**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
#include <iostream>

using namespace std;

int f[51];

int main()
{
    int t,i,n,j,a,x;
    cin >> t;
    for (i=0; i<t; i++){
        cin >> n;
        x=0;
        for (j=0; j<n; j++){
            cin >> a;
            f[a]++;
            x=max(x, f[a]);
        }
        cout << n-x << '\n';
        for (j=0; j<n; j++)
            f[j]=0;
    }
    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 4 2 2
```

### Explanation:
This test case is designed to expose the bug in the buggy code. The input array is `[5, 4, 4, 2, 2]`, which is non-increasing. The expected output should be `3` because we can make the array non-decreasing by performing the following operations:

1. Change the first element from `5` to `2` (array becomes `[2, 4, 4, 2, 2]`).
2. Change the second element from `4` to `2` (array becomes `[2, 2, 4, 2, 2]`).
3. Change the third element from `4` to `3` (array becomes `[2, 2, 3, 2, 2]`).

However, the buggy code will incorrectly calculate the number of operations needed. The array `f` is used to count the frequency of each height, but it does not correctly account for the non-decreasing order requirement. This test case should help reveal the issue in the logic of the buggy code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
#include <iostream>
using namespace std;
int main() {
    int t;
    cin>>t;
    for (int i=0;i<t;i++) {
        int n;
        cin>>n;
        int h[n];
        for (int j=0;j<n;j++) {
            cin>>h[j];
        }
        if(n==1)
            cout<<0<<endl;
        else if(n==2)
            cout<<1<<endl;
        else if (h[n/2]==h[n/2+1]==h[n/2-1])
            cout<<n-3<<endl;
        else if ((h[n/2]==h[n/2+1])||(h[n/2]==h[n/2-1]))
            cout<<n-2<<endl;
        else
            cout<<n-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 5 5 5 5
4
4 3 2 1
6
6 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: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
#include <iostream>
using namespace std;

int main (){
    int t; cin >> t;
    while (t--) {
        int n; cin >> n;
        int a[n + 1]; a[0] = -1;
        int x = 1;
        int y = 1;
        for (int i = 1; i <= n; i++) {
            cin >> a[i];
            if (a[i] == a[i - 1]) {
                y++;
                if (y > x) x = y;
            }
        }
        cout << n - x << 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
5 4 4 2 1
3
2 2 2
1
1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
a=int(input())
for i in range(a):
    b=int(input())
    c=list(map(int,input().split()))
    if c==(sorted(c))[::-1]:
        d=len(set(c))
        if d==len(c):
            print(len(c)-1)
        else:
            print(len(c)-d)
    else:
        print(0)

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to consider edge cases and scenarios where the code's logic fails. The main issue with the buggy code is that it does not correctly handle the transformation of the non-increasing array to a non-decreasing array. Specifically, it incorrectly calculates the number of operations needed when there are repeated values in the array.

Let's consider the following steps to generate a test input:

1. **Single Element Array**: This is a simple case that should return 0 operations.
2. **Array with All Elements Equal**: This should also return 0 operations.
3. **Array with Unique Elements in Non-Increasing Order**: This should return `n-1` operations.
4. **Array with Repeated Elements in Non-Increasing Order**: This should return a value less than `n-1` operations but more than 0.
5. **Array with a Mix of Unique and Repeated Elements**: This should return a value that reflects the correct number of operations.

Here is a challenging test input that covers these scenarios:

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

Explanation:
- The first test case has a single element, which is already non-decreasing.
- The second test case has all elements equal, which is already non-decreasing.
- The third test case has unique elements in non-increasing order, which should require 4 operations.
- The fourth test case has a mix of unique and repeated elements, which should require 2 operations.
- The fifth test case has a mix of unique and repeated elements, which should require 2 operations.

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: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
t = int(input())
for _ in range(t):
    n = int(input())
    lst = list(map(int, input().split()))
    count = 0
    for i in range(n - 1):
        if lst[i] > lst[i + 1]:
            count += 1
    print(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
1
5
5 4 4 3 2
```

### Explanation:
The provided test input is designed to expose the bug in the buggy code. The buggy code incorrectly counts the number of operations needed to make the array non-decreasing. Here's why this test input is challenging:

1. **Non-decreasing Array**: The array `[5, 4, 4, 3, 2]` is already in non-increasing order, but it contains a repeated element (`4` appears twice).

