**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Beautiful Triple Pairs
time_limit_ms: 4000
memory_limit_mb: 256
Description: Polycarp was given an array $a$ of $n$ integers. He really likes triples of numbers, so for each $j$ ($1 \le j \le n - 2$) he wrote down a triple of elements $[a_j, a_{j + 1}, a_{j + 2}]$.

Polycarp considers a pair of triples $b$ and $c$ beautiful if they differ in exactly one position, that is, one of the following conditions is satisfied:

  * $b_1 \ne c_1$ and $b_2 = c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 \ne c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 = c_2$ and $b_3 \ne c_3$.

Find the number of beautiful pairs of triples among the written triples $[a_j, a_{j + 1}, a_{j + 2}]$.

Input: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — the elements of the array.

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

Output: For each test case, output a single integer — the number of beautiful pairs of triples among the pairs of the form $[a_j, a_{j + 1}, a_{j + 2}]$.

Note that the answer may not fit into 32-bit data types.

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

Note: In the first example, $a = [3, 2, 2, 2, 3]$, Polycarp will write the following triples:

  1. $[3, 2, 2]$;    2. $[2, 2, 2]$;    3. $[2, 2, 3]$.

The beautiful pairs are triple $1$ with triple $2$ and triple $2$ with triple $3$.

In the third example, $a = [1, 2, 3, 2, 2, 3, 4, 2]$, Polycarp will write the following triples:

  1. $[1, 2, 3]$;    2. $[2, 3, 2]$;    3. $[3, 2, 2]$;    4. $[2, 2, 3]$;    5. $[2, 3, 4]$;    6. $[3, 4, 2]$;

The beautiful pairs are triple $1$ with triple $4$, triple $2$ with triple $5$, and triple $3$ with triple $6$.

Buggy Code:
import sys
input=lambda:sys.stdin.readline().strip()
from math import*
from collections import*
I=lambda: map(int,input().split())
l=lambda: list(map(int,input().split()))
li=lambda: [(int(v),j) for j,v in enumerate (input().split())]
def check(j,k):
    if (j[0]!=k[0] and j[1]==k[1] and j[2]==k[2] ) or (j[0]==k[0] and j[1]!=k[1] and j[2]==k[2]) or (j[0]==k[0] and j[1]==k[1] and j[2]!=k[2]):
        return 1

    return 0

'''g=["a","b","c","d","e","f","g","h","i","j","k","l","m","n","o","p","q","r","s","t","u","v","w","x","y","z"]'''
for i in range(int(input())):
    n=int(input())
    a=l()
    d={}
    c=0

    for j in range(n-2):
        if (a[j],a[j+1],a[j+2]) in d:
            d[a[j],a[j+1],a[j+2]]+=1
        else: d[(a[j],a[j+1],a[j+2])]=1
    for j in d:
        for k in d:
            if j!=k and check(j,k):
                c+=d[j]*d[k]
    print(c//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:
```plaintext
3
5
1 1 1 2 2
6
1 1 1 1 2 2
7
1 1 1 1 1 2 2
```

**Explanation:**

1. **Test Case 1:**
   - **Input:** `5 1 1 1 2 2`
   - **Expected Output:** `1`
   - **Explanation:** The array `a = [1, 1, 1, 2, 2]` generates the following triples:
     - `[1, 1, 1]`
     - `[1, 1, 2]`
     - `[1, 2, 2]`
   - The only beautiful pair is `[1, 1, 1]` with `[1, 1, 2]`.

2. **Test Case 2:**
   - **Input:** `6 1 1 1 1 2 2`
   - **Expected Output:** `4`
   - **Explanation:** The array `a = [1, 1, 1, 1, 2, 2]` generates the following triples:
     - `[1, 1, 1]`
     - `[1, 1, 1]`
     - `[1, 1, 2]`
     - `[1, 2, 2]`
   - The beautiful pairs are:
     - `[1, 1, 1]` with `[1, 1, 1]` (both instances)
     - `[1, 1, 1]` with `[1, 1, 2]` (both instances)
     - `[1, 1, 1]` with `[1, 2, 2]` (both instances)
   - Each pair is counted twice, so the total is `4`.

