SCORE: 1 1

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

Note: In the first example, a blue player goes to the middle of the grid, at the position of the Quaffle. He takes it, goes to the goal of the red team, and lets the ball there. He scores! The ball gets back to the middle of the field, a red player takes it and scores too.

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

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

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

#define ff first
#define ss second

ll ttt;
const ll INF=1e18;
const ll MOD=1e9+7;
const ll MOD2=998244353;
const ll N=200007;
const ll LG=20;
ll n,m,k;

struct position{
	int x;
	int y;

	position(int xx, int yy) : x(xx), y(yy) {}

	bool isEqual(position other){
		return this->x == other.x && this->y == other.y;
	}

	void move(char dir){
		if(dir=='L'){
			y--;
		}
		else if(dir=='R'){
			y++;
		}
		else if(dir=='U'){
			x--;
		}
		else{
			x++;
		}
	}
};

struct player : position{
	bool team;
	int number;

	player(bool tm, int num, int xx, int yy) : team(tm), number(num), position(xx, yy) {}
};

struct quaffle : position{
	quaffle() : position(0, 0) {}
	quaffle(int xx, int yy) : position(xx, yy) {}
};

struct goal : position{
	bool team;
	goal(bool tm, int xx, int yy) : team(tm), position(xx, yy) {}
};

struct field{
	vector<goal>goals;
	vector<player>p[2];
	quaffle q;
	pair<int,int>score={0,0};
	int time=-1;

	bool compPlayers(const player& x, const player& y){
		return x.number < y.number;
	}

	void init(){
        auto comparator = [this](const player& a, const player& b) {
            return compPlayers(a, b);
        };
        sort(p[0].begin(), p[0].end(), comparator);
        sort(p[1].begin(), p[1].end(), comparator);
	}

	void dummyAction(){
		time++;
	}

	void action(int i, int j, char tp){
		time++;
		if(tp=='T'){
			for(goal g:goals){
				if(g.isEqual(p[i][j])){
					if(g.team){
						score.ss++;
						cout<<time<<" BLUE GOAL"<<endl;
					}
					else{
						score.ff++;
						cout<<time<<" RED GOAL"<<endl;
					}
				}
			}
		}
		else{
			p[i][j].move(tp);
		}
	}
};

field f;

void precalc(){

}

void solve(){
	cin>>n>>m;
	for(int i=0;i<n;i++){
		for(int j=0;j<m;j++){
			string s;
			cin>>s;

			if(s==".."){
				continue;
			}

			if(s[0]=='R'){
				if(s[1]=='G'){
					f.goals.push_back(goal(true,i,j));
					continue;
				}
				f.p[0].push_back(player(true,s[1]-'0',i,j));
			}
			else if(s[0]=='B'){
				if(s[1]=='G'){
					f.goals.push_back(goal(false,i,j));
					continue;
				}
				f.p[1].push_back(player(false,s[1]-'0',i,j));
			}
			else{
				f.q=quaffle(i,j);
			}
		}
	}
	cin>>k;
	for(int i=0;i<k;i++){
		string s;
		cin>>s;
		char tp;
		cin>>tp;
		if(tp=='C'){
			cin>>s;
			f.dummyAction();
			continue;
		}
		if(s[0]=='R'){
			f.action(0,s[1]-'0',tp);
		}
		else{
			f.action(1,s[1]-'0',tp);
		}
	}
	cout<<"FINAL SCORE: "<<f.score.ff<<" "<<f.score.ss<<endl;
}

void clear(){

}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    // freopen("input.txt","r",stdin);
    // freopen("output.txt","w",stdout);
	precalc();
	ttt=1;
	// cin>>ttt;
	while(ttt--){
		clear();
		solve();
	}
}

**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 focus on edge cases or scenarios that might cause the code to fail. Here are the steps to create such a test input:

1. **Field Setup**: Ensure the field is small enough to be manageable but complex enough to test various scenarios.
2. **Initial Positions**: Place players and goals in positions that can lead to scoring or near-scoring scenarios.
3. **Actions**: Create a sequence of actions that can test the logic for scoring, especially focusing on the bug where the code might not correctly handle scoring in the wrong goal.

Let's create a small-scale test input that includes the following:
- A field with 3 rows and 5 columns.
- Players and goals placed in positions that can lead to scoring.
- A sequence of actions that includes a player scoring in the wrong goal and another player scoring correctly.