2. **Incorrect Counting**: The buggy code counts the number of times an element is greater than the next element, which is correct for a strictly decreasing sequence. However, it fails to account for the fact that repeated elements do not require an operation.

3. **Expected Output**: The correct output for this test case should be `3`, because:
   - Change `h[1]` (5) to 2.
   - Change `h[2]` (4) to 2.
   - Change `h[4]` (3) to 4.

4. **Buggy Code Output**: The buggy code will output `4` because it incorrectly counts the repeated `4` as requiring an operation.

This test input effectively highlights the bug in the code, making it a good candidate for exposing the issue.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
a=int(input())
for i in range(a):
    b=int(input())
    c=list(map(int,input().split()))
    d=0
    for e in range(1,b):
        if c[e]<c[e-1]:
            d+=1
    print(d)

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

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

Think step by step.

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

1. **Non-decreasing Requirement**: The buggy code incorrectly counts the number of operations needed to make the array non-decreasing by simply counting the number of times the current element is less than the previous element. This approach does not consider the actual changes needed to make the array non-decreasing.

2. **Edge Cases**: We need to test with arrays that have multiple elements where the current element is less than the previous element, and also consider cases where the array is already non-decreasing.

3. **Small Scale**: The test input should be small enough to be manageable but large enough to expose the bug effectively.

Let's create a test input that includes:
- An array where the current element is less than the previous element multiple times.
- An array that is already non-decreasing.
- An array with all elements being the same.

Here is the test input:

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

Explanation:
1. **Test Case 1**: `5 4 3 2 1` - This is the example given in the problem statement. The expected output is 4, but the buggy code will output 4, which is correct in this case.
2. **Test Case 2**: `2 2 1` - This is also an example given in the problem statement. The expected output is 1, but the buggy code will output 1, which is correct in this case.
3. **Test Case 3**: `1` - A single-element array. The expected output is 0, and the buggy code will output 0, which is correct.
4. **Test Case 4**: `3 3 3` - An array where all elements are the same. The expected output is 0, but the buggy code will output 0, which is correct in this case.

However, to expose the bug more clearly, we can add a more challenging test case:

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

Explanation:
1. **Test Case 1**: `5 4 3 2 1` - Expected output is 4.
2. **Test Case 2**: `2 2 1` - Expected output is 1.
3. **Test Case 3**: `1` - Expected output is 0.
4. **Test Case 4**: `3 3 3` - Expected output is 0.
5. **Test Case 5**: `6 5 5 4 4 4` - This array requires more operations to make it non-decreasing. The expected output is 3, but the buggy code will output 2, which is incorrect.

This test input should effectively 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: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

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

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();

        for (int i = 0; i < t; i++) {
            int n = scanner.nextInt();
            int[] heights = new int[n];
            for (int j = 0; j < n; j++) {
                heights[j] = scanner.nextInt();
            }

            int operations = 0;
            int lastHeight = 0;

            for (int j = 0; j < n; j++) {
                if (heights[j] < lastHeight) {
                    operations++;
                } else {
                    lastHeight = heights[j];
                }
            }
            System.out.println(operations);
        }

        scanner.close();
    }
}

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
import java.util.Scanner;

public class PMMonument {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            int[] h= new int[n];
            for(int i = 0; i < n; i++ ){
                h[i] = sc.nextInt();
            }

            int operations = 0;
            for (int i = n - 2; i >= 0; i--) {
                if (h[i] > h[i + 1]) {
                    operations = h[i] - h[i + 1];
                    h[i] = h[i + 1];
                }
            }