3. **Test Case 3:**
   - **Input:** `7 1 1 1 1 1 2 2`
   - **Expected Output:** `6`
   - **Explanation:** The array `a = [1, 1, 1, 1, 1, 2, 2]` generates the following triples:
     - `[1, 1, 1]`
     - `[1, 1, 1]`
     - `[1, 1, 1]`
     - `[1, 1, 2]`
     - `[1, 2, 2]`
   - The beautiful pairs are:
     - `[1, 1, 1]` with `[1, 1, 1]` (all instances)
     - `[1, 1, 1]` with `[1, 1, 2]` (all instances)
     - `[1, 1, 1]` with `[1, 2, 2]` (all instances)
   - Each pair is counted twice, so the total is `6`.

These test cases are designed to expose potential bugs in the code, particularly in handling repeated elements and counting pairs correctly.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Beautiful Triple Pairs
time_limit_ms: 4000
memory_limit_mb: 256
Description: Polycarp was given an array $a$ of $n$ integers. He really likes triples of numbers, so for each $j$ ($1 \le j \le n - 2$) he wrote down a triple of elements $[a_j, a_{j + 1}, a_{j + 2}]$.

Polycarp considers a pair of triples $b$ and $c$ beautiful if they differ in exactly one position, that is, one of the following conditions is satisfied:

  * $b_1 \ne c_1$ and $b_2 = c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 \ne c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 = c_2$ and $b_3 \ne c_3$.

Find the number of beautiful pairs of triples among the written triples $[a_j, a_{j + 1}, a_{j + 2}]$.

Input: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — the elements of the array.

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

Output: For each test case, output a single integer — the number of beautiful pairs of triples among the pairs of the form $[a_j, a_{j + 1}, a_{j + 2}]$.

Note that the answer may not fit into 32-bit data types.

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

Note: In the first example, $a = [3, 2, 2, 2, 3]$, Polycarp will write the following triples:

  1. $[3, 2, 2]$;    2. $[2, 2, 2]$;    3. $[2, 2, 3]$.

The beautiful pairs are triple $1$ with triple $2$ and triple $2$ with triple $3$.

In the third example, $a = [1, 2, 3, 2, 2, 3, 4, 2]$, Polycarp will write the following triples:

  1. $[1, 2, 3]$;    2. $[2, 3, 2]$;    3. $[3, 2, 2]$;    4. $[2, 2, 3]$;    5. $[2, 3, 4]$;    6. $[3, 4, 2]$;

The beautiful pairs are triple $1$ with triple $4$, triple $2$ with triple $5$, and triple $3$ with triple $6$.

Buggy Code:
from sys import stdin, setrecursionlimit, stdout
from itertools import permutations
#setrecursionlimit(1000000) #use "python" instead of "pypy" to avoid MLE
from io import BytesIO
import os
from functools import cmp_to_key
from collections import deque, Counter, defaultdict, OrderedDict
from math import sqrt, floor, ceil, log, log2, log10, pi, gcd, sin, cos, asin
from heapq import heapify, heappop, heappush, heapreplace, heappushpop
#	to use maxheap, invert all the number.. that means, multyply with -1
from bisect import bisect_right, bisect_left
#	number of elements in a range is bisect_right(a, el)-bisect_left(a, el)
from string import ascii_letters, ascii_lowercase, ascii_uppercase, digits, hexdigits, whitespace, punctuation

def ii(): return int(input().decode()) if not DEBUG else int(input())

def fi(): return float(input().decode()) if not DEBUG else float(input())

def mi(): return map(int, input().decode().split()) if not DEBUG else map(int, input().split())

def fmi(): return map(float, input().decode().split()) if not DEBUG else map(float, input().split())

def li(): return list(mi())

def si(): return input().decode().rstrip() if not DEBUG else input().rstrip()

def msi(): return map(str, input().decode().split()) if not DEBUG else map(str, input().split())

def lsi(): return list(si())

#######################################################################################
###########################    M Y     F U N C T I O N S    ###########################
#######################################################################################

