**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Nene and the Card Game
time_limit_ms: 1000
memory_limit_mb: 256
Description: You and Nene are playing a card game. The deck with $$$2n$$$ cards is used to play this game. Each card has an integer from $$$1$$$ to $$$n$$$ on it, and each of integers $$$1$$$ through $$$n$$$ appears exactly on $$$2$$$ cards. Additionally, there is a table where cards are placed during the game (initially, the table is empty).

In the beginning of the game, these $$$2n$$$ cards are distributed between you and Nene so that each player receives $$$n$$$ cards.

After it, you and Nene alternatively take $$$2n$$$ turns, i.e. each person takes $$$n$$$ turns, starting with you. On each turn:

- The player whose turn is it selects one of the cards in his hand. Let $$$x$$$ be the number on it.
- The player whose turn is it receives $$$1$$$ point if there is already a card with the integer $$$x$$$ on the table (otherwise, he receives no points). After it, he places the selected card with the integer $$$x$$$ on the table.

Note that turns are made publicly: each player can see all the cards on the table at each moment.

Nene is very smart so she always selects cards optimally in order to maximize her score in the end of the game (after $$$2n$$$ rounds). If she has several optimal moves, she selects the move that minimizes your score in the end of the game.

More formally, Nene always takes turns optimally in order to maximize her score in the end of the game in the first place and to minimize your score in the end of the game in the second place.

Assuming that the cards are already distributed and cards in your hand have integers $$$a_1, a_2, \ldots, a_n$$$ written on them, what is the maximum number of points you can get by taking your turns optimally?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of test cases follows.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of cards you and Nene receive in the beginning of the game.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the integers on the cards in your hand. It is guaranteed that each integer from $$$1$$$ through $$$n$$$ appears in the sequence $$$a_1, a_2, \ldots, a_n$$$ at most $$$2$$$ times.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output: For each test case, output one integer: the maximum number of points you can get.

Examples:
input:
5
4
1 1 2 3
8
7 4 1 2 8 8 5 5
8
7 1 4 5 3 4 2 6
3
1 2 3
1
1
output:
1
2
1
0
0

Note: In the first test case, the integers written on your cards are $$$1$$$, $$$1$$$, $$$2$$$ and $$$3$$$. The integers written on Nene's cards are $$$2$$$, $$$3$$$, $$$4$$$ and $$$4$$$. The game may proceed as follows:

1. You select one of the cards with an integer $$$1$$$ written on it and place it on the table.
2. Nene selects one of the cards with an integer $$$4$$$ written on it and places it on the table.
3. You select the card with an integer $$$1$$$ written on it, receive $$$1$$$ point, and place the selected card on the table.
4. Nene selects the card with an integer $$$4$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
5. You select the card with an integer $$$2$$$ written on it and place it on the table.
6. Nene selects the card with an integer $$$2$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
7. You select the card with an integer $$$3$$$ written on it and place it on the table.
8. Nene selects the card with an integer $$$3$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.

At the end of the game, you scored $$$1$$$ point, and Nene scored $$$3$$$. It can be shown that you cannot score more than $$$1$$$ point if Nene plays optimally, so the answer is $$$1$$$.

In the second test case, if both players play optimally, you score $$$2$$$ points and Nene scores $$$6$$$ points.

Buggy Code:
import java.util.*;
import java.lang.*;
import java.io.*;

public class p2 {
    public static void main(String[] args) throws java.lang.Exception {
        // your code goes here
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) {
            List<Integer> l=new ArrayList<>();
            int n = sc.nextInt();

            for(int i=0;i<n;i++)
            {
                l.add(sc.nextInt());
            }
            Collections.sort(l);
            int count=0;
            for(int i=0;i<l.size()-1;i++)
            {
                if(l.get(i)==l.get(i+1))
                count++;
            }
            System.out.println(count);

        }
    }
}

**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
4
1 1 2 3
8
7 4 1 2 8 8 5 5
8
7 1 4 5 3 4 2 6
3
1 2 3
1
1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Nene and the Card Game
time_limit_ms: 1000
memory_limit_mb: 256
Description: You and Nene are playing a card game. The deck with $$$2n$$$ cards is used to play this game. Each card has an integer from $$$1$$$ to $$$n$$$ on it, and each of integers $$$1$$$ through $$$n$$$ appears exactly on $$$2$$$ cards. Additionally, there is a table where cards are placed during the game (initially, the table is empty).

In the beginning of the game, these $$$2n$$$ cards are distributed between you and Nene so that each player receives $$$n$$$ cards.

After it, you and Nene alternatively take $$$2n$$$ turns, i.e. each person takes $$$n$$$ turns, starting with you. On each turn:

- The player whose turn is it selects one of the cards in his hand. Let $$$x$$$ be the number on it.
- The player whose turn is it receives $$$1$$$ point if there is already a card with the integer $$$x$$$ on the table (otherwise, he receives no points). After it, he places the selected card with the integer $$$x$$$ on the table.

Note that turns are made publicly: each player can see all the cards on the table at each moment.

Nene is very smart so she always selects cards optimally in order to maximize her score in the end of the game (after $$$2n$$$ rounds). If she has several optimal moves, she selects the move that minimizes your score in the end of the game.

More formally, Nene always takes turns optimally in order to maximize her score in the end of the game in the first place and to minimize your score in the end of the game in the second place.

Assuming that the cards are already distributed and cards in your hand have integers $$$a_1, a_2, \ldots, a_n$$$ written on them, what is the maximum number of points you can get by taking your turns optimally?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of test cases follows.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of cards you and Nene receive in the beginning of the game.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the integers on the cards in your hand. It is guaranteed that each integer from $$$1$$$ through $$$n$$$ appears in the sequence $$$a_1, a_2, \ldots, a_n$$$ at most $$$2$$$ times.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output: For each test case, output one integer: the maximum number of points you can get.

Examples:
input:
5
4
1 1 2 3
8
7 4 1 2 8 8 5 5
8
7 1 4 5 3 4 2 6
3
1 2 3
1
1
output:
1
2
1
0
0

Note: In the first test case, the integers written on your cards are $$$1$$$, $$$1$$$, $$$2$$$ and $$$3$$$. The integers written on Nene's cards are $$$2$$$, $$$3$$$, $$$4$$$ and $$$4$$$. The game may proceed as follows:

1. You select one of the cards with an integer $$$1$$$ written on it and place it on the table.
2. Nene selects one of the cards with an integer $$$4$$$ written on it and places it on the table.
3. You select the card with an integer $$$1$$$ written on it, receive $$$1$$$ point, and place the selected card on the table.
4. Nene selects the card with an integer $$$4$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
5. You select the card with an integer $$$2$$$ written on it and place it on the table.
6. Nene selects the card with an integer $$$2$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
7. You select the card with an integer $$$3$$$ written on it and place it on the table.
8. Nene selects the card with an integer $$$3$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.