### Test Input
```plaintext
3 5
.. .. R0 .. ..
RG .. .Q .. BG
.. .. B0 .. ..
5
R0 D
R0 C .Q
R0 L
R0 L
R0 T
```

### Explanation
1. **Field Setup**:
   - 3 rows and 5 columns.
   - Red goal (RG) at (1, 1).
   - Blue goal (BG) at (1, 4).
   - Red player (R0) at (1, 2).
   - Blue player (B0) at (2, 2).
   - Quaffle (.Q) at (1, 3).

2. **Initial Positions**:
   - Red player (R0) is near the red goal.
   - Blue player (B0) is near the blue goal.
   - Quaffle is between the two goals.

3. **Actions**:
   - R0 moves down (D).
   - R0 catches the Quaffle (C .Q).
   - R0 moves left (L) twice.
   - R0 throws the Quaffle (T).

### Expected Output
```plaintext
4 BLUE GOAL
FINAL SCORE: 0 1
```

### Explanation of Expected Output
- At time 4, the red player (R0) scores in the red goal, which means the blue team wins a point.
- The final score is 0 for the red team and 1 for the blue team.

This test input is designed to expose the bug where the code might not correctly handle scoring in the wrong goal. By ensuring the red player scores in the red goal, we can check if the code correctly awards the point to the blue team.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Easy)
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. Other types of balls will be available in the harder versions 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.

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.

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 in the next versions of the problem, several balls may 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.

The events must be printed in ascending order of t.

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:
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
13
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 C .Q
R0 D
R0 R
R0 R
R0 T
output:
6 BLUE GOAL
12 RED GOAL
FINAL SCORE: 1 1

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

Note: In the first example, a blue player goes to the middle of the grid, at the position of the Quaffle. He takes it, goes to the goal of the red team, and lets the ball there. He scores! The ball gets back to the middle of the field, a red player takes it and scores too.

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

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

struct Coord {
    int x, y;
};

bool operator==(Coord a, Coord b) {
    return a.x == b.x && a.y == b.y;
}

int main() {
    int n, m;
    std::cin >> n >> m;

    std::vector<std::vector<int>> red_team(n, std::vector<int>(m, -1));
    std::vector<std::vector<int>> blue_team(n, std::vector<int>(m, -1));
    std::vector<std::vector<bool>> red_goal(n, std::vector<bool>(m));
    std::vector<std::vector<bool>> blue_goal(n, std::vector<bool>(m));
    Coord quaffle = {(n + 1) / 2 - 1, (m + 1) / 2 - 1};
    int red_score = 0, blue_score = 0;
    std::string ball_held_by; // Stores the entity that is holding the ball right now
    for (int i = 0; i < n; ++ i) {
        for (int j = 0; j < m; ++ j) {
            std::string str;
            std::cin >> str;
            if (str == "RG") {
                red_goal[i][j] = true;
            } else if (str == "BG") {
                blue_goal[i][j] = true;
            } else if (str[0] == 'R') {
                red_team[i][j] = str[1] - '0';
            } else if (str[0] == 'B') {
                blue_team[i][j] = str[1] - '0';
            } else if (str == ".Q") {
                quaffle = {i, j};
            }
        }
    }

    auto find_in_grid = [](std::vector<std::vector<int>> &grid, int x) {
        Coord ans = {-1, -1};
        for (int i = 0; i < grid.size(); ++ i) {
            for (int j = 0; j < grid[i].size(); ++ j) {
                if (grid[i][j] == x) {
                    ans = {i, j};
                    break;
                }
            }
        }
        if (ans.x == -1) {
            throw std::runtime_error("find_in_grid didn't work!");
        }
        return ans;
    };
    auto check_goal = [&](Coord pos) {
        if (red_goal[pos.x][pos.y]) {
            return 'R';
        }
        if (blue_goal[pos.x][pos.y]) {
            return 'B';
        }
        return '-';
    };

    int t;
    std::cin >> t;
    for (int i = 0; i < t; ++ i) {
        std::string entity;
        std::cin >> entity;
        int entity_num = entity[1] - '0';
        char action;
        std::cin >> action;
        std::string ball;
        if (action == 'C') {
            std::cin >> ball;
            if ((entity[0] == 'R' && find_in_grid(red_team, entity_num) == quaffle) || (entity[0] == 'B' && find_in_grid(blue_team, entity_num) == quaffle)) {
                ball_held_by = entity;
            }
        }