#######################################################################################
###########################    M A I N     P R O G R A M    ###########################
#######################################################################################

def main():
	def numbers(i):
		x=a[i+1]*10 +a[i+2]
		y=a[i]*100 + a[i+2]
		z=a[i]*100 + a[i+1]*10
		return [x, y, z]
	n=ii()
	a=li()
	tot=0
	d= {}
	vis= {}
	for i in range(n-2):
		cur=a[i]*100 + a[i+1]*10+a[i+2]
		if cur not in vis:
			vis[cur]=0
		val=numbers(i)
		for x in val:
			if x in d:
				tot+=d[x]-vis[cur]
				d[x]+=1
			else:
				d[x]=1
		vis[cur]+=1
	#print(d)
	#print(vis)
	print(tot)

#######################################################################################
###########################    S T A R T E R     P A C K    ###########################
#######################################################################################

if __name__ == "__main__":
	DEBUG = os.environ.get("__DEBUG__")

	if DEBUG:
		if os.stat("input.txt").st_size == 0:
			input = stdin.readline
		else:
			input = open('input.txt', 'r').readline
	else:
		input = BytesIO(os.read(0, os.fstat(0).st_size)).readline

	vow = {'A', 'E', 'I', 'O', 'U'}
	mod = 1000000007

	mod1 = 100000110709
	mod2 = 100000110719
	res = ['NO', 'YES']
	adj4 = [[-1, 0], [0, -1], [0, 1], [1, 0]]
	adj8 = [[-1, -1], [-1, 0], [-1, 1], [0, -1], [0, 1], [1, -1], [1, 0], [1, 1]]

	test, test_case = 0, 1
	test_case = int(input())

	while test < test_case:
		test += 1
		if DEBUG:
			print('>>>>>>>>>>>>> Case #{} >>>>>>>>>>>>>'.format(test))
			pass
		#print('Case ', test, ': ', sep='', end='')
		main()

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

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

Think step by step.

Response:
```plaintext
1
6
1 1 1 2 1 1
```

### Explanation:
This test case is designed to expose potential issues in the buggy code by creating a sequence where the majority of the elements are the same, with a single differing element in the middle. Here’s why this input is challenging:

1. **Sequence Structure**: The sequence `1 1 1 2 1 1` has a single element `2` in the middle, surrounded by `1`s. This creates a pattern where the triples will have significant overlap, but with one differing element in the middle.

2. **Beautiful Pairs**:
   - The triples generated are:
     - `[1, 1, 1]` (index 0)
     - `[1, 1, 2]` (index 1)
     - `[1, 2, 1]` (index 2)
     - `[2, 1, 1]` (index 3)
   - The beautiful pairs are:
     - `[1, 1, 1]` and `[1, 1, 2]` (differ in the third element)
     - `[1, 1, 2]` and `[1, 2, 1]` (differ in the second element)
     - `[1, 2, 1]` and `[2, 1, 1]` (differ in the first element)

3. **Expected Output**: The expected output is `3` because there are three beautiful pairs of triples.

This input is small enough to be manageable but complex enough to test the logic of the algorithm, particularly the handling of overlapping elements and the correct counting of beautiful pairs.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Beautiful Triple Pairs
time_limit_ms: 4000
memory_limit_mb: 256
Description: Polycarp was given an array $a$ of $n$ integers. He really likes triples of numbers, so for each $j$ ($1 \le j \le n - 2$) he wrote down a triple of elements $[a_j, a_{j + 1}, a_{j + 2}]$.

Polycarp considers a pair of triples $b$ and $c$ beautiful if they differ in exactly one position, that is, one of the following conditions is satisfied:

  * $b_1 \ne c_1$ and $b_2 = c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 \ne c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 = c_2$ and $b_3 \ne c_3$.

Find the number of beautiful pairs of triples among the written triples $[a_j, a_{j + 1}, a_{j + 2}]$.

Input: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — the elements of the array.

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

Output: For each test case, output a single integer — the number of beautiful pairs of triples among the pairs of the form $[a_j, a_{j + 1}, a_{j + 2}]$.

Note that the answer may not fit into 32-bit data types.

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

Note: In the first example, $a = [3, 2, 2, 2, 3]$, Polycarp will write the following triples:

  1. $[3, 2, 2]$;    2. $[2, 2, 2]$;    3. $[2, 2, 3]$.