            System.out.println(operations);
        }
        sc.close();
    }
}

**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
4
5
5 4 4 2 1
4
4 3 2 1
3
3 3 1
2
2 1
```

### Explanation:
1. **Test Case 1:**
   - Input: `5 5 4 4 2 1`
   - Expected Output: `3`
   - Explanation: The initial array is `[5, 4, 4, 2, 1]`. The minimum number of operations needed to make it non-decreasing is 3:
     - Change `h[1]` to 2: `[2, 4, 4, 2, 1]`
     - Change `h[2]` to 2: `[2, 2, 4, 2, 1]`
     - Change `h[3]` to 2: `[2, 2, 2, 2, 1]`
     - Change `h[4]` to 2: `[2, 2, 2, 2, 2]`

2. **Test Case 2:**
   - Input: `4 4 3 2 1`
   - Expected Output: `3`
   - Explanation: The initial array is `[4, 3, 2, 1]`. The minimum number of operations needed to make it non-decreasing is 3:
     - Change `h[1]` to 1: `[1, 3, 2, 1]`
     - Change `h[2]` to 1: `[1, 1, 2, 1]`
     - Change `h[3]` to 1: `[1, 1, 1, 1]`

3. **Test Case 3:**
   - Input: `3 3 3 1`
   - Expected Output: `1`
   - Explanation: The initial array is `[3, 3, 1]`. The minimum number of operations needed to make it non-decreasing is 1:
     - Change `h[3]` to 3: `[3, 3, 3]`

4. **Test Case 4:**
   - Input: `2 2 1`
   - Expected Output: `1`
   - Explanation: The initial array is `[2, 1]`. The minimum number of operations needed to make it non-decreasing is 1:
     - Change `h[2]` to 2: `[2, 2]`

These test cases cover a range of scenarios, including repeated elements and different lengths, to ensure the code handles various edge cases correctly.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
/*
    Author : kmv a.k.a kzhi
    K41 IT CHV
*/
#include <bits/stdc++.h>
using namespace std;

//#define int long long
#define ll long long
#define FOR(i,a,b) for (int i = a ; i <= b; ++ i)
#define FOD(i,a,b) for (int i = a; i >= b; -- i)

#define BIT(mask,i)       ((mask >> i) & 1)
#define MASK(i)                (1ll << (i))
#define OFFBIT(mask,i)  (mask &~(1ll<<(i)))
#define ONBIT(mask,i) (mask | (1ll << (i)))
#define lg2(x)    (63 - __builtin_clzll(x))
#define c_bit          __builtin_popcountll

#define vi vector < int >
#define all(a) a.begin(), a.end()
#define pb push_back

#define ii pair<int,int>
#define fi first
#define se second

#define openfile(TASK) if (fopen(TASK".inp","r"))\
        {freopen(TASK".inp","r",stdin);freopen(TASK".out","w",stdout);}
#define endl '\n'
#define Faster ios_base::sync_with_stdio(false); \
                        cin.tie(0);  cout.tie(0);

#define mid(l,r) ((l + r) >> 1)
#define left(id) (id << 1)
#define right(id) ((id << 1) | 1)
#define ci const int

template <class X, class Y> bool maximize(X &a, const Y &b){if(a < b) return a = b, true;return false;}
template <class X, class Y> bool minimize(X &a, const Y &b){if(a > b) return a = b, true;return false;}

const int N = 55;

int n, a[N];

void SOLVE(){
    cin >> n;
    FOR (i, 1, n)
        cin >> a[i];

    int cnt = 0;

    FOR (i, 2, n)
        if (a[i] < a[i - 1]){
            a[i] = a[i - 1];
            cnt ++;
        }

    cout << cnt << endl;
}

signed main(){
    Faster
    openfile("test")

    int q = 1;

    cin >> q;

    while (q --){
        SOLVE();
    }

    return 0;
}

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

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

Think step by step.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
#include <bits/stdc++.h>
#define int long long
using namespace std;
int32_t main() {
    int t;
    cin>>t;
    while(t--){
        int n;
        cin>>n;
        vector <int> vec;

        for (int i=0; i<n; i++){
            int x=0;
            cin>>x;
            vec.push_back(x);
        }
        sort(vec.begin(), vec.end());
        vector <int> vec1(vec[n-1],0);
        for (int i=0; i<n; i++){
            vec1[vec[i]-1]++;
        }
        sort(vec1.begin(), vec1.end());
        int count=0;
        for (int i=0; i<vec1.size(); i++){
            if (vec1[vec1.size()-1]==1){
                count=1;
                break;
            }
            if (vec1[i]==vec1[vec1.size()-1] && vec1[vec1.size()-1]!=1){
                count+=vec1[i];
            }
        }
        if (n==1){
            cout<<0<<endl;
        }
        else{
            cout<<vec.size()-count<<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
5 4 4 3 3
3
2 2 2
1
1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
def min_operations_to_non_decreasing(n, heights):
    operations = 0
    max_height = heights[0]

    # Iterate through array starting from second element
    for i in range(1, n):
        # If current height is less than previous maximum
        # We need to increase it to at least max_height
        if heights[i] < max_height:
            operations += 1
        else:
            # Update max_height if current height is larger
            max_height = heights[i]

    return operations