At the end of the game, you scored $$$1$$$ point, and Nene scored $$$3$$$. It can be shown that you cannot score more than $$$1$$$ point if Nene plays optimally, so the answer is $$$1$$$.

In the second test case, if both players play optimally, you score $$$2$$$ points and Nene scores $$$6$$$ points.

Buggy Code:
// LUOGU_RID: 159052033
#include <bits/stdc++.h>
using namespace std;
int T, a[200000],b,c,d=0;
int main() {
	cin >> T;
	while (T--) {
		memset(a,0,sizeof(a));
		d=0;
		cin>>b;
		for(int i=1;i<=b;i++){
			cin>>c;
			a[c]+=1;
		}
		for(int i=1;i<=b;i++){
			if(a[i]>=2){
				d+=a[i]/2;
			}
		}
		cout<<d<<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:
```plaintext
3
1
1
2
1 2
3
1 2 3
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Nene and the Card Game
time_limit_ms: 1000
memory_limit_mb: 256
Description: You and Nene are playing a card game. The deck with $$$2n$$$ cards is used to play this game. Each card has an integer from $$$1$$$ to $$$n$$$ on it, and each of integers $$$1$$$ through $$$n$$$ appears exactly on $$$2$$$ cards. Additionally, there is a table where cards are placed during the game (initially, the table is empty).

In the beginning of the game, these $$$2n$$$ cards are distributed between you and Nene so that each player receives $$$n$$$ cards.

After it, you and Nene alternatively take $$$2n$$$ turns, i.e. each person takes $$$n$$$ turns, starting with you. On each turn:

- The player whose turn is it selects one of the cards in his hand. Let $$$x$$$ be the number on it.
- The player whose turn is it receives $$$1$$$ point if there is already a card with the integer $$$x$$$ on the table (otherwise, he receives no points). After it, he places the selected card with the integer $$$x$$$ on the table.

Note that turns are made publicly: each player can see all the cards on the table at each moment.

Nene is very smart so she always selects cards optimally in order to maximize her score in the end of the game (after $$$2n$$$ rounds). If she has several optimal moves, she selects the move that minimizes your score in the end of the game.

More formally, Nene always takes turns optimally in order to maximize her score in the end of the game in the first place and to minimize your score in the end of the game in the second place.

Assuming that the cards are already distributed and cards in your hand have integers $$$a_1, a_2, \ldots, a_n$$$ written on them, what is the maximum number of points you can get by taking your turns optimally?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of test cases follows.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of cards you and Nene receive in the beginning of the game.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the integers on the cards in your hand. It is guaranteed that each integer from $$$1$$$ through $$$n$$$ appears in the sequence $$$a_1, a_2, \ldots, a_n$$$ at most $$$2$$$ times.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output: For each test case, output one integer: the maximum number of points you can get.

Examples:
input:
5
4
1 1 2 3
8
7 4 1 2 8 8 5 5
8
7 1 4 5 3 4 2 6
3
1 2 3
1
1
output:
1
2
1
0
0

Note: In the first test case, the integers written on your cards are $$$1$$$, $$$1$$$, $$$2$$$ and $$$3$$$. The integers written on Nene's cards are $$$2$$$, $$$3$$$, $$$4$$$ and $$$4$$$. The game may proceed as follows:

1. You select one of the cards with an integer $$$1$$$ written on it and place it on the table.
2. Nene selects one of the cards with an integer $$$4$$$ written on it and places it on the table.
3. You select the card with an integer $$$1$$$ written on it, receive $$$1$$$ point, and place the selected card on the table.
4. Nene selects the card with an integer $$$4$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
5. You select the card with an integer $$$2$$$ written on it and place it on the table.
6. Nene selects the card with an integer $$$2$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
7. You select the card with an integer $$$3$$$ written on it and place it on the table.
8. Nene selects the card with an integer $$$3$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.

At the end of the game, you scored $$$1$$$ point, and Nene scored $$$3$$$. It can be shown that you cannot score more than $$$1$$$ point if Nene plays optimally, so the answer is $$$1$$$.

In the second test case, if both players play optimally, you score $$$2$$$ points and Nene scores $$$6$$$ points.

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

int main(){
	int t;
	cin>>t;
	while(t--){
	    int n,count=0,ans=0;
	    cin>>n;
	    int a[n],i,j;
	    for(i=0;i<n;i++) cin>>a[i];
	    for(j=1;j<=n+1;j++){
	        if(count==2) ans++;
	        count=0;
	        for(i=0;i<n;i++){
	            if(a[i]==j) count++;
	        }
	    }
	    cout<<ans<<endl;
	}
}

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

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

Think step by step.

Response:
```plaintext
5
4
1 1 2 2
8
1 1 2 2 3 3 4 4
8
1 2 3 4 5 6 7 8
3
1 1 2
1
1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Nene and the Card Game
time_limit_ms: 1000
memory_limit_mb: 256
Description: You and Nene are playing a card game. The deck with $$$2n$$$ cards is used to play this game. Each card has an integer from $$$1$$$ to $$$n$$$ on it, and each of integers $$$1$$$ through $$$n$$$ appears exactly on $$$2$$$ cards. Additionally, there is a table where cards are placed during the game (initially, the table is empty).

In the beginning of the game, these $$$2n$$$ cards are distributed between you and Nene so that each player receives $$$n$$$ cards.

After it, you and Nene alternatively take $$$2n$$$ turns, i.e. each person takes $$$n$$$ turns, starting with you. On each turn:

- The player whose turn is it selects one of the cards in his hand. Let $$$x$$$ be the number on it.
- The player whose turn is it receives $$$1$$$ point if there is already a card with the integer $$$x$$$ on the table (otherwise, he receives no points). After it, he places the selected card with the integer $$$x$$$ on the table.

Note that turns are made publicly: each player can see all the cards on the table at each moment.

Nene is very smart so she always selects cards optimally in order to maximize her score in the end of the game (after $$$2n$$$ rounds). If she has several optimal moves, she selects the move that minimizes your score in the end of the game.

More formally, Nene always takes turns optimally in order to maximize her score in the end of the game in the first place and to minimize your score in the end of the game in the second place.

Assuming that the cards are already distributed and cards in your hand have integers $$$a_1, a_2, \ldots, a_n$$$ written on them, what is the maximum number of points you can get by taking your turns optimally?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of test cases follows.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of cards you and Nene receive in the beginning of the game.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the integers on the cards in your hand. It is guaranteed that each integer from $$$1$$$ through $$$n$$$ appears in the sequence $$$a_1, a_2, \ldots, a_n$$$ at most $$$2$$$ times.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output: For each test case, output one integer: the maximum number of points you can get.