        if (action == 'T' && entity == ball_held_by) {
            ball_held_by.clear();
            // Check if we made a goal (and if so, which goal)
            Coord our_pos;
            if (entity[0] == 'R') {
                our_pos = find_in_grid(red_team, entity_num);
            } else {
                our_pos = find_in_grid(blue_team, entity_num);
            }
            char goal_present = check_goal(our_pos);
            if (goal_present == 'R') { // Someone scored in the red goal: blue gets the point
                std::cout << i << " BLUE GOAL\n";
                blue_score++;
                quaffle = {(n + 1) / 2 - 1, (m + 1) / 2 - 1};
            } else if (goal_present == 'B') {
                std::cout << i << " RED GOAL\n";
                red_score++;
                quaffle = {(n + 1) / 2 - 1, (m + 1) / 2 - 1};
            }
        }

        if (action == 'U') {
            if (entity[0] == 'R') {
                Coord pos = find_in_grid(red_team, entity_num);
                red_team[pos.x - 1][pos.y] = entity_num, red_team[pos.x][pos.y] = -1;
            } else {
                Coord pos = find_in_grid(blue_team, entity_num);
                blue_team[pos.x - 1][pos.y] = entity_num, blue_team[pos.x][pos.y] = -1;
            }
        } else if (action == 'D') {
            if (entity[0] == 'R') {
                Coord pos = find_in_grid(red_team, entity_num);
                red_team[pos.x + 1][pos.y] = entity_num, red_team[pos.x][pos.y] = -1;
            } else {
                Coord pos = find_in_grid(blue_team, entity_num);
                blue_team[pos.x + 1][pos.y] = entity_num, blue_team[pos.x][pos.y] = -1;
            }
        } else if (action == 'L') {
            if (entity[0] == 'R') {
                Coord pos = find_in_grid(red_team, entity_num);
                red_team[pos.x][pos.y - 1] = entity_num, red_team[pos.x][pos.y] = -1;
            } else {
                Coord pos = find_in_grid(blue_team, entity_num);
                blue_team[pos.x][pos.y - 1] = entity_num, blue_team[pos.x][pos.y] = -1;
            }
        } else if (action == 'R') {
            if (entity[0] == 'R') {
                Coord pos = find_in_grid(red_team, entity_num);
                red_team[pos.x][pos.y + 1] = entity_num, red_team[pos.x][pos.y] = -1;
            } else {
                Coord pos = find_in_grid(blue_team, entity_num);
                blue_team[pos.x][pos.y + 1] = entity_num, blue_team[pos.x][pos.y] = -1;
            }
        }

        if (entity == ball_held_by) {
            if (entity[0] == 'R') {
                quaffle = find_in_grid(red_team, entity_num);
            } else {
                quaffle = find_in_grid(blue_team, entity_num);
            }
        }
    }

    std::cout << "FINAL SCORE: " << red_score << " " << blue_score << "\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 code, we need to consider the following points:

1. **Initial Setup:**
   - Ensure the field dimensions and the initial positions of players, goals, and the Quaffle are set up in a way that can lead to edge cases.
   - Use small dimensions to keep the input manageable.

2. **Actions:**
   - Design actions that can lead to unexpected behaviors, such as a player moving to a goal and scoring, but the code incorrectly handles the score.
   - Include actions where a player catches the Quaffle and then performs actions that should result in a goal but don't due to the bug.

3. **Edge Cases:**
   - Consider scenarios where the Quaffle is initially in a goal.
   - Test scenarios where a player scores in their own goal.
   - Ensure the Quaffle is moved correctly after a goal.

Given these considerations, let's create a test input:

```plaintext
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
12
B0 R
B0 C .Q
B0 R
B0 R
B0 R
B0 T
R0 L
R0 L
R0 L
R0 T
B1 U
B1 T
```

### Explanation:
- **Field Setup:**
  - The field is 5x5 with goals for both teams.
  - The Quaffle is initially at the position of player B0.

- **Actions:**
  - **Steps 0-4:** B0 moves right, catches the Quaffle, and moves to the red goal.
  - **Step 5:** B0 throws the Quaffle at the red goal, which should score a point for the blue team.
  - **Steps 6-9:** R0 moves left to the blue goal.
  - **Step 10:** R0 throws the Quaffle at the blue goal, which should score a point for the red team.
  - **Steps 11-12:** B1 moves up and throws the Quaffle at the red goal, which should score a point for the blue team.

### Expected Output:
```plaintext
5 BLUE GOAL
10 RED GOAL
12 BLUE GOAL
FINAL SCORE: 1 2
```

This test input is designed to expose potential issues in the code, such as incorrect goal scoring and Quaffle placement.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Playing Quidditch (Easy)
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. Other types of balls will be available in the harder versions 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.

