**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<char> vc;
typedef vector<long long> vll;
typedef unsigned long long ull;
typedef vector<pair<int,int>> vpii;
typedef vector<pair<int,char>> vpic;
#define for1(i, n1, n2) for(int i = n1; i < n2; i++)
#define for2(i, n2, n1) for(int i = n2; i > n1; i--)
#define vecMAX(a) *max_element(a.begin(), a.end())
#define vecMIN(a) *min_element(a.begin(), a.end())
#define srt(v) sort(v.begin(), v.end())
#define rev(v) reverse(v.begin(), v.end())
#define pb push_back
#define inx int x; cin >> x;
#define vin(v) for(auto &x : v) cin >> x;
#define mp make_pair
#define ff first
#define ss second
#define v_erase(i) v.erase(v.begin()+i);
#define sum(v) accumulate(v.begin(), v.end(), 0)
#define INF 1e9
#define MOD 1000000007
#define sz(x) ((int)(x).size())
#define Code_by_millenialkid_07 ios::sync_with_stdio(0); cin.tie(0);
#ifndef ONLINE_JUDGE

    #include "Jatt_don't_Care.h"
#else
    #define see(...) 42
#endif
ll middle(ll a,ll b,ll c){
    if(a>=b&&a<=c) return a;
    if(b>=a&&b<=c) return b;
    return c;
}
void solve() {
ll n;
    cin>>n;
    vll v(n);
    vin(v);
   ll ans=0;

    for1(i,1,n-1){
        ans=max(ans,middle(v[i-1],v[i],v[i+1]));
    }
    if(n==1){
            cout<<v[0]<<"\n";
        }else if(n==2){
            cout<<min(v[0],v[1])<<"\n";
        }else{
    cout<<ans<<"\n";
        }
}

signed main() {
   Code_by_millenialkid_07
   int t;
    cin >> t;

    for (int i = 0; i < t; i++) {
        #ifndef ONLINE_JUDGE

            cout << "-----------------" << i + 1 << endl;
        #endif

       solve();
    }

    return 0;
}

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

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

Think step by step.

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

1. **Edge Cases**:
   - The code does not handle cases where the array has repeated elements correctly.
   - The code does not consider the entire array when determining the maximum possible value.

2. **Scenarios**:
   - An array with all elements being the same.
   - An array where the maximum value is in the middle.
   - An array where the maximum value is at the ends.

3. **Small-Scale Test Input**:
   - We need to create a test case that will highlight the bug in the code's logic. Specifically, the code only checks the middle values of subarrays of length 3, which is insufficient for determining the maximum possible value.

Let's create a test case where the maximum value is not in the middle of any subarray of length 3 but can be achieved through the operations described in the problem.

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

### Explanation:
1. **Test Case 1**:
   - Array: `[1, 3, 2]`
   - The maximum value that can be achieved is `3`, but the code will only check the middle values of subarrays of length 3, which are `[1, 3, 2]` and will output `2` instead of `3`.

2. **Test Case 2**:
   - Array: `[1, 2, 4, 3, 5]`
   - The maximum value that can be achieved is `4`. The code will only check the middle values of subarrays of length 3, which are `[1, 2, 4]`, `[2, 4, 3]`, and `[4, 3, 5]`. The middle values are `2`, `4`, and `3`, respectively. The code will output `4`, which is correct in this case, but it does not handle all cases correctly.

This test input should 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: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
#include<bits/stdc++.h>
using namespace std;
#define int long long
int32_t main()
{
   int t;
   cin>>t;
   while(t--)
   {
   int n;
   cin>>n;
    vector<int>a(n);
    int maxy=INT_MIN;
    for(int i=0;i<n;i++)
    cin>>a[i];
    if(n>2)
    {for(int i=0;i<n-2;i++)
    {
        vector<int>b(3);
        b[0]=a[i];
        b[1]=a[i+1];
        b[2]=a[i+2];
        sort(b.begin(),b.end());
        int q=b[1];
        maxy=max(maxy,q);