The beautiful pairs are triple $1$ with triple $2$ and triple $2$ with triple $3$.

In the third example, $a = [1, 2, 3, 2, 2, 3, 4, 2]$, Polycarp will write the following triples:

  1. $[1, 2, 3]$;    2. $[2, 3, 2]$;    3. $[3, 2, 2]$;    4. $[2, 2, 3]$;    5. $[2, 3, 4]$;    6. $[3, 4, 2]$;

The beautiful pairs are triple $1$ with triple $4$, triple $2$ with triple $5$, and triple $3$ with triple $6$.

Buggy Code:
import java.io.*;
import java.util.*;
public class Main
{

    public static void main(String[] args) throws IOException
    {
        int a = nextInt();
        for (int i = 0; i < a; i++) {
            int n = nextInt();
            int c [] [] = new int[n][3];
            int f [] = new int[n];
            for (int j = 0; j < n; j++) {
                f[j] = nextInt();
            }
            for (int j = 0; j < n-2; j++) {
                c[j][0] = (f[j]);
                c[j][1] =(f[j+1]);
                c[j][2] = (f[j+2]);
            }
            long ans = 0;
            for (int j = 0; j < n; j++) {
                for (int k = 0; k < n; k++) {
                    int cnt = 0;
                    if(k == j){
                        continue;
                    }
                    if(c[j][0] != c[k][0] && c[j][1] == c[k][1] && c[j][2] == c[k][2] || c[j][1] != c[k][1] && c[j][2] == c[k][2] && c[j][0] == c[k][0] ||c[j][2] != c[k][2] && c[j][1] == c[k][1] && c[j][0] == c[k][0] ){
                        ans++;
                    }
                }
            }
            out.println(ans / 2);
        }
        out.close();
    }
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter out = new PrintWriter(System.out);
    static StringTokenizer in = new StringTokenizer("");

    public static boolean hasNext() throws IOException {
        if (in.hasMoreTokens()) return true;
        String s;
        while ((s = br.readLine()) != null) {
            in = new StringTokenizer(s);
            if (in.hasMoreTokens()) return true;
        }
        return false;
    }

    public static String nextToken() throws IOException {
        while (!in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

    public static int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public static double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public static long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
}

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

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

Think step by step.

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

1. **Edge Cases**: Test inputs that push the boundaries of the input constraints.
2. **Complexity**: Inputs that maximize the number of comparisons and increase the likelihood of logical errors.
3. **Special Patterns**: Inputs that create specific patterns in the array to test the conditions for beautiful pairs.

Given the constraints and the nature of the problem, let's consider the following test input:

```plaintext
1
6
1 2 2 1 2 2
```

### Explanation:

1. **Test Case Count**: We use a single test case (`1`), which is valid and keeps the input small.
2. **Array Length**: We choose an array length of `6` to ensure it's within the constraints and provides enough elements to form multiple triples.
3. **Array Elements**: The array `1 2 2 1 2 2` is chosen to create a specific pattern that can expose the bug in the code:
   - The triples formed are:
     - `[1, 2, 2]`
     - `[2, 2, 1]`
     - `[2, 1, 2]`
     - `[1, 2, 2]`
   - This pattern ensures that there are multiple opportunities for the triples to differ in exactly one position, which is the condition for a beautiful pair.

### Expected Output:
For the input `1 2 2 1 2 2`, the expected output should be `4` because:
- Triple `[1, 2, 2]` (index 0) is beautiful with `[1, 2, 2]` (index 3).
- Triple `[2, 2, 1]` (index 1) is beautiful with `[2, 1, 2]` (index 2).
- Triple `[2, 1, 2]` (index 2) is beautiful with `[2, 2, 1]` (index 1).
- Triple `[1, 2, 2]` (index 3) is beautiful with `[1, 2, 2]` (index 0).

This test input should effectively expose the bug in the provided code, which might be missing some conditions or incorrectly counting the beautiful pairs.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Beautiful Triple Pairs
time_limit_ms: 4000
memory_limit_mb: 256
Description: Polycarp was given an array $a$ of $n$ integers. He really likes triples of numbers, so for each $j$ ($1 \le j \le n - 2$) he wrote down a triple of elements $[a_j, a_{j + 1}, a_{j + 2}]$.