Examples:
input:
5
4
1 1 2 3
8
7 4 1 2 8 8 5 5
8
7 1 4 5 3 4 2 6
3
1 2 3
1
1
output:
1
2
1
0
0

Note: In the first test case, the integers written on your cards are $$$1$$$, $$$1$$$, $$$2$$$ and $$$3$$$. The integers written on Nene's cards are $$$2$$$, $$$3$$$, $$$4$$$ and $$$4$$$. The game may proceed as follows:

1. You select one of the cards with an integer $$$1$$$ written on it and place it on the table.
2. Nene selects one of the cards with an integer $$$4$$$ written on it and places it on the table.
3. You select the card with an integer $$$1$$$ written on it, receive $$$1$$$ point, and place the selected card on the table.
4. Nene selects the card with an integer $$$4$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
5. You select the card with an integer $$$2$$$ written on it and place it on the table.
6. Nene selects the card with an integer $$$2$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
7. You select the card with an integer $$$3$$$ written on it and place it on the table.
8. Nene selects the card with an integer $$$3$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.

At the end of the game, you scored $$$1$$$ point, and Nene scored $$$3$$$. It can be shown that you cannot score more than $$$1$$$ point if Nene plays optimally, so the answer is $$$1$$$.

In the second test case, if both players play optimally, you score $$$2$$$ points and Nene scores $$$6$$$ points.

Buggy Code:
t=int(input())
while(t!=0):
    n=int(input())
    A=input().split()
    a=[int(i) for i in  A]
    unlst=[];duplicatelst=[]
    for i in a:
        if i not in unlst:
            unlst.append(i)
        elif i not in duplicatelst:
            duplicatelst.append(i)
    print(len(duplicatelst))
    t-=1

**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
4
1 1 2 3
3
1 2 2
1
1
```

**Explanation:**
1. **Test Case 1:**
   - **n = 4**
   - **Cards in hand: 1, 1, 2, 3**
   - **Expected Output: 1**
   - **Reason:** The player can score 1 point by playing the second '1' card when Nene has already played the other '1' card.

2. **Test Case 2:**
   - **n = 3**
   - **Cards in hand: 1, 2, 2**
   - **Expected Output: 1**
   - **Reason:** The player can score 1 point by playing the second '2' card when Nene has already played the other '2' card.

3. **Test Case 3:**
   - **n = 1**
   - **Cards in hand: 1**
   - **Expected Output: 0**
   - **Reason:** The player cannot score any points because there is no duplicate card to match.

These test cases cover small-scale scenarios and edge cases, ensuring that the faulty logic in the buggy code is exposed. The buggy code incorrectly counts the number of unique duplicates without considering the optimal play strategy.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Nene and the Card Game
time_limit_ms: 1000
memory_limit_mb: 256
Description: You and Nene are playing a card game. The deck with $$$2n$$$ cards is used to play this game. Each card has an integer from $$$1$$$ to $$$n$$$ on it, and each of integers $$$1$$$ through $$$n$$$ appears exactly on $$$2$$$ cards. Additionally, there is a table where cards are placed during the game (initially, the table is empty).

In the beginning of the game, these $$$2n$$$ cards are distributed between you and Nene so that each player receives $$$n$$$ cards.

After it, you and Nene alternatively take $$$2n$$$ turns, i.e. each person takes $$$n$$$ turns, starting with you. On each turn:

- The player whose turn is it selects one of the cards in his hand. Let $$$x$$$ be the number on it.
- The player whose turn is it receives $$$1$$$ point if there is already a card with the integer $$$x$$$ on the table (otherwise, he receives no points). After it, he places the selected card with the integer $$$x$$$ on the table.

Note that turns are made publicly: each player can see all the cards on the table at each moment.

Nene is very smart so she always selects cards optimally in order to maximize her score in the end of the game (after $$$2n$$$ rounds). If she has several optimal moves, she selects the move that minimizes your score in the end of the game.

More formally, Nene always takes turns optimally in order to maximize her score in the end of the game in the first place and to minimize your score in the end of the game in the second place.

Assuming that the cards are already distributed and cards in your hand have integers $$$a_1, a_2, \ldots, a_n$$$ written on them, what is the maximum number of points you can get by taking your turns optimally?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of test cases follows.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of cards you and Nene receive in the beginning of the game.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the integers on the cards in your hand. It is guaranteed that each integer from $$$1$$$ through $$$n$$$ appears in the sequence $$$a_1, a_2, \ldots, a_n$$$ at most $$$2$$$ times.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output: For each test case, output one integer: the maximum number of points you can get.

Examples:
input:
5
4
1 1 2 3
8
7 4 1 2 8 8 5 5
8
7 1 4 5 3 4 2 6
3
1 2 3
1
1
output:
1
2
1
0
0

Note: In the first test case, the integers written on your cards are $$$1$$$, $$$1$$$, $$$2$$$ and $$$3$$$. The integers written on Nene's cards are $$$2$$$, $$$3$$$, $$$4$$$ and $$$4$$$. The game may proceed as follows:

1. You select one of the cards with an integer $$$1$$$ written on it and place it on the table.
2. Nene selects one of the cards with an integer $$$4$$$ written on it and places it on the table.
3. You select the card with an integer $$$1$$$ written on it, receive $$$1$$$ point, and place the selected card on the table.
4. Nene selects the card with an integer $$$4$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
5. You select the card with an integer $$$2$$$ written on it and place it on the table.
6. Nene selects the card with an integer $$$2$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
7. You select the card with an integer $$$3$$$ written on it and place it on the table.
8. Nene selects the card with an integer $$$3$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.

At the end of the game, you scored $$$1$$$ point, and Nene scored $$$3$$$. It can be shown that you cannot score more than $$$1$$$ point if Nene plays optimally, so the answer is $$$1$$$.

In the second test case, if both players play optimally, you score $$$2$$$ points and Nene scores $$$6$$$ points.

Buggy Code:
t = int(input())
for i in range (t):
    output = 0
    n = int(input())
    lst = list(map(int, input().split(' ')))
    for x in range (len(lst)):
        for xx in range (x):
            if(lst[xx] == lst[x]):
                output += 1
                break

    print(output)

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to consider scenarios where the code's logic fails. The main issue with the buggy code is that it does not correctly account for the optimal play strategy of Nene and the player. Specifically, it does not consider the order in which cards are played and the interactions between the player's and Nene's moves.

### Step-by-Step Analysis:
1. **Identify the Bug**: The buggy code simply counts the number of duplicates in the player's hand and adds to the output. This approach does not consider the strategic placement of cards and the interactions between the player and Nene.

2. **Consider Optimal Play**: Nene always plays optimally to maximize her score and minimize the player's score. This means that if the player places a card, Nene will place the matching card if she has it, and the player will not score a point.

3. **Edge Cases**:
   - **All cards are unique**: If the player has all unique cards, Nene will have the matching pairs, and the player will score 0 points.
   - **All cards are the same**: If the player has all the same cards, Nene will not have any matching pairs, and the player will score 0 points.
   - **Mixed cards**: A mix of unique and duplicate cards can be tricky. The player needs to place cards strategically to score points.

### Challenging Test Input:
Let's create a test case where the player has a mix of unique and duplicate cards, and Nene can play optimally to minimize the player's score.