    }
   cout<<maxy<<endl;
   }
   else
   {
    cout<<a[0]<<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
3
1 2 3
4
1 3 2 4
5
4 1 2 3 5
```

**Explanation:**

1. **Test Case 1:**
   - Array: `[1, 2, 3]`
   - The median of any subarray of length 3 will be the middle element after sorting. The possible medians are 2. The maximum value that can be achieved is 2.

2. **Test Case 2:**
   - Array: `[1, 3, 2, 4]`
   - The median of any subarray of length 3 or 4 will be the middle element after sorting. The possible medians are 2 and 3. The maximum value that can be achieved is 3.

3. **Test Case 3:**
   - Array: `[4, 1, 2, 3, 5]`
   - The median of any subarray of length 3 or 5 will be the middle element after sorting. The possible medians are 2, 3, and 4. The maximum value that can be achieved is 4.

These test cases are designed to cover different lengths of arrays and to ensure that the bug in the buggy code, which only considers subarrays of length 3, is exposed. The correct solution should consider all possible subarrays and their medians to find the maximum possible value.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
from math import ceil, floor, gcd, inf, sqrt
from collections import Counter, defaultdict
import heapq, bisect
import sys,math

t = int(input())
for _ in range(t):
    n = int(input())
    a = list(map(int, input().split()))
    a.sort()
    mxleft = max(a[:n-1])
    print(mxleft)

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

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

Think step by step.

Response:
To create a challenging test input that exposes the bug in the given buggy code, let's analyze the code and identify the potential issues:

### Buggy Code Analysis:
1. **Sorting the Array:** The code sorts the array `a`.
2. **Finding the Maximum of the First `n-1` Elements:** It calculates `mxleft` as the maximum of the first `n-1` elements of the sorted array.
3. **Output:** It prints `mxleft`.

### Issues:
- **Sorting the Array:** Sorting the array is not necessary for finding the maximum possible value after performing the operations.
- **Finding the Maximum of the First `n-1` Elements:** This step is incorrect because the maximum possible value in the final array is not necessarily the maximum of the first `n-1` elements of the sorted array. The correct approach should be to find the median of the entire array, which is the value that can be achieved by performing the operations.

### Challenging Test Case:
To expose the bug, we need a test case where the maximum value in the final array is not the maximum of the first `n-1` elements of the sorted array. A good candidate is an array where the median is not the largest element.

### Example Test Case:
Consider the following test case:
- **Array:** `[1, 3, 2, 4, 5]`
- **Sorted Array:** `[1, 2, 3, 4, 5]`
- **Median:** `3` (the middle element of the sorted array)
- **Maximum of the First `n-1` Elements:** `4` (which is incorrect)

The correct answer should be `3`, but the buggy code will output `4`.

### Test Input:
```plaintext
1
5
1 3 2 4 5
```

This test case will expose the bug in the code because the maximum value in the final array should be `3`, but the buggy code will incorrectly output `4`.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
t = int(input())
while t>0:
    t-=1
    len = int(input())
    user = input()
    arr = [int(i) for i in user.split()]
    print(max(arr[0:len-1]))

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

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

Think step by step.

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

### Explanation:
1. **Test Case 1:**
   - **Input:** `2 1 2`
   - **Expected Output:** `1`
   - **Reason:** The only possible interval is (1, 2), and the median is 1. After the operation, the array becomes `[1, 1]`.

2. **Test Case 2:**
   - **Input:** `5 5 4 3 2 1`
   - **Expected Output:** `3`
   - **Reason:** The array is in descending order. The median of the entire array is 3. By choosing the interval (1, 5), the array becomes `[3, 3, 3, 3, 3]`.

### Why This Test Input is Challenging:
- **Test Case 1:** This simple test case checks if the code correctly handles the smallest possible array where the median is the smallest element.
- **Test Case 2:** This test case checks if the code can handle a descending array, where the median is not the largest or smallest element but the middle one. The buggy code in the problem only considers the maximum of the first `len-1` elements, which will fail in this case because the correct answer is the median of the entire array.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
import java.util.*;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class mocha {

	public static void main(String[] args) {
		int t = ii();
		while(t-- > 0) solve();
	}

	public static void solve() {
		int n = ii();
		int [] A = iir(n);
		int max = -inf;
		for(int i=0;i<n-1;++i) {
			max = Math.max(max,A[i]);
		}
		System.out.println(max);
	}

	static FastReader sc = new FastReader();
	final static int mod = 1_000_000_007;
	final static int inf = Integer.MAX_VALUE;
	final static long INF = Long.MAX_VALUE;

	static class FastReader {
    	BufferedReader br;
    	StringTokenizer st;
    	public FastReader() {
    		br = new BufferedReader(new InputStreamReader(System.in));
        }
    	String next() {
    		while (st == null || !st.hasMoreElements()) {
    			try {
    				st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
    		}
            return st.nextToken();
        }
        int nextInt() {return Integer.parseInt(next());}
        long nextLong() {return Long.parseLong(next());}
        double nextDouble() {return Double.parseDouble(next());}
        String nextLine(){
            String str = "";
            try {
                if(st.hasMoreTokens()){
                    str = st.nextToken("\n");
                }
                else{
                    str = br.readLine();
                }
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

	public static int ii() {
		return sc.nextInt();
	}

	public static long il() {
		return sc.nextLong();
	}

	public static String is() {
		return sc.next();
	}

	public static int [] iir(int n) {
		int [] A = new int[n];
		for(int i=0;i<n;++i)
			A[i] = ii();
		return A;
	}

	public static long [] ilr(int n) {
		long [] A = new long[n];
		for(int i=0;i<n;++i)
			A[i] = il();
		return A;
	}

	public static void sort(int [] A) {
		Arrays.sort(A);
	}

	public static void sort(List<Integer> A) {
		Collections.sort(A);
	}
}

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
import java.util.Scanner;

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];
            int max = 0;

            for (int i = 0; i < n; i++) {
                a[i] = sc.nextInt();
            }
            for(int i=0;i<n;i++){
              if (i != n - 1) {
                    if ((i != 0 && a[i] <= a[i - 1]) || (a[i] <= a[i + 1])) {
                        max = Math.max(a[i], max);
                    }
                }
            }
            System.out.println(max);
        }
        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
3
2
5 4
4
5 4 3 2
5
5 4 3 2 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
#include <bits/stdc++.h>
#include <string>
using namespace std;
#define ll long long
#define ull unsigned long long
#define si(X) scanf("%d", &(X))
#define sll(X) scanf("%lld",&(X))
#define INFL 0x3f3f3f3f3f3f3f3fLL
const int mod = 1e9+7;
ll gcd(ll a,ll b){
if(b==0)
return a;return gcd(b,a%b);
}
ll expo(ll base,ll pow){
ll ans = 1;
while(pow!=0){
if((pow&1)==1){
ans = ans*base;
ans = ans%mod;
}
base *= base;base%=mod;
pow/=2;
}return ans;
}
ll inv(ll x){return expo(x,mod-2);}
const int M = 2e5 + 5;

int arr[M];
int main(){

    int t;
    si(t);

    while(t--){
        int n;
        si(n);

        int ans = mod;

        for(int i = 1 ; i <= n ; i++){
            si(arr[i]);
            ans = min(ans, arr[i]);
        }

        for(int i = 2 ; i < n ; i++){
            if((arr[i] < arr[i - 1]) || (arr[i] < arr[i + 1])){
                ans = max(ans, arr[i]);
            }
        }
        if(arr[1] <= arr[2]){
            ans = max(ans, arr[1]);
        }
        if(arr[n] <= arr[n - 1]){
            ans = max(ans, arr[n]);
        }

        cout<<ans<<endl;
    }

}

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

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

Think step by step.

Response:
To expose the bug in the given buggy code, we need to focus on edge cases and scenarios where the code might fail. The buggy code incorrectly updates the `ans` variable by setting it to the minimum value of the array and then trying to find the maximum value that can be set as the final value. However, it does not correctly handle the logic for finding the maximum possible value after performing the operations.

### Key Points to Consider:
1. **Initial Minimum Value**: The code initializes `ans` to the minimum value in the array. This is a good start but might not be the correct final answer.
2. **Checking Middle Elements**: The code checks if the middle elements are less than their neighbors and updates `ans` to the maximum of these values. This logic is flawed because it doesn't consider all possible subarrays and their medians.
3. **Edge Elements**: The code also checks the first and last elements, but it does not correctly handle the logic for these elements.

### Test Input to Expose the Bug:
To expose the bug, we can create a test case where the initial minimum value is not the maximum possible final value. A good example is an array where the middle elements are smaller than the edge elements, but the edge elements can be set as the final value through the operations.

### Example Test Input:
```plaintext
2
5
1 3 2 4 5
3
1 2 3
```

### Explanation:
1. **First Test Case**:
   - Array: `[1, 3, 2, 4, 5]`
   - The initial minimum value is `1`.
   - The code will check the middle elements and update `ans` to `2` (the maximum of the middle elements that are less than their neighbors).
   - However, the correct final value should be `4` because Mocha can perform the following operations:
     - Choose the interval `(4, 5)`, then `a = [1, 3, 2, 4, 4]`.
     - Choose the interval `(3, 5)`, then `a = [1, 3, 4, 4, 4]`.
     - Choose the interval `(1, 5)`, then `a = [4, 4, 4, 4, 4]`.

2. **Second Test Case**:
   - Array: `[1, 2, 3]`
   - The initial minimum value is `1`.
   - The code will check the middle element and update `ans` to `2`.
   - However, the correct final value should be `2` because Mocha can perform the following operations:
     - Choose the interval `(2, 3)`, then `a = [1, 2, 2]`.
     - Choose the interval `(1, 3)`, then `a = [2, 2, 2]`.

### Expected Output:
```plaintext
4
2
```

This test input should expose the bug in the given buggy code by showing that the initial minimum value is not always the correct final value.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll max(ll a, ll b){
    if(a>b){
        return a;
    }
    return b;
}
ll min(ll a, ll b){
    if(a<b){
        return a;
    }
    return b;
}
int main(){
    int t;
    cin>>t;
    while(t--){
        ll n,m;
        cin>>n;
        ll arr[n];
        int le=1e9;
        for(int i=0;i<n;i++){
            cin>>arr[i];
            // if(arr[i]<le){
            //     le=arr[i];
            // }
        }
        int flag=0;
        // cout<<le<<"\n";
        sort(arr,arr+n-1);
        cout<<arr[n-2]<<"\n";
    }

}

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

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

Think step by step.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
def solve():
    n = int(input())
    nums = [int(i) for i in input().split()]
    find  = []
    if(len(nums) == 1 or len(nums) == 2):
        print(nums[0])
        return
    if(len(nums) == 3):
        nums.sort()
        print(nums[1])
        return
    if(nums[0]<nums[1]):
        find.append(nums[0])
    if(nums[-1]<nums[-2]):
        find.append(nums[-1])
    for i in range(1, len(nums)-1):
        if(nums[i]<nums[i-1] or nums[i]<nums[i+1]):
            find.append(nums[i])
    print(max(find)) if len(find) != 0 else print(max(nums))

for i in range(int(input())):
    solve()

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

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

Think step by step.

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

### Explanation:
1. **Test Case 1:**
   - Input: `4 5 5 5 5`
   - Expected Output: `5`
   - This test case is designed to check the scenario where all elements in the array are the same. The buggy code should handle this correctly by printing the maximum value, which is `5`.

2. **Test Case 2:**
   - Input: `6 1 2 3 4 5 6`
   - Expected Output: `4`
   - This test case is designed to check a more complex scenario where the array has a range of values. The buggy code should correctly identify the maximum value that can be achieved by performing the operations, which is `4`.

These test cases are chosen to ensure that the buggy code is tested for both uniform arrays and arrays with a range of values, maximizing the probability of exposing any bugs.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
import heapq

def max_possible_number(n, arr):
    # Convert the list to a max-heap
    max_heap = [-num for num in arr]
    heapq.heapify(max_heap)

    max_value = float('-inf')

    while len(max_heap) > 1:
        # Get the top two elements (largest and second largest)
        largest = -heapq.heappop(max_heap)
        second_largest = -heapq.heappop(max_heap)

        # Calculate the median of the current subarray
        median = (largest + second_largest) // 2

        # Update the maximum value
        max_value = max(max_value, median)

        # Push the median back into the heap
        heapq.heappush(max_heap, -median)

    return max_value

# Read input
t = int(input())
for _ in range(t):
    n = int(input())
    arr = list(map(int, input().split()))

    result = max_possible_number(n, arr)
    print(result)

**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
2
1 2
5
1 2 3 4 5
4
1 1000000000 1 1000000000
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
import java.lang.reflect.Array;
import java.util.*;
public class six{
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        while(t-->0){
            int n=sc.nextInt();
            long arr[]=new long[n];
            for(int i=0;i<n;i++) arr[i]=sc.nextLong();
            System.out.println(answer(arr, n));
        }
    }
    public static long answer(long arr[],int n){
        long sl=0;
        Arrays.sort(arr);
        return arr[n-2];
    }
}

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the given buggy code, we need to focus on the logic of the code. The buggy code sorts the array and returns the second largest element (`arr[n-2]`). This approach is incorrect because the problem requires finding the maximum possible value that the array can be made to contain after performing the allowed operations, which is not necessarily the second largest element.

### Step-by-Step Reasoning:

1. **Understand the Bug:**
   - The bug in the code is that it returns the second largest element after sorting the array.
   - This does not consider the operations that Mocha can perform to change the array.

2. **Identify the Correct Solution:**
   - The correct solution should find the maximum possible value that the array can be made to contain.
   - This value is the maximum element that can be the median of any subarray after performing the operations.

3. **Generate a Test Case:**
   - We need a test case where the second largest element is not the correct answer.
   - A good candidate is an array where the maximum element can be the median of some subarray.

### Challenging Test Input:

Let's consider an array where the maximum element can be the median of a subarray, and the second largest element is not the correct answer.

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

### Explanation:

- **Array:** `[1, 2, 5, 4, 3]`
- **Sorted Array:** `[1, 2, 3, 4, 5]`
- **Buggy Code Output:** The buggy code will return `4` (the second largest element).
- **Correct Output:** The correct output should be `5` because:
  - Mocha can choose the interval `(l, r) = (1, 5)`, which includes the entire array.
  - The median of the subarray `[1, 2, 5, 4, 3]` is `3` (after sorting: `[1, 2, 3, 4, 5]`).
  - However, Mocha can also choose the interval `(l, r) = (3, 5)`, which includes the subarray `[5, 4, 3]`.
  - The median of `[5, 4, 3]` is `4` (after sorting: `[3, 4, 5]`).
  - Mocha can then choose the interval `(l, r) = (1, 5)` again, and the median of `[1, 2, 4, 4, 4]` is `4` (after sorting: `[1, 2, 4, 4, 4]`).
  - Finally, Mocha can choose the interval `(l, r) = (1, 5)` one more time, and the median of `[4, 4, 4, 4, 4]` is `4` (after sorting: `[4, 4, 4, 4, 4]`).

However, the maximum possible value that the array can be made to contain is `5`, which is the maximum element in the array.

Thus, the correct output is `5`.

### Final Test Input:
```plaintext
1
5
1 2 5 4 3
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Chamo and Mocha's Array
time_limit_ms: 2000
memory_limit_mb: 256
Description: Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.

Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:

  1. Choose indices $l$ and $r$ ($1 \leq l < r \leq n$)    2. Let $x$ be the median$^\dagger$ of the subarray $[a_l, a_{l+1},\ldots, a_r]$    3. Set all values $a_l, a_{l+1},\ldots, a_r$ to $x$

Suppose $a=[1,2,3,4,5]$ initially:

  * If Mocha chooses $(l,r)=(3,4)$ in the first operation, then $x=3$, the array will be changed into $a=[1,2,3,3,5]$.    * If Mocha chooses $(l,r)=(1,3)$ in the first operation, then $x=2$, the array will be changed into $a=[2,2,2,4,5]$.

Mocha will perform the operation until the array contains only the same number. Mocha wants to know what is the maximum possible value of this number.

$^\dagger$ The median in an array $b$ of length $m$ is an element that occupies position number $\lfloor \frac{m+1}{2} \rfloor$ after we sort the elements in non-decreasing order. For example, the median of $[3,1,4,1,5]$ is $3$ and the median of $[5,25,20,24]$ is $20$.

Input: Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2\leq n\leq 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i \leq 10^9$) — the elements of the array $a$.

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

Output: For each test case, output the maximum value of the number.

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

Note: In the first test case, $a=[1,2]$. Mocha can only choose the interval $(l,r)=(1,2)$. The array will be changed to $a=[1,1]$. Therefore, the answer is $1$.

In the second test case, Mocha can perform the following operations:

  * Choose the interval $(l,r)=(4,5)$, then $a=[1,2,3,4,4]$.    * Choose the interval $(l,r)=(3,5)$, then $a=[1,2,4,4,4]$.    * Choose the interval $(l,r)=(1,5)$, then $a=[4,4,4,4,4]$.

The array contains only the same number, which is $4$. It can be proven that the maximum value of the final number cannot be greater than $4$.

Buggy Code:
import java.io.*;

import java.util.*;

public class Main{
    public static void main(String [] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        int t = Integer.parseInt(br.readLine());
        for(int i=0; i<t; i++){
            int n = Integer.parseInt(br.readLine());
            long [] arr =new long[n];
            StringTokenizer st = new StringTokenizer(br.readLine());
            for (int j = 0; j < n; j++) {
                arr[j] = Long.parseLong(st.nextToken());
            }
            Arrays.sort(arr);
            System.out.println(arr[arr.length-2]);
        }
        pw.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:
To generate a challenging test input that exposes the bug in the given buggy code, we need to consider the following:

1. **Understanding the Bug**: The buggy code sorts the array and always prints the second largest element (`arr[arr.length-2]`). This approach is incorrect because it does not consider the median operations and their impact on the array.

2. **Edge Cases**:
   - **Single Element Arrays**: These are not applicable since the problem constraints state \(2 \leq n \leq 10^5\).
   - **Arrays with All Elements the Same**: The code will output the second largest element, which is the same as the largest element.
   - **Arrays with Unique Elements**: The code will output the second largest element, which is not necessarily the correct answer.
   - **Arrays with Repeated Elements**: The code will output the second largest element, which might not be the correct answer.

3. **Challenging Scenario**:
   - An array where the median operations can significantly change the array, leading to a different result than the second largest element.

4. **Example**:
   - Consider an array where the median operations can lead to a different final value than the second largest element. For example, an array where the median is not the second largest element but a smaller value that can be propagated through the array.

Given these considerations, a challenging test input could be:

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

**Explanation**:
- For the array `[1, 2, 3, 4, 5, 6]`, the correct answer should be `4` because Mocha can perform the following operations:
  - Choose the interval `(l, r) = (4, 6)`, then the array becomes `[1, 2, 3, 4, 4, 4]`.
  - Choose the interval `(l, r) = (3, 6)`, then the array becomes `[1, 2, 4, 4, 4, 4]`.
  - Choose the interval `(l, r) = (1, 6)`, then the array becomes `[4, 4, 4, 4, 4, 4]`.

The buggy code will output `5` (the second largest element), which is incorrect. This test input will expose the bug in the code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: A Gift From Orangutan
time_limit_ms: 1000
memory_limit_mb: 256
Description: While exploring the jungle, you have bumped into a rare orangutan with a bow tie! You shake hands with the orangutan and offer him some food and water. In return...

The orangutan has gifted you an array $a$ of length $n$. Using $a$, you will construct two arrays $b$ and $c$, both containing $n$ elements, in the following manner:

  * $b_i = \min(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.    * $c_i = \max(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.

Define the score of $a$ as $\sum_{i=1}^n c_i - b_i$ (i.e. the sum of $c_i - b_i$ over all $1 \leq i \leq n$). Before you calculate the score, you can shuffle the elements of $a$ however you want.

Find the maximum score that you can get if you shuffle the elements of $a$ optimally.

Input: The first line contains $t$ ($1 \leq t \leq 100$) — the number of test cases.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 1000$) — the number of elements in $a$.

The following line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 1000$) — the elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $1000$.

Output: For each test case, output the maximum score that you can get.

Examples:
input:
3
1
69
3
7 6 5
5
1 1 1 2 2
output:
0
4
4

Note: In the first test case, there is no other way to rearrange $a$. So, $b = [69]$ and $c = [69]$. The only possible score is $69 - 69 = 0$.

In the second test case, you can rearrange $a$ as $[7, 5, 6]$. Here, $b = [7, 5, 5]$ and $c = [7, 7, 7]$. The score in this case is $(7 - 7) + (7 - 5) + (7 - 5) = 4$. It can be shown this is the maximum possible score.

Buggy Code:
#include <bits/stdc++.h>
typedef long long ll;
typedef long double ld;
#define pb push_back
#define mp make_pair
using namespace std;

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int t = 1;
    cin >> t;
    while(t--)
    {
        int n;
        cin >> n;
        int a[n];
        for (int i = 0; i < n; i++)
        {
            cin >> a[i];
        }
        long long int sum = 0;
        sort(a, a + n);
        for (int i = 0; i < n; i++)
        {
            sum += abs(a[i] - a[n - i - 1]);
        }
        cout << sum << endl;
    }
    return 0;
}

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

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

Think step by step.