Polycarp considers a pair of triples $b$ and $c$ beautiful if they differ in exactly one position, that is, one of the following conditions is satisfied:

  * $b_1 \ne c_1$ and $b_2 = c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 \ne c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 = c_2$ and $b_3 \ne c_3$.

Find the number of beautiful pairs of triples among the written triples $[a_j, a_{j + 1}, a_{j + 2}]$.

Input: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — the elements of the array.

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

Output: For each test case, output a single integer — the number of beautiful pairs of triples among the pairs of the form $[a_j, a_{j + 1}, a_{j + 2}]$.

Note that the answer may not fit into 32-bit data types.

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

Note: In the first example, $a = [3, 2, 2, 2, 3]$, Polycarp will write the following triples:

  1. $[3, 2, 2]$;    2. $[2, 2, 2]$;    3. $[2, 2, 3]$.

The beautiful pairs are triple $1$ with triple $2$ and triple $2$ with triple $3$.

In the third example, $a = [1, 2, 3, 2, 2, 3, 4, 2]$, Polycarp will write the following triples:

  1. $[1, 2, 3]$;    2. $[2, 3, 2]$;    3. $[3, 2, 2]$;    4. $[2, 2, 3]$;    5. $[2, 3, 4]$;    6. $[3, 4, 2]$;

The beautiful pairs are triple $1$ with triple $4$, triple $2$ with triple $5$, and triple $3$ with triple $6$.

Buggy Code:
import java.util.*;
import java.math.*;
import java.io.*;
public class A1{
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    static BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
    static StringTokenizer st;
    static final long mod=1000000007;
    static final int mod1=998244353;

    static class Triples{
        int a,b,c;
        Triples(int a,int b,int c){
            this.a=a;
            this.b=b;
            this.c=c;
        }
    }
    public static void Solve() throws IOException{
        //st=new StringTokenizer(br.readLine());
        int n=Integer.parseInt(br.readLine());
        int[] ar=getArrIn(n);
        List<Triples> al=new ArrayList<>();
        for(int i=0;i<n-2;i++) al.add(new Triples(ar[i],ar[i+1],ar[i+2]));
        n=al.size();
        long ans=0;
        for (int i=0;i<n;i++) {
            Triples t=al.get(i);
            for(int j=i+1;j<n;j++){
                Triples t1=al.get(j);
                if((t.a!=t1.a && t.b==t1.b && t.c==t1.c) || (t.a==t1.a && t.b!=t1.b && t.c==t1.c)
                        || (t.a==t1.a && t.b==t1.b && t.c!=t1.c)) ans++;
            }
        }
        bw.write(ans+"\n");
    }

    /** Main Method**/
    public static void main(String[] YDSV) throws IOException{
        //int t=1;
        int t=Integer.parseInt(br.readLine());
        while(t-->0) Solve();
        bw.flush();
    }

    /** Helpers**/
    private static int[] getArrIn(int n) throws IOException{
        st=new StringTokenizer(br.readLine());
        int[] ar=new int[n];
        for(int i=0;i<n;i++) ar[i]=Integer.parseInt(st.nextToken());
        return ar;
    }
    private static long[] getArrLo(int n) throws IOException{
        st=new StringTokenizer(br.readLine());
        long[] ar=new long[n];
        for(int i=0;i<n;i++) ar[i]=Long.parseLong(st.nextToken());
        return ar;
    }
    private static List<Integer> getListIn(int n) throws IOException{
        st=new StringTokenizer(br.readLine());
        List<Integer> al=new ArrayList<>();
        for(int i=0;i<n;i++) al.add(Integer.parseInt(st.nextToken()));
        return al;
    }
    private static List<Long> getListLo(int n) throws IOException{
        st=new StringTokenizer(br.readLine());
        List<Long> al=new ArrayList<>();
        for(int i=0;i<n;i++) al.add(Long.parseLong(st.nextToken()));
        return al;
    }
    private static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }
    private static void sort(long[] a) {
        ArrayList<Long> l=new ArrayList<>();
        for (long i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }
    private static long pow_mod(long a,long b) {
        long result=1;
        while(b!=0){
            if((b&1)!=0) result=(result*a)%mod;
            a=(a*a)%mod;
            b>>=1;
        }
        return result;
    }
    private static int pow_mod(int a,int b) {
        int result=1;
        int mod2=(int)mod;
        while(b!=0){
            if((b&1)!=0) result=(result*a)%mod2;
            a=(a*a)%mod2;
            b>>=1;
        }
        return result;
    }
    private static int Gcd(int a,int b){
        if(b==0) return a;
        return Gcd(b,a%b);
    }
    private static long Gcd(long a,long b){
        if(b==0) return a;
        return Gcd(b,a%b);
    }
    private static boolean Sqrt(int x){
        int a=(int)Math.sqrt(x);
        return a*a==x;
    }
    private static boolean Sqrt(long x){
        long a=(long)Math.sqrt(x);
        return a*a==x;
    }
}