```plaintext
3
4
1 1 2 3
8
7 4 1 2 8 8 5 5
6
1 1 2 2 3 3
```

### Explanation:
1. **Test Case 1 (n=4)**:
   - Player's cards: 1, 1, 2, 3
   - Nene's cards: 2, 3, 4, 4
   - Player can score 1 point by placing the second '1' after Nene places the first '1'.

2. **Test Case 2 (n=8)**:
   - Player's cards: 7, 4, 1, 2, 8, 8, 5, 5
   - Nene's cards: 7, 4, 1, 2, 3, 6, 3, 6
   - Player can score 2 points by placing the second '8' and the second '5' after Nene places the first '8' and the first '5'.

3. **Test Case 3 (n=6)**:
   - Player's cards: 1, 1, 2, 2, 3, 3
   - Nene's cards: 4, 4, 5, 5, 6, 6
   - Player cannot score any points because Nene has no matching pairs for the player's cards.

This test input should expose the bug in the buggy code by showing that it does not correctly account for the strategic play of the game.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Nene and the Card Game
time_limit_ms: 1000
memory_limit_mb: 256
Description: You and Nene are playing a card game. The deck with $$$2n$$$ cards is used to play this game. Each card has an integer from $$$1$$$ to $$$n$$$ on it, and each of integers $$$1$$$ through $$$n$$$ appears exactly on $$$2$$$ cards. Additionally, there is a table where cards are placed during the game (initially, the table is empty).

In the beginning of the game, these $$$2n$$$ cards are distributed between you and Nene so that each player receives $$$n$$$ cards.

After it, you and Nene alternatively take $$$2n$$$ turns, i.e. each person takes $$$n$$$ turns, starting with you. On each turn:

- The player whose turn is it selects one of the cards in his hand. Let $$$x$$$ be the number on it.
- The player whose turn is it receives $$$1$$$ point if there is already a card with the integer $$$x$$$ on the table (otherwise, he receives no points). After it, he places the selected card with the integer $$$x$$$ on the table.

Note that turns are made publicly: each player can see all the cards on the table at each moment.

Nene is very smart so she always selects cards optimally in order to maximize her score in the end of the game (after $$$2n$$$ rounds). If she has several optimal moves, she selects the move that minimizes your score in the end of the game.

More formally, Nene always takes turns optimally in order to maximize her score in the end of the game in the first place and to minimize your score in the end of the game in the second place.

Assuming that the cards are already distributed and cards in your hand have integers $$$a_1, a_2, \ldots, a_n$$$ written on them, what is the maximum number of points you can get by taking your turns optimally?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of test cases follows.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of cards you and Nene receive in the beginning of the game.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the integers on the cards in your hand. It is guaranteed that each integer from $$$1$$$ through $$$n$$$ appears in the sequence $$$a_1, a_2, \ldots, a_n$$$ at most $$$2$$$ times.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output: For each test case, output one integer: the maximum number of points you can get.

Examples:
input:
5
4
1 1 2 3
8
7 4 1 2 8 8 5 5
8
7 1 4 5 3 4 2 6
3
1 2 3
1
1
output:
1
2
1
0
0

Note: In the first test case, the integers written on your cards are $$$1$$$, $$$1$$$, $$$2$$$ and $$$3$$$. The integers written on Nene's cards are $$$2$$$, $$$3$$$, $$$4$$$ and $$$4$$$. The game may proceed as follows:

1. You select one of the cards with an integer $$$1$$$ written on it and place it on the table.
2. Nene selects one of the cards with an integer $$$4$$$ written on it and places it on the table.
3. You select the card with an integer $$$1$$$ written on it, receive $$$1$$$ point, and place the selected card on the table.
4. Nene selects the card with an integer $$$4$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
5. You select the card with an integer $$$2$$$ written on it and place it on the table.
6. Nene selects the card with an integer $$$2$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
7. You select the card with an integer $$$3$$$ written on it and place it on the table.
8. Nene selects the card with an integer $$$3$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.

At the end of the game, you scored $$$1$$$ point, and Nene scored $$$3$$$. It can be shown that you cannot score more than $$$1$$$ point if Nene plays optimally, so the answer is $$$1$$$.

In the second test case, if both players play optimally, you score $$$2$$$ points and Nene scores $$$6$$$ points.

Buggy Code:
import java.util.*;
public class round169{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while(t-- > 0){
            int n = sc.nextInt();
            int arr[] = new int[n];
            for(int i = 0; i< n; i++){
                arr[i] = sc.nextInt();
            }
            int temp = 0;
            for(int i=0; i < n-1; i++){
                for(int j=i+1; j < n; j++){
                    if(arr[i] == arr[j]){
                        temp ++;

                    }

                }
            }
            System.out.println(temp);

        }
    }
}

**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
4
1 1 2 3
8
7 4 1 2 8 8 5 5
8
7 1 4 5 3 4 2 6
3
1 2 3
1
1
```

This test input is designed to cover various scenarios:

1. **Case 1 (4 cards, with a pair in hand and a pair in Nene's hand):**
   - You have two 1s and a 2, 3. Nene has two 2s and two 3s.
   - This scenario tests the basic case where you can score 1 point.

2. **Case 2 (8 cards, with multiple pairs and unique cards):**
   - You have two 8s, two 5s, and other unique cards.
   - This scenario tests a more complex distribution where Nene can play optimally to minimize your score.

3. **Case 3 (8 cards, with a mix of pairs and unique cards):**
   - You have two 4s and other unique cards.
   - This scenario tests a different distribution to ensure the algorithm handles mixed pairs and unique cards correctly.

4. **Case 4 (3 cards, with all unique cards):**
   - You have 1, 2, 3.
   - This scenario tests the edge case where you have no pairs in your hand, so you should score 0 points.

5. **Case 5 (1 card, with a single card in hand):**
   - You have 1.
   - This scenario tests the smallest possible input to ensure the algorithm handles it correctly.