Response:
```plaintext
3
1
1000
2
1000 1
10
1 2 3 4 5 6 7 8 9 10
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: A Gift From Orangutan
time_limit_ms: 1000
memory_limit_mb: 256
Description: While exploring the jungle, you have bumped into a rare orangutan with a bow tie! You shake hands with the orangutan and offer him some food and water. In return...

The orangutan has gifted you an array $a$ of length $n$. Using $a$, you will construct two arrays $b$ and $c$, both containing $n$ elements, in the following manner:

  * $b_i = \min(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.    * $c_i = \max(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.

Define the score of $a$ as $\sum_{i=1}^n c_i - b_i$ (i.e. the sum of $c_i - b_i$ over all $1 \leq i \leq n$). Before you calculate the score, you can shuffle the elements of $a$ however you want.

Find the maximum score that you can get if you shuffle the elements of $a$ optimally.

Input: The first line contains $t$ ($1 \leq t \leq 100$) — the number of test cases.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 1000$) — the number of elements in $a$.

The following line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 1000$) — the elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $1000$.

Output: For each test case, output the maximum score that you can get.

Examples:
input:
3
1
69
3
7 6 5
5
1 1 1 2 2
output:
0
4
4

Note: In the first test case, there is no other way to rearrange $a$. So, $b = [69]$ and $c = [69]$. The only possible score is $69 - 69 = 0$.

In the second test case, you can rearrange $a$ as $[7, 5, 6]$. Here, $b = [7, 5, 5]$ and $c = [7, 7, 7]$. The score in this case is $(7 - 7) + (7 - 5) + (7 - 5) = 4$. It can be shown this is the maximum possible score.

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

int solve(){
    int n;
    cin>>n;
    vector<int>a(n);
    for(int i=0;i<n;i++){
        cin>>a[i];
    }
    if(n == 1) return 0;
    vector<int>b(n);
    vector<int>c(n);
    for(int i=0;i<n;i++){
        b[i] = a[i];
        c[i] = a[i];
    }
    sort(b.begin(), b.end());
    sort(c.rbegin(), c.rend());
    int count = 0;
    for(int i=0;i<n;i++){
        count = count + abs(b[i] - c[i]);
    }
    return count;
}

int main(){
    int t;
    cin>>t;
    while(t>0){
        cout<<solve()<<endl;
        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
1
1000
2
1000 1
10
1 2 3 4 5 6 7 8 9 10
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: A Gift From Orangutan
time_limit_ms: 1000
memory_limit_mb: 256
Description: While exploring the jungle, you have bumped into a rare orangutan with a bow tie! You shake hands with the orangutan and offer him some food and water. In return...

The orangutan has gifted you an array $a$ of length $n$. Using $a$, you will construct two arrays $b$ and $c$, both containing $n$ elements, in the following manner:

  * $b_i = \min(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.    * $c_i = \max(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.

Define the score of $a$ as $\sum_{i=1}^n c_i - b_i$ (i.e. the sum of $c_i - b_i$ over all $1 \leq i \leq n$). Before you calculate the score, you can shuffle the elements of $a$ however you want.

Find the maximum score that you can get if you shuffle the elements of $a$ optimally.

Input: The first line contains $t$ ($1 \leq t \leq 100$) — the number of test cases.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 1000$) — the number of elements in $a$.

The following line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 1000$) — the elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $1000$.

Output: For each test case, output the maximum score that you can get.

Examples:
input:
3
1
69
3
7 6 5
5
1 1 1 2 2
output:
0
4
4

Note: In the first test case, there is no other way to rearrange $a$. So, $b = [69]$ and $c = [69]$. The only possible score is $69 - 69 = 0$.

In the second test case, you can rearrange $a$ as $[7, 5, 6]$. Here, $b = [7, 5, 5]$ and $c = [7, 7, 7]$. The score in this case is $(7 - 7) + (7 - 5) + (7 - 5) = 4$. It can be shown this is the maximum possible score.

Buggy Code:
#include <iostream>
#include <vector>
#include <algorithm>
#include <climits>

using namespace std;

int main() {
    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        vector<int> arr(n);
        for (int i = 0; i < n; ++i) {
            cin >> arr[i];
        }

        vector<int> l;
        l.push_back(arr[n - 1]);
        for (int i = 0; i < n - 1; ++i) {
            l.push_back(arr[i]);
        }

        int max_val = 0;
        long long sum = 0;
        int min_val = INT_MAX;
        for (int i = 0; i < n; ++i) {
            max_val = max(max_val, l[i]);
            min_val = min(min_val, l[i]);
            sum += max_val - min_val;
        }

        cout << sum << endl;
    }

    return 0;
}

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

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

Think step by step.

Response:
```plaintext
3
1
1000
2
1 1000
3
1000 1 1
```

**Explanation:**

1. **Test Case 1:**
   - **Input:** `1 1000`
   - **Output:** `0`
   - **Explanation:** With only one element, the array cannot be shuffled, and the score is `0`.

2. **Test Case 2:**
   - **Input:** `2 1 1000`
   - **Output:** `999`
   - **Explanation:** By shuffling the array to `[1000, 1]`, the arrays `b` and `c` are:
     - `b = [1000, 1]`
     - `c = [1000, 1000]`
     - The score is `(1000 - 1000) + (1000 - 1) = 999`.

3. **Test Case 3:**
   - **Input:** `3 1000 1 1`
   - **Output:** `999`
   - **Explanation:** By shuffling the array to `[1000, 1, 1]`, the arrays `b` and `c` are:
     - `b = [1000, 1, 1]`
     - `c = [1000, 1000, 1000]`
     - The score is `(1000 - 1000) + (1000 - 1) + (1000 - 1) = 999`.

These test cases are designed to expose the bug in the given buggy code by ensuring that the maximum possible score is achieved in each case. The buggy code incorrectly constructs the arrays `b` and `c`, leading to incorrect scores. These test cases will help identify the issue.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: A Gift From Orangutan
time_limit_ms: 1000
memory_limit_mb: 256
Description: While exploring the jungle, you have bumped into a rare orangutan with a bow tie! You shake hands with the orangutan and offer him some food and water. In return...

The orangutan has gifted you an array $a$ of length $n$. Using $a$, you will construct two arrays $b$ and $c$, both containing $n$ elements, in the following manner:

  * $b_i = \min(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.    * $c_i = \max(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.

Define the score of $a$ as $\sum_{i=1}^n c_i - b_i$ (i.e. the sum of $c_i - b_i$ over all $1 \leq i \leq n$). Before you calculate the score, you can shuffle the elements of $a$ however you want.

Find the maximum score that you can get if you shuffle the elements of $a$ optimally.

Input: The first line contains $t$ ($1 \leq t \leq 100$) — the number of test cases.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 1000$) — the number of elements in $a$.

The following line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 1000$) — the elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $1000$.

Output: For each test case, output the maximum score that you can get.

Examples:
input:
3
1
69
3
7 6 5
5
1 1 1 2 2
output:
0
4
4

Note: In the first test case, there is no other way to rearrange $a$. So, $b = [69]$ and $c = [69]$. The only possible score is $69 - 69 = 0$.

In the second test case, you can rearrange $a$ as $[7, 5, 6]$. Here, $b = [7, 5, 5]$ and $c = [7, 7, 7]$. The score in this case is $(7 - 7) + (7 - 5) + (7 - 5) = 4$. It can be shown this is the maximum possible score.

Buggy Code:
tests = int(input())

for _ in range(tests):
    n = int(input())
    arr = list(map(int, input().split(" ")))

    arr.sort()

    score = 0
    for i in range(n):
        score += abs(arr[i] - arr[n-1-i])

    print(score)

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

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

Think step by step.

Response:
To create a challenging test input that exposes the bug in the provided code, we need to focus on the logic of the code and identify where it might fail. The code calculates the score by summing the absolute differences between each element and its counterpart from the end of the sorted array. However, this approach does not correctly compute the score as defined in the problem.

The correct approach should be to calculate the score based on the definitions of `b` and `c` arrays, where `b_i` is the minimum of the first `i` elements, and `c_i` is the maximum of the first `i` elements. The score is then the sum of `c_i - b_i` for all `i` from 1 to `n`.

The provided code fails because it uses the wrong formula to calculate the score. To expose this, we need a test case where the elements of the array, when sorted, do not align with the correct `b` and `c` values in a way that the incorrect formula would produce a different result.

Let's consider a test case where the array has a few unique values that, when sorted, create a clear discrepancy between the correct and incorrect score calculations.

### Challenging Test Input
```plaintext
3
4
1 4 2 3
5
5 5 5 5 5
6
1 2 3 4 5 6
```

### Explanation
1. **Test Case 1:**
   - Array: `[1, 4, 2, 3]`
   - Sorted Array: `[1, 2, 3, 4]`
   - Correct `b` and `c`:
     - `b = [1, 1, 1, 1]`
     - `c = [1, 2, 3, 4]`
   - Correct Score: `(1-1) + (2-1) + (3-1) + (4-1) = 0 + 1 + 2 + 3 = 6`
   - Buggy Code Output: `10` (Incorrect)

2. **Test Case 2:**
   - Array: `[5, 5, 5, 5, 5]`
   - Sorted Array: `[5, 5, 5, 5, 5]`
   - Correct `b` and `c`:
     - `b = [5, 5, 5, 5, 5]`
     - `c = [5, 5, 5, 5, 5]`
   - Correct Score: `(5-5) + (5-5) + (5-5) + (5-5) + (5-5) = 0`
   - Buggy Code Output: `0` (Correct)

3. **Test Case 3:**
   - Array: `[1, 2, 3, 4, 5, 6]`
   - Sorted Array: `[1, 2, 3, 4, 5, 6]`
   - Correct `b` and `c`:
     - `b = [1, 1, 1, 1, 1, 1]`
     - `c = [1, 2, 3, 4, 5, 6]`
   - Correct Score: `(1-1) + (2-1) + (3-1) + (4-1) + (5-1) + (6-1) = 0 + 1 + 2 + 3 + 4 + 5 = 15`
   - Buggy Code Output: `30` (Incorrect)

This test input will clearly show the discrepancy between the correct and incorrect score calculations, exposing 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: A Gift From Orangutan
time_limit_ms: 1000
memory_limit_mb: 256
Description: While exploring the jungle, you have bumped into a rare orangutan with a bow tie! You shake hands with the orangutan and offer him some food and water. In return...

The orangutan has gifted you an array $a$ of length $n$. Using $a$, you will construct two arrays $b$ and $c$, both containing $n$ elements, in the following manner:

  * $b_i = \min(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.    * $c_i = \max(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.

Define the score of $a$ as $\sum_{i=1}^n c_i - b_i$ (i.e. the sum of $c_i - b_i$ over all $1 \leq i \leq n$). Before you calculate the score, you can shuffle the elements of $a$ however you want.

Find the maximum score that you can get if you shuffle the elements of $a$ optimally.

Input: The first line contains $t$ ($1 \leq t \leq 100$) — the number of test cases.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 1000$) — the number of elements in $a$.

The following line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 1000$) — the elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $1000$.

Output: For each test case, output the maximum score that you can get.

Examples:
input:
3
1
69
3
7 6 5
5
1 1 1 2 2
output:
0
4
4

Note: In the first test case, there is no other way to rearrange $a$. So, $b = [69]$ and $c = [69]$. The only possible score is $69 - 69 = 0$.

In the second test case, you can rearrange $a$ as $[7, 5, 6]$. Here, $b = [7, 5, 5]$ and $c = [7, 7, 7]$. The score in this case is $(7 - 7) + (7 - 5) + (7 - 5) = 4$. It can be shown this is the maximum possible score.

Buggy Code:
t=int(input())
for i in range(t):
    n=int(input())
    a=list(map(int,input().split()))
    maxi=a[0]
    mini=a[0]
    second_largest=0
    d=0
    f=0
    e=0
    for i in range(n):
        if a[i]>maxi:
            maxi=a[i]
            second_largest=a[i]
            d=i
        elif second_largest < a[i] and a[i]!=maxi:
            second_largest=a[i]
            f=i
        elif a[i]<mini:
            mini=a[i]
            e=i
    a[0],a[d]=a[d],a[0]
    a[f],a[e]=a[e],a[f]
    b=[]
    c=[]
    maximum=0
    minimum=1001
    for i in range(0,n):
        minimum=min(minimum,a[i])
        b.append(minimum)
        maximum=max(maximum,a[i])
        c.append(maximum)
    sum=0
    for i in range(n):
        sum+=(c[i]-b[i])
    print(sum)

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on edge cases and scenarios that can highlight the issues in the logic. Here are the steps to think through this:

1. **Understand the Bug**: The buggy code has a flawed approach to finding the maximum and second largest values. It swaps the maximum value to the start and the second largest value to the position of the minimum value. This approach can lead to incorrect results if the array has duplicate values or if the second largest value is not correctly identified.

2. **Edge Cases**:
   - **Single Element Array**: This is already handled correctly in the code.
   - **Array with All Elements Equal**: This should result in a score of 0.
   - **Array with Two Different Elements**: This should test the logic of finding the maximum and second largest values.
   - **Array with Multiple Duplicates**: This can expose issues in the swapping logic.
   - **Array with a Large Difference Between Maximum and Other Elements**: This can test the ability to maximize the score.

3. **Generate Test Input**:
   - **Array with Multiple Duplicates**: This can cause issues if the second largest value is not correctly identified.
   - **Array with a Large Difference Between Maximum and Other Elements**: This can test the ability to maximize the score.

Based on these considerations, a small-scale test input that can expose the bug is:

```plaintext
3
5
1 1 1 1 1
4
1 2 2 3
5
1 2 3 4 1000
```

This test input includes:
- An array with all elements equal to 1.
- An array with two different elements, including duplicates.
- An array with a large difference between the maximum element and the other elements.

This should help in identifying the issues in the buggy code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: A Gift From Orangutan
time_limit_ms: 1000
memory_limit_mb: 256
Description: While exploring the jungle, you have bumped into a rare orangutan with a bow tie! You shake hands with the orangutan and offer him some food and water. In return...

The orangutan has gifted you an array $a$ of length $n$. Using $a$, you will construct two arrays $b$ and $c$, both containing $n$ elements, in the following manner:

  * $b_i = \min(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.    * $c_i = \max(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.

Define the score of $a$ as $\sum_{i=1}^n c_i - b_i$ (i.e. the sum of $c_i - b_i$ over all $1 \leq i \leq n$). Before you calculate the score, you can shuffle the elements of $a$ however you want.

Find the maximum score that you can get if you shuffle the elements of $a$ optimally.

Input: The first line contains $t$ ($1 \leq t \leq 100$) — the number of test cases.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 1000$) — the number of elements in $a$.

The following line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 1000$) — the elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $1000$.

Output: For each test case, output the maximum score that you can get.

Examples:
input:
3
1
69
3
7 6 5
5
1 1 1 2 2
output:
0
4
4

Note: In the first test case, there is no other way to rearrange $a$. So, $b = [69]$ and $c = [69]$. The only possible score is $69 - 69 = 0$.

In the second test case, you can rearrange $a$ as $[7, 5, 6]$. Here, $b = [7, 5, 5]$ and $c = [7, 7, 7]$. The score in this case is $(7 - 7) + (7 - 5) + (7 - 5) = 4$. It can be shown this is the maximum possible score.

Buggy Code:
t = int(input())
for _ in range(t):
    n = int(input())
    a = list(map(int,input().split()))
    b = sorted(a)
    c = sorted(a,reverse=True)
    result = [y - x for x,y in zip(b,c)]
    result = [abs(num) for num in result]
    print(sum(result))

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

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

Think step by step.

Response:
```plaintext
3
1
1
2
1 1
3
1 2 2
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: A Gift From Orangutan
time_limit_ms: 1000
memory_limit_mb: 256
Description: While exploring the jungle, you have bumped into a rare orangutan with a bow tie! You shake hands with the orangutan and offer him some food and water. In return...