# Read number of test cases
t = int(input())

for _ in range(t):
    # Read number of pillars
    n = int(input())
    # Read heights array
    heights = list(map(int, input().split()))
    # Print minimum operations needed
    print(min_operations_to_non_decreasing(n, heights))

**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
3
2 2 2
4
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: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
t=int(input())
while t>0:
    t-=1
    n=int(input())
    li=list(map(int,input().split(" ")))
    s=set(li)
    print(len(s)-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:
To expose the bug in the given code, we need to focus on the logic it uses. The buggy code calculates the number of unique elements in the list and subtracts 1 from it. This approach is incorrect because it does not consider the actual operations needed to make the list non-decreasing.

Let's consider the following edge cases and scenarios:

1. **All elements are the same**: In this case, no operations are needed.
2. **Elements are already in non-decreasing order**: No operations are needed.
3. **Elements are in non-increasing order**: This is the most common case, and the code should ideally transform the list to a non-decreasing order.
4. **Elements are in a random order**: This is a more complex case that the code should handle.

The code's logic fails when the list has multiple unique elements, and the transformation requires more than one operation. Specifically, the code will fail when the list has a large number of unique elements, but the transformation to a non-decreasing order requires fewer operations than the number of unique elements minus one.

Let's construct a test case that exposes this issue:

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

This test case has 5 unique elements, and the code will output `4` (since `5 - 1 = 4`). However, the correct number of operations needed to make the list non-decreasing is also `4`, which is coincidentally correct but for the wrong reason. To make it more challenging, we can use a different set of values:

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

In this case, the list has 4 unique elements, and the code will output `3` (since `4 - 1 = 3`). However, the correct number of operations needed to make the list non-decreasing is `3`, which is again coincidentally correct but for the wrong reason.

To further challenge the code, let's use a list with a more complex structure:

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

In this case, the list has 4 unique elements (5, 4, 3, 1), and the code will output `3` (since `4 - 1 = 3`). However, the correct number of operations needed to make the list non-decreasing is `2`:

- Change the first `5` to `3`.
- Change the last `1` to `3`.

Thus, the correct output should be `2`, but the buggy code will output `3`.

So, the final test input that exposes the bug is:

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

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

public class sub {

	/*
	 * /\_/\ (= ._.) / > \>
	 */
	static int mod = 998244353;

	public static void main(String args[]) {
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int a[] = new int[n];
			for(int i = 0;i<n;i++)a[i]=sc.nextInt();
			int ans = 0;
			for(int i = 0;i<n-1;i++) {
				if(a[i]>a[i+1]) {
					ans++;
					a[i+1]=a[i];
				}
			}
			out.println(ans);

		}
		out.close();
	}

	/*
	 * public static long bincoef(int n, int k) { if(n < k) return 0L; return (p[n]
	 * * pow((p[n - k] * p[k]) % mod, mod - 2,mod))%mod; }
	 */
	static long pow(long a, long b, long mod) {
		if (b == 0) {
			return 1L;
		}
		long val = pow(a, b / 2, mod);
		if (b % 2 == 0) {
			return val * val % mod;
		}
		return val * val % mod * a % mod;
	}

	static int gcd(int a, int b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	static int lcm(int a, int b) {
		return a * b / gcd(a, b);
	}

	static Kattio sc = new Kattio();
	static PrintWriter out = new PrintWriter(System.out);

	static class Kattio {

		static BufferedReader r;
		static StringTokenizer st;

		public Kattio() {
			r = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() {
			try {
				while (st == null || !st.hasMoreTokens()) {
					st = new StringTokenizer(r.readLine());
				}
				return st.nextToken();
			} catch (Exception e) {
				return null;
			}
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			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 generate a challenging test input that exposes the bug in the provided buggy code, we need to consider the following points:

1. **Non-increasing order**: The input array `h` must be in non-increasing order.
2. **Minimum operations**: The code should correctly determine the minimum number of operations needed to make the array non-decreasing.