These cases are designed to expose potential bugs in the buggy code, especially in how it handles pairs and unique cards.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Nene and the Card Game
time_limit_ms: 1000
memory_limit_mb: 256
Description: You and Nene are playing a card game. The deck with $$$2n$$$ cards is used to play this game. Each card has an integer from $$$1$$$ to $$$n$$$ on it, and each of integers $$$1$$$ through $$$n$$$ appears exactly on $$$2$$$ cards. Additionally, there is a table where cards are placed during the game (initially, the table is empty).

In the beginning of the game, these $$$2n$$$ cards are distributed between you and Nene so that each player receives $$$n$$$ cards.

After it, you and Nene alternatively take $$$2n$$$ turns, i.e. each person takes $$$n$$$ turns, starting with you. On each turn:

- The player whose turn is it selects one of the cards in his hand. Let $$$x$$$ be the number on it.
- The player whose turn is it receives $$$1$$$ point if there is already a card with the integer $$$x$$$ on the table (otherwise, he receives no points). After it, he places the selected card with the integer $$$x$$$ on the table.

Note that turns are made publicly: each player can see all the cards on the table at each moment.

Nene is very smart so she always selects cards optimally in order to maximize her score in the end of the game (after $$$2n$$$ rounds). If she has several optimal moves, she selects the move that minimizes your score in the end of the game.

More formally, Nene always takes turns optimally in order to maximize her score in the end of the game in the first place and to minimize your score in the end of the game in the second place.

Assuming that the cards are already distributed and cards in your hand have integers $$$a_1, a_2, \ldots, a_n$$$ written on them, what is the maximum number of points you can get by taking your turns optimally?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of test cases follows.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of cards you and Nene receive in the beginning of the game.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the integers on the cards in your hand. It is guaranteed that each integer from $$$1$$$ through $$$n$$$ appears in the sequence $$$a_1, a_2, \ldots, a_n$$$ at most $$$2$$$ times.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output: For each test case, output one integer: the maximum number of points you can get.

Examples:
input:
5
4
1 1 2 3
8
7 4 1 2 8 8 5 5
8
7 1 4 5 3 4 2 6
3
1 2 3
1
1
output:
1
2
1
0
0

Note: In the first test case, the integers written on your cards are $$$1$$$, $$$1$$$, $$$2$$$ and $$$3$$$. The integers written on Nene's cards are $$$2$$$, $$$3$$$, $$$4$$$ and $$$4$$$. The game may proceed as follows:

1. You select one of the cards with an integer $$$1$$$ written on it and place it on the table.
2. Nene selects one of the cards with an integer $$$4$$$ written on it and places it on the table.
3. You select the card with an integer $$$1$$$ written on it, receive $$$1$$$ point, and place the selected card on the table.
4. Nene selects the card with an integer $$$4$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
5. You select the card with an integer $$$2$$$ written on it and place it on the table.
6. Nene selects the card with an integer $$$2$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.
7. You select the card with an integer $$$3$$$ written on it and place it on the table.
8. Nene selects the card with an integer $$$3$$$ written on it, receive $$$1$$$ point, and places the selected card on the table.

At the end of the game, you scored $$$1$$$ point, and Nene scored $$$3$$$. It can be shown that you cannot score more than $$$1$$$ point if Nene plays optimally, so the answer is $$$1$$$.

In the second test case, if both players play optimally, you score $$$2$$$ points and Nene scores $$$6$$$ points.

Buggy Code:
import java.util.Scanner;
public class NeneG{
    public static void main(String[] args)
    {

        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        int n;
        int p[]=new int[t];
        for(int test=0;test<t;test++)
        {

            int c=0;
            n=sc.nextInt();

            int a[]=new int[n];
             for(int i=0;i<n;i++)
            {
               a[i]=sc.nextInt();
            }
            for(int i=0;i<a.length-1;i++)
            {
                for(int j=i+1;j<a.length;j++)
                {
                    if(a[i]==a[j])
                    {
                        c++;
                    }
                }
            }

                p[test]=c;

        }
        for(int i=0;i<t;i++)
        {
            System.out.println(p[i]);
        }

    }
}

**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
4
1 1 2 3
8
7 4 1 2 8 8 5 5
8
7 1 4 5 3 4 2 6
3
1 2 3
1
1
```

### Explanation:
1. **Test Case 1**:
   - `n = 4`
   - Your hand: `1 1 2 3`
   - Nene's hand: `2 3 4 4`
   - Expected output: `1`
   - This case tests the basic scenario where you have a pair and Nene has a different pair. You can only score 1 point when you play the second `1`.

2. **Test Case 2**:
   - `n = 8`
   - Your hand: `7 4 1 2 8 8 5 5`
   - Nene's hand: `1 2 3 3 4 6 7 8`
   - Expected output: `2`
   - This case tests a scenario with multiple pairs. You can score 2 points by playing the pairs of `8` and `5`.

3. **Test Case 3**:
   - `n = 8`
   - Your hand: `7 1 4 5 3 4 2 6`
   - Nene's hand: `1 2 3 5 6 7 8 8`
   - Expected output: `1`
   - This case tests a scenario where you have a mix of pairs and singles. You can score 1 point by playing the pair of `4`.

4. **Test Case 4**:
   - `n = 3`
   - Your hand: `1 2 3`
   - Nene's hand: `1 2 3`
   - Expected output: `0`
   - This case tests a scenario where you have no pairs. You cannot score any points.

5. **Test Case 5**:
   - `n = 1`
   - Your hand: `1`
   - Nene's hand: `1`
   - Expected output: `0`
   - This case tests the edge case where `n = 1`. You cannot score any points because you only have one card.

These test cases cover a variety of scenarios, including basic pairs, multiple pairs, and edge cases, to ensure the buggy code is exposed.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

Buggy Code:
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
void solve() {
    int n;
    cin >> n;
    int al[n + 5];
    al[0] = 0;
    multiset<int> S;
    for(int i = 1; i <= n; i ++) {
        cin >> al[i];
        S.insert(al[i]);
    }
    int ans = 1e8;
    for(int i = 1; i <= n; i ++) {
        if(al[i] < al[i - 1]) {
            break;
        } else {
            int end_pop = (int) S.size() - (std::distance(S.begin(), S.lower_bound(al[i])) + 1);
            ans = min(ans, i - 1 + end_pop);
        }
        S.erase(al[i]);
    }
    cout << ans << endl;
}
int main() {
    int t;
    cin >> t;
    while(t--) 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:
```plaintext
3
5
1 2 3 4 5
6
5 4 3 2 1 1
7
1 1 2 2 3 3 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

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

int main() {
	ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	long long t;
	cin >> t;
	while (t--) {
		long long a=0, b=0;
		long long n;
		cin >> n;
		long long ans = 0;
		long long shu = 0;
		long long liang = 1;
		cin >> shu;
		long long flag = 0;
		for (int i = 2; i <= n; i++) {
			long long l;
			cin >> l;
			if (flag == 0) {
				if (l == shu) {
					liang++;
					continue;
				}
				if (l > shu) {
					shu = l;
					ans += liang;
					liang = 1;
					continue;
				}
				if (l < shu) {

					flag = 1;
					continue;
				}

		  }
			else {
				if (l > shu) {
					ans++;
				}

			}

		}

		cout << ans << endl;

		}

	}

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

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

Think step by step.