The orangutan has gifted you an array $a$ of length $n$. Using $a$, you will construct two arrays $b$ and $c$, both containing $n$ elements, in the following manner:

  * $b_i = \min(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.    * $c_i = \max(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.

Define the score of $a$ as $\sum_{i=1}^n c_i - b_i$ (i.e. the sum of $c_i - b_i$ over all $1 \leq i \leq n$). Before you calculate the score, you can shuffle the elements of $a$ however you want.

Find the maximum score that you can get if you shuffle the elements of $a$ optimally.

Input: The first line contains $t$ ($1 \leq t \leq 100$) — the number of test cases.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 1000$) — the number of elements in $a$.

The following line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 1000$) — the elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $1000$.

Output: For each test case, output the maximum score that you can get.

Examples:
input:
3
1
69
3
7 6 5
5
1 1 1 2 2
output:
0
4
4

Note: In the first test case, there is no other way to rearrange $a$. So, $b = [69]$ and $c = [69]$. The only possible score is $69 - 69 = 0$.

In the second test case, you can rearrange $a$ as $[7, 5, 6]$. Here, $b = [7, 5, 5]$ and $c = [7, 7, 7]$. The score in this case is $(7 - 7) + (7 - 5) + (7 - 5) = 4$. It can be shown this is the maximum possible score.

Buggy Code:
import java.util.Scanner;

public class A_A_Gift_From_Orangutan{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for(int i =0 ; i<t ; i++){
            int n = sc.nextInt();
            int a[] = new int[n];

            int max=0;
            int min=1000;
            int sum=0 ;

            for(int j =0 ; j<n ; j++){
                a[j]= sc.nextInt();
                if(max<a[j]){
                    max=a[j];
                }else if(min>a[j]){
                    min= a[j];
                }
            }
            if(n==1){
                System.out.println(0);
            }
            else{
              if(n<=1000 && n>=1){  sum = (n-1)*(max-min);
                 System.out.println(sum);}

            }
        }

        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:
To expose the bug in the provided code, we need to focus on the logic that calculates the score. The buggy code incorrectly assumes that the maximum score can be calculated by simply using the maximum and minimum values in the array and applying the formula `(n-1) * (max - min)`. This approach fails to consider the correct construction of arrays `b` and `c` as described in the problem statement.

### Key Points to Consider:
1. **Single Element Array**: The code correctly handles the case where `n = 1`.
2. **Multiple Elements**: The code fails to correctly handle the construction of arrays `b` and `c` for multiple elements. It only considers the global maximum and minimum values, which is not sufficient.

### Challenging Test Input:
To expose this bug, we can use a test case where the elements are not all the same and are in a specific order that maximizes the difference between `c_i` and `b_i`.

### Test Input:
```plaintext
3
1
69
3
7 6 5
5
1 2 3 4 5
```

### Explanation:
1. **First Test Case**:
   - `n = 1`
   - `a = [69]`
   - The score is `0` because there is only one element, and `b = [69]`, `c = [69]`.

2. **Second Test Case**:
   - `n = 3`
   - `a = [7, 6, 5]`
   - The score is `4` because:
     - `b = [7, 6, 5]`
     - `c = [7, 7, 7]`
     - The score is `(7-7) + (7-6) + (7-5) = 4`

3. **Third Test Case**:
   - `n = 5`
   - `a = [1, 2, 3, 4, 5]`
   - The score is `10` because:
     - `b = [1, 1, 1, 1, 1]`
     - `c = [1, 2, 3, 4, 5]`
     - The score is `(1-1) + (2-1) + (3-1) + (4-1) + (5-1) = 10`

This test input will help expose the bug in the buggy code, as the correct score for the third test case should be `10`, but the buggy code will output `(5-1) * (5-1) = 16`, which is incorrect.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: A Gift From Orangutan
time_limit_ms: 1000
memory_limit_mb: 256
Description: While exploring the jungle, you have bumped into a rare orangutan with a bow tie! You shake hands with the orangutan and offer him some food and water. In return...

The orangutan has gifted you an array $a$ of length $n$. Using $a$, you will construct two arrays $b$ and $c$, both containing $n$ elements, in the following manner:

  * $b_i = \min(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.    * $c_i = \max(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.