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.

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 in the next versions of the problem, several balls may 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.

The events must be printed in ascending order of t.

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:
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
13
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 C .Q
R0 D
R0 R
R0 R
R0 T
output:
6 BLUE GOAL
12 RED GOAL
FINAL SCORE: 1 1

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

Note: In the first example, a blue player goes to the middle of the grid, at the position of the Quaffle. He takes it, goes to the goal of the red team, and lets the ball there. He scores! The ball gets back to the middle of the field, a red player takes it and scores too.

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

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

struct Coord {
    int x, y;
};

bool operator==(Coord a, Coord b) {
    return a.x == b.x && a.y == b.y;
}

int main() {
    int n, m;
    std::cin >> n >> m;

    std::vector<std::vector<int>> red_team(n, std::vector<int>(m, -1));
    std::vector<std::vector<int>> blue_team(n, std::vector<int>(m, -1));
    std::vector<std::vector<bool>> red_goal(n, std::vector<bool>(m));
    std::vector<std::vector<bool>> blue_goal(n, std::vector<bool>(m));
    Coord quaffle = {(n + 1) / 2 - 1, (m + 1) / 2 - 1};
    int red_score = 0, blue_score = 0;
    std::string ball_held_by; // Stores the entity that is holding the ball right now
    for (int i = 0; i < n; ++ i) {
        for (int j = 0; j < m; ++ j) {
            std::string str;
            std::cin >> str;
            if (str == "RG") {
                red_goal[i][j] = true;
            } else if (str == "BG") {
                blue_goal[i][j] = true;
            } else if (str[0] == 'R') {
                red_team[i][j] = str[1] - '0';
            } else if (str[0] == 'B') {
                blue_team[i][j] = str[1] - '0';
            } else if (str == ".Q") {
                quaffle = {i, j};
            }
        }
    }

    auto find_in_grid = [](std::vector<std::vector<int>> &grid, int x) {
        Coord ans = {-1, -1};
        for (int i = 0; i < grid.size(); ++ i) {
            for (int j = 0; j < grid[i].size(); ++ j) {
                if (grid[i][j] == x) {
                    ans = {i, j};
                    break;
                }
            }
        }
        if (ans.x == -1) {
            throw std::runtime_error("find_in_grid didn't work!");
        }
        return ans;
    };
    auto check_goal = [&](Coord pos) {
        if (red_goal[pos.x][pos.y]) {
            return 'R';
        }
        if (blue_goal[pos.x][pos.y]) {
            return 'B';
        }
        return '-';
    };

    int t;
    std::cin >> t;
    for (int i = 0; i < t; ++ i) {
        std::string entity;
        std::cin >> entity;
        int entity_num = entity[1] - '0';
        char action;
        std::cin >> action;
        std::string ball;
        if (action == 'C') {
            std::cin >> ball;
            if ((entity[0] == 'R' && find_in_grid(red_team, entity_num) == quaffle) || (entity[0] == 'B' && find_in_grid(blue_team, entity_num) == quaffle)) {
                ball_held_by = entity;
            }
        }

        if (action == 'T' && entity == ball_held_by) {
            ball_held_by.clear();
            // Check if we made a goal (and if so, which goal)
            Coord our_pos;
            if (entity[0] == 'R') {
                our_pos = find_in_grid(red_team, entity_num);
            } else {
                our_pos = find_in_grid(blue_team, entity_num);
            }
            char goal_present = check_goal(our_pos);
            if (goal_present == 'R') { // Someone scored in the red goal: blue gets the point
                std::cout << i << " BLUE GOAL\n";
                blue_score++;
                quaffle = {(n + 1) / 2 - 1, (m + 1) / 2 - 1};
            } else if (goal_present == 'B') {
                std::cout << i << " RED GOAL\n";
                red_score++;
                quaffle = {(n + 1) / 2 - 1, (m + 1) / 2 - 1};
            }
        }