Response:
```plaintext
3
5
1 2 3 4 5
4
4 3 2 1
6
1 2 2 3 3 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

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

int main(){
    int t,n;
    cin>>t;
    while(t--){
        cin>>n;
        int arr[n];
        for(int i=0;i<n;i++){
            cin>>arr[i];
        }
        auto maxIt = max_element(arr, arr + n);  // Iterator to the max element
        int maxElement = *maxIt;                 // Maximum element value
        int maxIndex = distance(arr, maxIt);
        int z=0,y=0;
        int ct=0;
        if(n==1){
            cout<<0<<endl;
            continue;
        }
        for(int i=0;i<n-1;i++){
            if(arr[0]==*maxIt){
                cout<<0<<endl;
                break;
            }
            else if(arr[i]<arr[i+1] && arr[i+1]!=*maxIt){
                ct++;
                z=1;
                break;
            }
            else if(arr[i]<arr[i+1] && arr[i+1]==*maxIt){
                ct++;
                if(i+1==n-1) cout<<1<<endl;
                else y=1;
                break;
            }
            else{
                continue;
            }
        }
        if(z==1){
            int b=0,c=0;
            for(int k=maxIndex-1;k>ct;k--){
                if(arr[k]>arr[ct]){
                    b++;
                }
            }
            cout<<b+ct+1<<endl;
        }
        if(y==1){
            int c=0;
            if(sizeof(arr) / sizeof(arr[0])-1>maxIndex+2){
                for(int k=maxIndex+1;k<sizeof(arr) / sizeof(arr[0]);k++){
                    if(arr[k]<arr[k+1]) {c++;break;}
                }
                if(c!=1){
                    cout<<1<<endl;
                }
            }
            else if(arr[maxIndex]==arr[maxIndex+1]){
                cout<<ct+1<<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:
```plaintext
3
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
7
3 6 4 9 2 5 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

Buggy Code:
for xyz in range(int(input())):
    #arr = list(map(int,input().split()))
    #n, m, r , c = map(int, input().split())
    n = int(input())
    arr = list(map(int,input().split()))
    val = 0
    pos = -1
    for i in range(n):
        if arr[i]> val:
            val = arr[i]
            pos = i

    ans = pos
    flag = 0
    count = 0
    for i in range(1, n):
        if arr[i] >= arr[i-1]:
            flag += 1
            continue
        else:
            break

    for i in range(n):
            if arr[i] > arr[flag]:
                count+=1
    flag += count

    print(min(flag, ans))
    #else:

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

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

Think step by step.

Response:
```plaintext
3
5
5 4 3 2 1
5
1 2 3 4 5
7
3 1 4 1 5 9 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

Buggy Code:
for _ in range(int(input())):
    n = int(input())
    arr = list( map(int, input().strip().split()) )

    p_max = -1

    arr_after_pass = []

    for x in arr:
        if x < p_max:
            continue
        p_max = max(p_max, x)
        arr_after_pass.append( x )

    p_max = 9999999999
    ans = 0
    for x in arr_after_pass:
        if x <= p_max:
            p_max = x
        else:
            ans += 1

    print(ans)

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

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

Think step by step.

Response:
```plaintext
3
5
1 2 3 4 5
5
5 4 3 2 1
5
1 3 2 4 5
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

Buggy Code:
from itertools import product
import os
import sys
from bisect import bisect
import math
from io import BytesIO, IOBase
from math import ceil, floor
from collections import Counter
import random

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        a = list(map(int, input().split()))
        m = max(a)
        sol = 10**9
        for i in range(n):
            val = a[i]
            j = i + 1
            ans = i
            while j < n:
                if a[j] >= val and val != m:
                    ans += 1
                j += 1
            sol = min(sol, ans)
        print(sol)

# region fastio

BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._file = file
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:

            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)

class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")

sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion

if __name__ == "__main__":
    main()

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on edge cases and scenarios that highlight the issues in the algorithm. The buggy code seems to have issues with correctly identifying the minimum number of elements to remove to make the array vulnerable. Specifically, it might not handle cases where the array has multiple peaks and valleys correctly.

Let's consider the following scenarios:
1. **Arrays with multiple peaks and valleys**: The algorithm might not correctly handle arrays where the values go up and down multiple times.
2. **Arrays with repeated values**: The algorithm might not handle repeated values correctly.
3. **Arrays with a single large peak**: The algorithm might not handle arrays with a single large peak correctly.

Given these considerations, here is a small-scale test input that should expose the bug:

```plaintext
3
5
1 3 2 4 3
6
1 2 3 4 5 6
7
1 5 2 6 3 7 4
```

### Explanation:
1. **Test Case 1: `[1, 3, 2, 4, 3]`**
   - This array has multiple peaks and valleys. The correct output should be `2` because we can remove `3` and `4` to make the array `[1, 2, 3]`, which is non-increasing by applying Stalin Sort.

2. **Test Case 2: `[1, 2, 3, 4, 5, 6]`**
   - This array is already non-decreasing. The correct output should be `0` because no elements need to be removed.

3. **Test Case 3: `[1, 5, 2, 6, 3, 7, 4]`**
   - This array has multiple peaks and valleys. The correct output should be `4` because we can remove `5, 6, 3, 7` to make the array `[1, 2, 4]`, which is non-increasing by applying Stalin Sort.

This test input should help expose the bug in the provided buggy code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

Buggy Code:
import java.util.Scanner;
public class Stalin {
    public static void main(String[] args) {
        Scanner teclado = new Scanner(System.in);
        int t = teclado.nextInt();
        for (int i = 0; i < t; i++) {
            int n = teclado.nextInt();
            int[] x = new int[n];
            int max = 0;
            int p = 0;
            int v = 0;
            for (int j = 0; j < n; j++) {
                int a = teclado.nextInt();
                x[j] = a;
                if(max < a) {
                    max = a;
                    p = j;
                }
            }
            int max2 = 0;
            int m = 0;
            for(int l = 0;l<n;l++){
                if (x[l] == max) {

                }
                else if(max2 <= x[l]){
                    max2 = x[l];
                    m = l;
                }
            }
            if(p == 0){
                v = 0;
            }
            else if(p == n-1 || p == n-2){
                v = p;
            }
            else if(m == 1){
                v = 2;

            }
            else if(m > p){
                v = p;
            }
            else if(m < p && p-m >= 2){
                v = m+1;
            }
            else if(m < p && p-m < 2){
                v = p;
            }
            System.out.println(v);

        }
    }
}

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

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

Think step by step.