Define the score of $a$ as $\sum_{i=1}^n c_i - b_i$ (i.e. the sum of $c_i - b_i$ over all $1 \leq i \leq n$). Before you calculate the score, you can shuffle the elements of $a$ however you want.

Find the maximum score that you can get if you shuffle the elements of $a$ optimally.

Input: The first line contains $t$ ($1 \leq t \leq 100$) — the number of test cases.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 1000$) — the number of elements in $a$.

The following line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 1000$) — the elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $1000$.

Output: For each test case, output the maximum score that you can get.

Examples:
input:
3
1
69
3
7 6 5
5
1 1 1 2 2
output:
0
4
4

Note: In the first test case, there is no other way to rearrange $a$. So, $b = [69]$ and $c = [69]$. The only possible score is $69 - 69 = 0$.

In the second test case, you can rearrange $a$ as $[7, 5, 6]$. Here, $b = [7, 5, 5]$ and $c = [7, 7, 7]$. The score in this case is $(7 - 7) + (7 - 5) + (7 - 5) = 4$. It can be shown this is the maximum possible score.

Buggy Code:
/*
        Codeforces Round 979 (Div. 2).
        Problem A. A Gift From Orangutan
        2024/10/21
*/

import java.io.*;
import java.util.*;

public class AGiftFromOrangutan {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());

        while (t-- > 0) {
            String[] h = br.readLine().split(" ");
            int n = Integer.parseInt(h[0]);

            int[] nums = new int[n];
            h = br.readLine().split(" ");
            for (int i = 0; i < n; i++) {
                nums[i] = Integer.parseInt(h[i]);
            }

            Arrays.sort(nums); // 从小到大排序
            int sum = 0;
            for (int i = 0, j = n - 1; i < n; i++, j--) {
                sum += Math.abs(nums[i] - nums[j]);
            }
            System.out.println(sum);
        }
    }
}

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

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

Think step by step.

Response:
To expose the bug in the provided buggy code, we need to craft a test input that highlights the incorrect logic in the code. The buggy code sorts the array and then calculates the sum of the absolute differences between the elements at symmetric positions. However, this approach does not correctly maximize the score as defined in the problem.

The correct approach should involve sorting the array in descending order to maximize the differences between the maximum and minimum values at each step.

### Test Input
Let's create a test case where the array has elements that, when sorted, do not maximize the score. A good candidate is an array with repeated elements and a few distinct values to highlight the issue.

```plaintext
3
1
69
3
7 6 5
4
3 3 2 2
```

### Explanation
1. **Test Case 1:**
   - `n = 1`
   - `a = [69]`
   - The score is `0` because there is only one element.

2. **Test Case 2:**
   - `n = 3`
   - `a = [7, 6, 5]`
   - The optimal shuffle is `[7, 5, 6]` or `[7, 6, 5]`.
   - `b = [7, 5, 5]`
   - `c = [7, 7, 7]`
   - The score is `(7 - 7) + (7 - 5) + (7 - 5) = 4`.

3. **Test Case 3:**
   - `n = 4`
   - `a = [3, 3, 2, 2]`
   - The optimal shuffle is `[3, 3, 2, 2]` or `[3, 2, 3, 2]`.
   - `b = [3, 3, 2, 2]`
   - `c = [3, 3, 3, 3]`
   - The score is `(3 - 3) + (3 - 3) + (3 - 2) + (3 - 2) = 2`.

### Expected Output
The correct output for the test cases should be:
```plaintext
0
4
2
```

### Why This Test Case?
- **Test Case 1** is straightforward and ensures the basic logic works.
- **Test Case 2** is from the example and ensures the logic for a small array with distinct values works.
- **Test Case 3** introduces repeated elements, which the buggy code might not handle correctly. The buggy code sorts the array and calculates the sum of absolute differences, which does not maximize the score in this case.

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: A Gift From Orangutan
time_limit_ms: 1000
memory_limit_mb: 256
Description: While exploring the jungle, you have bumped into a rare orangutan with a bow tie! You shake hands with the orangutan and offer him some food and water. In return...

The orangutan has gifted you an array $a$ of length $n$. Using $a$, you will construct two arrays $b$ and $c$, both containing $n$ elements, in the following manner:

  * $b_i = \min(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.    * $c_i = \max(a_1, a_2, \ldots, a_i)$ for each $1 \leq i \leq n$.

Define the score of $a$ as $\sum_{i=1}^n c_i - b_i$ (i.e. the sum of $c_i - b_i$ over all $1 \leq i \leq n$). Before you calculate the score, you can shuffle the elements of $a$ however you want.

Find the maximum score that you can get if you shuffle the elements of $a$ optimally.

Input: The first line contains $t$ ($1 \leq t \leq 100$) — the number of test cases.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 1000$) — the number of elements in $a$.

The following line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 1000$) — the elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $1000$.

Output: For each test case, output the maximum score that you can get.

Examples:
input:
3
1
69
3
7 6 5
5
1 1 1 2 2
output:
0
4
4

Note: In the first test case, there is no other way to rearrange $a$. So, $b = [69]$ and $c = [69]$. The only possible score is $69 - 69 = 0$.

In the second test case, you can rearrange $a$ as $[7, 5, 6]$. Here, $b = [7, 5, 5]$ and $c = [7, 7, 7]$. The score in this case is $(7 - 7) + (7 - 5) + (7 - 5) = 4$. It can be shown this is the maximum possible score.

Buggy Code:
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

#define ll long long
#define yes cout << "YES" << endl
#define no cout << "NO" << endl
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pbds;

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int t;
    cin >> t;
    while (t--)
    {
        int n;
        cin >> n;
        vector<int> a;
        int maxi = INT_MIN;
        int mini = INT_MAX;
        int ind1, ind2;
        for (int i = 0; i < n; i++)
        {
            int temp;
            cin >> temp;
            a.push_back(temp);
            if (maxi < temp)
            {
                maxi = temp;
                ind1 = i;
            }
            if (mini > temp)
            {
                mini = temp;
                ind2 = i;
            }
        }
        if (a.size() == 1)
        {
            cout << 0 << endl;
            continue;
        }
        swap(a[0], a[ind1]);
        swap(a[1], a[ind2]);
        vector<int> b, c;
        b.push_back(a[0]);
        c.push_back(a[0]);
        int sum = 0;

        for (int i = 1; i < n; i++)
        {
            b.push_back(max(b[i - 1], a[i]));
            c.push_back(min(c[i - 1], a[i]));
            sum += b[i] - c[i];
        }
        // for (int i = 0; i < n; i++)
        // {
        //     cout << c[i] << " ";
        // }
        cout << sum << endl;
    }

    return 0;
}

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

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

Think step by step.

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