3. **Edge cases**: We should test scenarios where the array has repeated values, and where the array is already in non-decreasing order.

The buggy code has a flaw in its logic for determining the minimum number of operations. Specifically, it only increments the `ans` counter when `a[i] > a[i+1]` and then sets `a[i+1] = a[i]`. This approach does not always yield the correct minimum number of operations, especially when there are repeated values or when the array is already in non-decreasing order.

Let's consider a small-scale test input that can expose this issue:

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

### Explanation:

1. **Test Case 1**: `5 5 4 3 2`
   - The initial array is non-increasing.
   - To make it non-decreasing, we need to change the array to something like `2 2 3 4 5`.
   - The correct number of operations is 4, but the buggy code might not handle this correctly due to the repeated values and the incorrect logic.

2. **Test Case 2**: `2 2 2`
   - The array is already non-decreasing.
   - The correct number of operations is 0, but the buggy code might incorrectly increment the `ans` counter.

3. **Test Case 3**: `1`
   - The array is already non-decreasing.
   - The correct number of operations is 0, and this should be straightforward.

This test input should expose the issues in the buggy code's logic for determining the minimum number of operations.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
import java.util.*;
public class monument {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t=sc.nextInt();
        while(t>0)
        {
            int n=sc.nextInt();
            int A[]=new int[n];
            for(int i=0;i<n;i++)
            {
                A[i]=sc.nextInt();
            }
            Arrays.sort(A);
            int count=0;
            for(int i=0;i<n-1;i++)
            {
                if(A[i]<A[i+1])
                count++;
            }
            System.out.println(count);
            t--;

        }

}
}

**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
3
3 2 2
1
1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
#include<bits/stdc++.h>
using namespace std;
const int N=5e5;
int n,a[N];

void solve(){
	cin>>n;
	map<int,int> mp;
	for(int i=1;i<=n;i++){
		cin>>a[i];
		mp[a[i]]=1;
	}
	cout<<mp.size()-1<<'\n';
}

signed main(){
	ios::sync_with_stdio(false);
	cin.tie(0);

	int t=1;
	cin>>t;
	while(t--){
		solve();
	}

	return 0;
}

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

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

Think step by step.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
#include<bits/stdc++.h>
using namespace std;
#define int long long
const int N = 3e5+9;
int a[N], b[N];
void haha()
{
	int n;cin >> n;int cnt =0;
	if(n == 1) cnt = 0;
	else if(n == 2)
	{
		if(a[1] > a[2]) cnt = 1;
	}
	else if(n >= 3)
	{
		for(int i = 1; i <= n; i++)
		{
			cin >> a[i];
			b[i] = a[i];
		}
		sort(b+1, b+n+1);
		int x = b[(n+1)/2];
		//cout << x << "\n";
		for(int i = 1; i <= n/2; i++) if(a[i] > x) cnt ++;
		for(int i = n/2+1; i <= n; i++) if(a[i] < x) cnt ++;
	}
	cout << cnt << "\n";
	return ;
}

signed main()
{
	ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
	int t; cin >> t;
	while(t--) haha();
	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 5 5 5 5
3
3 2 2
1
1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
t = int(input())

for i in range(t):
  h = int(input())

  k = list(map(int,input().split()))

  print(k[0]-k[-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:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to consider the following:

1. **Understanding the Bug**: The buggy code always prints `k[0] - k[-1]`, which is the difference between the first and last elements of the array. This approach is incorrect because it does not consider the actual number of operations needed to make the array non-decreasing.

2. **Edge Cases**:
   - **Single Element Array**: The code should handle a single element array correctly.
   - **Array with All Elements Equal**: The code should handle an array where all elements are the same correctly.
   - **Array with Steep Decrease**: The code should handle an array where the heights decrease significantly from the first to the last element.
   - **Array with Small Decrease**: The code should handle an array where the heights decrease slightly from the first to the last element.

3. **Challenging Scenarios**:
   - **Array with a Large Number of Elements**: To test the algorithm's performance and correctness with a larger input.
   - **Array with Elements in a Non-Increasing Order**: To ensure the algorithm can handle the given constraint.

Given these considerations, let's create a test input that exposes the bug:

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

### Explanation:
1. **Test Case 1**: `5 4 3 2 1`
   - The correct answer is 4, as shown in the example.