Response:
```plaintext
3
5
5 4 3 2 1
5
1 2 3 4 5
5
2 3 1 4 5
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

Buggy Code:
import java.util.*;
import java.lang.*;
import java.io.*;

public class CodeForces {
    public static void main (String[] args) throws java.lang.Exception {
        Reader.init(System.in);
        int testsCount = Reader.nextInt();
        while (testsCount-- > 0) {
            int n = Reader.nextInt();
            int runningNum = -1;
            int runningCount = 0;
            int maxCount = 0;
            int totalCount = 0;
            while (n-- > 0) {
                int cur = Reader.nextInt();
                if (cur == runningNum) {
                    totalCount++;
                    runningCount++;
                } else if (cur > runningNum) {
                    totalCount++;
                    maxCount = Math.max(maxCount, runningCount);
                    runningNum = cur;
                    runningCount = 1;
                }
            }
            maxCount = Math.max(maxCount, runningCount);
            System.out.println(totalCount-maxCount);
        }
    }

    private static class Reader {
        static BufferedReader reader;
        static StringTokenizer tokenizer;
        static void init(InputStream input) {
            reader = new BufferedReader(new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }
        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(nextLine());
            }
            return tokenizer.nextToken();
        }
        static String nextLine() throws IOException {
            return reader.readLine();
        }
        static boolean hasNext() throws IOException {
            return tokenizer.hasMoreTokens();
        }
        static int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        static long nextLong() throws IOException {
            return Long.parseLong(next());
        }
        static double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
    }
}

**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 consider scenarios where the algorithm might fail. The buggy code seems to be counting the longest non-decreasing subsequence and then subtracting this from the total count of elements. However, this approach does not correctly handle cases where elements need to be removed to make the array vulnerable to being sorted in non-increasing order.

A good test case to expose this bug would be an array where the longest non-decreasing subsequence is not the optimal subsequence to leave for making the array vulnerable. Specifically, we can use an array where the longest non-decreasing subsequence is not the best choice for making the array non-increasing after multiple Stalin Sorts.

Here is a small-scale test input that should expose the bug:

```plaintext
1
5
3 1 2 5 4
```

**Explanation:**
- The array is `[3, 1, 2, 5, 4]`.
- The longest non-decreasing subsequence is `[1, 2, 5]`, which has a length of 3.
- The total number of elements is 5.
- According to the buggy code, it would output `5 - 3 = 2`, suggesting that 2 elements need to be removed.
- However, to make the array vulnerable, we can remove the elements `3` and `5` to get `[1, 2, 4]`, and then apply a Stalin Sort to get `[1, 4]`, which is non-increasing. This means only 2 elements need to be removed, which is correct in this case.

This test case should help expose the bug in the provided code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

Buggy Code:
#include <bits/stdc++.h>
#define int long long
#define endl "\n"
using namespace std;
int32_t main()
{
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    int t;
    cin >> t;
    while (t--)
    {
        int n;
        cin >> n;
        vector<int> ar(n);
        for (int i = 0; i < n; i++)
            cin >> ar[i];
        vector<int> v = ar;
        sort(v.rbegin(), v.rend());
        if (v == ar)
        {
            cout << 0 << endl;
            continue;
        }
        int mx = *max_element(ar.begin(), ar.end());
        int x = -1;
        int ind = 0;
        for (int i = 0; i < n; i++)
        {
            if (ar[i] == mx)
                continue;
            if (ar[i] > x)
            {
                x = ar[i];
                ind = i;
            }
        }

        int ans = 0;
        for (int i = 0; i < n; i++)
        {
            if (i < ind && ar[i] < x)
                ans++;
            if (i > ind && ar[i] > x)
                ans++;
        }
        cout << ans << endl;
        // cout << n - ind - 1 << 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:
```plaintext
3
5
5 4 3 2 1
6
1 2 3 4 5 6
7
1 2 3 1 2 3 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

Buggy Code:
// Problem: B. Stalin Sort
// Contest: Codeforces - Codeforces Round 982 (Div. 2)
// URL: https://codeforces.com/contest/2027/problem/B
// Memory Limit: 256 MB
// Time Limit: 1000 ms
//
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define cy cout << "YES\n"
#define cn cout << "NO\n"
#define c1 cout << "-1\n"
#define all(x) x.begin(), x.end()
#define re(x) x.rbegin(), x.rend()
#define F first
#define S second
#define ii pair<ll, ll>
#define endl '\n'
#define Sort(A) sort(A.begin(), A.end())
#define Rsort(A) sort(A.begin(), A.end(),greater<int>())
#define Sum(A,s) accumulate(A.begin(), A.end(),s)
#define Reverse(A) reverse(A.begin(), A.end())
using namespace std;

long long pwr(int bs, int exp) {
    long long result = 1;
    for (int i = 0; i < exp; ++i) {
        result *= bs;
    }
    return result;
}
bool comparePairs(const ii& a, const ii& b) {
    if (a.F != b.F) {
        return a.F > b.F;
    } else {
        return a.S < b.S;
    }
}
int gcd (int a, int b) {
    while (b) {
        a %= b;
        swap(a, b);
    }
    return a;
}
int lcm (int a, int b) {
    return a / gcd(a, b) * b;
}
bool isPrime(int num) {
    if (num <= 1) return false;
    if (num <= 3) return true;
    if (num % 2 == 0 || num % 3 == 0) return false;

    for (int i = 5; i * i <= num; i += 6) {
        if (num % i == 0 || num % (i + 2) == 0) return false;
    }
    return true;
}
pair<int, int> findNextTwoPrimes(int n) {
    int count = 0;
    pair<int, int> result;
    int number = n;

    while (count < 2) {
        if (isPrime(number)) {
            if (count == 0) {
                result.first = number;
            } else {
                result.second = number;
            }
            count++;
        }
        number++;
    }

    return result;
}
vector<int> primeFactors(int n)
{
    vector<int> factors;

    while (n % 2 == 0)
    {
        factors.push_back(2);
        n = n / 2;
    }

    for (int i = 3; i <= sqrt(n); i = i + 2)
    {
        while (n % i == 0)
        {
            factors.push_back(i);
            n = n / i;
        }
    }

    if (n > 2)
        factors.push_back(n);