        if (action == 'U') {
            if (entity[0] == 'R') {
                Coord pos = find_in_grid(red_team, entity_num);
                if (pos.x - 1 < 0) {
                    throw std::runtime_error("Going out of bounds while moving up!");
                }
                red_team[pos.x - 1][pos.y] = entity_num, red_team[pos.x][pos.y] = -1;
            } else {
                Coord pos = find_in_grid(blue_team, entity_num);
                if (pos.x - 1 < 0) {
                    throw std::runtime_error("Going out of bounds while moving up!");
                }
                blue_team[pos.x - 1][pos.y] = entity_num, blue_team[pos.x][pos.y] = -1;
            }
        } else if (action == 'D') {
            if (entity[0] == 'R') {
                Coord pos = find_in_grid(red_team, entity_num);
                if (pos.x + 1 >= n) {
                    throw std::runtime_error("Going out of bounds while moving down!");
                }
                red_team[pos.x + 1][pos.y] = entity_num, red_team[pos.x][pos.y] = -1;
            } else {
                Coord pos = find_in_grid(blue_team, entity_num);
                if (pos.x + 1 >= n) {
                    throw std::runtime_error("Going out of bounds while moving down!");
                }
                blue_team[pos.x + 1][pos.y] = entity_num, blue_team[pos.x][pos.y] = -1;
            }
        } else if (action == 'L') {
            if (entity[0] == 'R') {
                Coord pos = find_in_grid(red_team, entity_num);
                if (pos.y - 1 < 0) {
                    throw std::runtime_error("Going out of bounds while moving left!");
                }
                red_team[pos.x][pos.y - 1] = entity_num, red_team[pos.x][pos.y] = -1;
            } else {
                Coord pos = find_in_grid(blue_team, entity_num);
                if (pos.y - 1 < 0) {
                    throw std::runtime_error("Going out of bounds while moving left!");
                }
                blue_team[pos.x][pos.y - 1] = entity_num, blue_team[pos.x][pos.y] = -1;
            }
        } else if (action == 'R') {
            if (entity[0] == 'R') {
                Coord pos = find_in_grid(red_team, entity_num);
                if (pos.y + 1 >= m) {
                    throw std::runtime_error("Going out of bounds while moving right!");
                }
                red_team[pos.x][pos.y + 1] = entity_num, red_team[pos.x][pos.y] = -1;
            } else {
                Coord pos = find_in_grid(blue_team, entity_num);
                if (pos.y + 1 >= m) {
                    throw std::runtime_error("Going out of bounds while moving right!");
                }
                blue_team[pos.x][pos.y + 1] = entity_num, blue_team[pos.x][pos.y] = -1;
            }
        }

        if (entity == ball_held_by) {
            if (entity[0] == 'R') {
                quaffle = find_in_grid(red_team, entity_num);
            } else {
                quaffle = find_in_grid(blue_team, entity_num);
            }
        }
    }

    std::cout << "FINAL SCORE: " << red_score << " " << blue_score << "\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 focus on scenarios that might cause the code to fail. The key areas to consider are:

1. **Goal Scoring**: Ensure that the code correctly handles scoring in both the correct and incorrect goals.
2. **Ball Holding and Throwing**: Ensure that the code correctly tracks who is holding the ball and handles the ball's movement correctly.
3. **Movement Boundaries**: Ensure that the code correctly handles player movements within the field boundaries.
4. **Initial Ball Position**: Ensure that the ball starts in the correct position and moves as expected.

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

1. **Correct Goal Scoring**: A player scores in the correct goal.
2. **Incorrect Goal Scoring**: A player scores in the wrong goal.
3. **Ball Movement**: Ensure the ball moves correctly when a player throws it.

Here is the test input:

```plaintext
5 5
.. R1 .. B1 ..
RG .. .. .. BG
RG R0 .Q B0 BG
RG .. .. .. BG
.. R2 .. B2 ..
10
B2 U
B2 U
B2 L
B2 C .Q
B2 L
B2 L
B2 T
R0 R
R0 T
R2 T
```

### Explanation:
1. **Initial Field Setup**:
   - The field is a 5x5 grid.
   - Red goals (RG) are at positions (1,0), (2,0), and (3,0).
   - Blue goals (BG) are at positions (1,4), (2,4), and (3,4).
   - Players R1, R0, R2, B1, B0, and B2 are placed on the field.
   - The Quaffle (.Q) is initially at position (2,2).

2. **Actions**:
   - **B2 U**: B2 moves up.
   - **B2 U**: B2 moves up again.
   - **B2 L**: B2 moves left.
   - **B2 C .Q**: B2 catches the Quaffle.
   - **B2 L**: B2 moves left.
   - **B2 L**: B2 moves left again.
   - **B2 T**: B2 throws the Quaffle, scoring a blue goal.
   - **R0 R**: R0 moves right.
   - **R0 T**: R0 throws the Quaffle, but does not score.
   - **R2 T**: R2 throws the Quaffle, but does not score.

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

This test input should expose any issues with the goal scoring logic and the ball movement tracking in the buggy code.