   - The buggy code will output `5 - 1 = 4`, which is correct by coincidence.

2. **Test Case 2**: `2 2 2`
   - The correct answer is 0, since the array is already non-decreasing.
   - The buggy code will output `2 - 2 = 0`, which is correct by coincidence.

3. **Test Case 3**: `3 2 1`
   - The correct answer is 1, as shown in the example.
   - The buggy code will output `3 - 1 = 2`, which is incorrect.

4. **Test Case 4**: `1`
   - The correct answer is 0, since a single element is already non-decreasing.
   - The buggy code will output `1 - 1 = 0`, which is correct by coincidence.

This test input includes a variety of scenarios to challenge the buggy code and expose its incorrect logic.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
t=int(input())
for _ in range(t):
    n=int(input())
    h=list(map(int,input().split(" ")))
    le=len(h)
    mle=le*-1
    if len(h)==1:
        print(0)
        continue
    else:
        c=0
        for i in range(n-1):
            if h[i]>h[i+1]:
                c+=1
                h[i],h[i+1]=h[i+1],h[i]
            else:
                continue
    print(c)

**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
3
3 3 2
4
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: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Buggy Code:
import java.util.*;
public class Main {
    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];
            int min=Integer.MAX_VALUE;
            int max=Integer.MIN_VALUE;
            int count=0;
            for(int i=0;i<n;i++){
                arr[i]=sc.nextInt();
                min=Math.min(min,arr[i]);
                max=Math.max(max,arr[i]);
            }
            int mid=n/2;
            for(int i=0;i<n/2;i++){
                if(arr[i]>arr[i+1]){
                      arr[i]=min;
                      count++;
                      if(i==n/2){
                          break;
                      }
                  }
                }
                for(int i=(n/2)+1;i<n;i++){if(arr[i]<arr[i-1]){
                      arr[i]=max;
                      count++;
                      if(i==n-1){
                          break;
                      }
                  }
                }
                if(n==1){
                System.out.println("0");
               }
               else{
                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
3
5
5 5 5 5 5
3
3 2 2
2
2 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Penchick and Modern Monument
time_limit_ms: 1000
memory_limit_mb: 256
Description: Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $$$n$$$ pillars.

The heights of the monument's pillars can be represented as an array $$$h$$$ of $$$n$$$ positive integers, where $$$h_i$$$ represents the height of the $$$i$$$-th pillar for all $$$i$$$ between $$$1$$$ and $$$n$$$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $$$h_i \le h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $$$h_i \ge h_{i + 1}$$$ for all $$$i$$$ between $$$1$$$ and $$$n - 1$$$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

- Modify the height of a pillar to any positive integer. Formally, choose an index $$$1\le i\le n$$$ and a positive integer $$$x$$$. Then, assign $$$h_i := x$$$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the number of pillars.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le n$$$ and $$$h_i\ge h_{i+1}$$$) — the height of the pillars.

Please take note that the given array $$$h$$$ is non-increasing.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output: For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Examples:
input:
3
5
5 4 3 2 1
3
2 2 1
1
1
output:
4
1
0

Note: In the first test case, the initial heights of pillars are $$$h = [5, 4, 3, 2, 1]$$$.

- In the first operation, Penchick changes the height of pillar $$$1$$$ to $$$h_1 := 2$$$.
- In the second operation, he changes the height of pillar $$$2$$$ to $$$h_2 := 2$$$.
- In the third operation, he changes the height of pillar $$$4$$$ to $$$h_4 := 4$$$.
- In the fourth operation, he changes the height of pillar $$$5$$$ to $$$h_5 := 4$$$.

After the operation, the heights of the pillars are $$$h = [2, 2, 3, 4, 4]$$$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $$$4$$$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $$$3$$$ to $$$h_3 := 2$$$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

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

            if(n==1)
            {
                System.out.println(0);
            }
            else
            {
                int c=0;
            for(int i=0;i<n-1;i++)
            {
                if(a[i]>a[i+1])
                {
                    c++;
                }
            }
            System.out.println(c);
            }
        }
    }
}

**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 5 4 3 2
4
4 3 3 2
2
2 2
```