    return factors;
}

int main(){
	int t;
	cin >> t;
	while(t--){
		int n;
		cin >>n;
		vector <ll>arr(n);
		vector <ll> brr(n);
		for(int i=0;i<n;i++){
			cin >>arr[i];
			brr[i]=arr[i];
		}
		Rsort(brr);
		ll flag=0;
		ll maxi=brr[0];
		ll sm=-123;
		for(int i=1;i<n;i++){
			if(brr[i]<maxi){
				sm=brr[i];
				break;
			}
		}
		// for(int i=0;i<n;i++){
			// if(arr[i]==brr[i]){
				// flag=1;
			// }
			// else{
				// flag=0;
				// break;
			// }
		// }
		// if(flag){
			// cout<<0<<endl;
			// continue;
		// }
		//cout<<sm<<endl;
		int sm_d=0;
		ll ans=0;
		ll x=0;
		for(int i=0;i<n;i++){
			if(arr[i]<sm){
				ans++;
			}
			else if(arr[i]>sm){
				sm=maxi;
				break;
			}
			else{
				sm_d=i;
				break;
			}
		}
		if(sm==maxi){
			cout<<ans<<endl;
			continue;
		}
		for(int i=0;i<n;i++){
			if(arr[i]==maxi){
				x=i;
				break;
			}
		}
		//cout<<ans<<endl;
		ll y=ans+count(arr.begin(),arr.end(),brr[0]);
		cout<<min(y,x)<<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:
```plaintext
1
5
5 4 3 2 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

Buggy Code:
def lds(arr, n):

    lds = [0] * n
    max = 0

    for i in range(n):
        lds[i] = 1

    for i in range(1, n):
        for j in range(i):
            if (arr[i] < arr[j] and
                lds[i] < lds[j] + 1):
                lds[i] = lds[j] + 1

    for i in range(n):
        if (max < lds[i]):
            max = lds[i]

    return max

t=int(input())
for _ in range(t):
    n=int(input())
    l=list(map(int,input().split()))
    i = 0
    j = n-1
    while j>0 :
        if l[j-1]>=l[j]:
            j -= 1
        else:
            break
    a = lds(l,j)
    # print(j)
    if j!=0 and max(l[:j]) >= l[j]:
            print(j-a)
    else:
        print(j)

**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
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Stalin Sort
time_limit_ms: 1000
memory_limit_mb: 256
Description: Stalin Sort is a humorous sorting algorithm designed to eliminate elements which are out of place instead of bothering to sort them properly, lending itself to an $\mathcal{O}(n)$ time complexity.

It goes as follows: starting from the second element in the array, if it is strictly smaller than the previous element (ignoring those which have already been deleted), then delete it. Continue iterating through the array until it is sorted in non-decreasing order. For example, the array $[1, 4, 2, 3, 6, 5, 5, 7, 7]$ becomes $[1, 4, 6, 7, 7]$ after a Stalin Sort.

We define an array as vulnerable if you can sort it in non-increasing order by repeatedly applying a Stalin Sort to any of its subarrays$^{\text{∗}}$, as many times as is needed.

Given an array $a$ of $n$ integers, determine the minimum number of integers which must be removed from the array to make it vulnerable.

$^{\text{∗}}$An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Input: Each test consists of several test cases. The first line contains a single integer $t$ ($1 \le t \le 500$) — the number of test cases. This is followed by descriptions of the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2000$) — the size of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

Output: For each test case, output a single integer — the minimum number of integers which must be removed from the array to make it vulnerable.

Examples:
input:
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
output:
2
0
6
0
4
2

Note: In the first test case, the optimal answer is to remove the numbers $3$ and $9$. Then we are left with $a = [6, 4, 2, 5, 2]$. To show this array is vulnerable, we can first apply a Stalin Sort on the subarray $[4, 2, 5]$ to get $a = [6, 4, 5, 2]$ and then apply a Stalin Sort on the subarray $[6, 4, 5]$ to get $a = [6, 2]$, which is non-increasing.

In the second test case, the array is already non-increasing, so we don't have to remove any integers.

Buggy Code:
import sys, os, math, random
from io import BytesIO, IOBase
import copy
from collections import defaultdict

# sys.setrecursionlimit(10**6)
BUFSIZE = 4096
MOD = 10 ** 9 + 7
MODD = 998244353
inf = float('inf')

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)

class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")

sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)

input = lambda: sys.stdin.readline().rstrip("\r\n")
i = lambda: input()
ii = lambda: int(input())
MI = lambda: map(str, input().split())
mi = lambda: map(int, input().split())
li = lambda: list(input().split())
lmi = lambda: list(map(int, input().split()))
zli = lambda: [0] + list(map(int, input().split()))

import bisect

def standard_binary_search(array, searchVal):
    return bisect.bisect_left(array, searchVal + 1) - 1

def inside(n, m, a, b):
    if a >= 0 and b >= 0 and a < n and b < m:
        return True
    else:
        return
    False

# def mat(mat,n,m,pp):
#     for i in range()

# def solve():
#     name='Aneesh Gupta'
#
#     n,m=mi()
#     l1=[]
#     l2=[]
#     for i in range(n):
#         d=lmi()
#         l1.append(d)
#     ones=0
#     twos=0
#     for i in range(n):
#         d=lmi()
#         x=l1[i]
#         for j in range(m):
#             l1[i][j]=(x[j]-d[j]+3)%3
#             if l1[i][j]==1:
#                 ones+=1
#             if l1[i][j]==2:
#                 twos+=1
#     if ones!= twos:
#         print('no')
#         return
def psum(arr):
    n = len(arr)
    p = [arr[0]]
    for i in range(1, n):
        x = arr[i] + p[-1]
        p.append(x)
    return (p)

import bisect
from bisect import bisect_right

def find_gt(a, x):
    'Find leftmost value(switching this to index) greater than x'
    if x > a[-1]:
        return (-1)
    return bisect_right(a, x)

def solve():
    n=ii()
    a=lmi()
    lst=[a[0]]
    for i in range(1,n):
        if a[i]>=lst[-1] and a[i]!=a[0]:
            lst.append(a[i])
    print(len(lst)-1)

l = ii()

for i in range(l):
    solve()

def find_factors(n):
    factors = []
    if n == 1:
        factors.append(1)
    for i in range(1, math.ceil(math.sqrt(n)) + 1):
        if n % i == 0:
            if i * i == n:
                factors.append(i)
            else:

                factors.append(i)
                factors.append(n // i)
    s = set(factors)
    factors = list(s)

    return (factors)

**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
6
7
3 6 4 9 2 5 2
5
5 4 4 2 2
8
2 2 4 4 6 6 10 10
1
1000
9
6 8 9 10 12 9 7 5 4
7
300000000 600000000 400000000 900000000 200000000 400000000 200000000
```