**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 2 1 2
```

### Explanation:
This test case is designed to challenge the given buggy code by creating a scenario where the triples are similar but not identical, which can potentially expose any issues in the comparison logic.

- **Array**: `1 2 2 1 2`
- **Triples**:
  - `[1, 2, 2]`
  - `[2, 2, 1]`
  - `[2, 1, 2]`

- **Beautiful Pairs**:
  - `[1, 2, 2]` and `[2, 2, 1]` (differ in the first position)
  - `[2, 2, 1]` and `[2, 1, 2]` (differ in the second position)

The expected output for this test case is `2`.

This test case is small and manageable but still covers a variety of positions where the triples can differ, making it a good candidate to expose any 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: Beautiful Triple Pairs
time_limit_ms: 4000
memory_limit_mb: 256
Description: Polycarp was given an array $a$ of $n$ integers. He really likes triples of numbers, so for each $j$ ($1 \le j \le n - 2$) he wrote down a triple of elements $[a_j, a_{j + 1}, a_{j + 2}]$.

Polycarp considers a pair of triples $b$ and $c$ beautiful if they differ in exactly one position, that is, one of the following conditions is satisfied:

  * $b_1 \ne c_1$ and $b_2 = c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 \ne c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 = c_2$ and $b_3 \ne c_3$.

Find the number of beautiful pairs of triples among the written triples $[a_j, a_{j + 1}, a_{j + 2}]$.

Input: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — the elements of the array.

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

Output: For each test case, output a single integer — the number of beautiful pairs of triples among the pairs of the form $[a_j, a_{j + 1}, a_{j + 2}]$.

Note that the answer may not fit into 32-bit data types.

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

Note: In the first example, $a = [3, 2, 2, 2, 3]$, Polycarp will write the following triples:

  1. $[3, 2, 2]$;    2. $[2, 2, 2]$;    3. $[2, 2, 3]$.

The beautiful pairs are triple $1$ with triple $2$ and triple $2$ with triple $3$.

In the third example, $a = [1, 2, 3, 2, 2, 3, 4, 2]$, Polycarp will write the following triples:

  1. $[1, 2, 3]$;    2. $[2, 3, 2]$;    3. $[3, 2, 2]$;    4. $[2, 2, 3]$;    5. $[2, 3, 4]$;    6. $[3, 4, 2]$;

The beautiful pairs are triple $1$ with triple $4$, triple $2$ with triple $5$, and triple $3$ with triple $6$.

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

long long beautiful(int array[], int array_length);
bool sortcomp(int a[3], int b[3]);

int main(void){
    short test_cases;
    cin >> test_cases;
    for(short i = 0; i < test_cases; i++){
        int array_length;
        cin >> array_length;
        int array[array_length];
        for(int j = 0; j < array_length; j++){
            cin >> array[j];
        }

        cout << beautiful(array, array_length) << endl;
    }
}

bool sortcomp(int a[3], int b[3]){
    return (a[0]<b[0]);
}

long long beautiful(int array[], int array_length){
    long long count = 0;

    //Array of triples
    int triple_array[array_length-2][3];
    for(int i = 0; i < array_length - 2; i++){
        for(short j = 0; j < 3; j++){
            triple_array[i][j] = array[i + j];
            //cout << array[i + j] << " ";
        }
        //cout << endl;
    }

    //Finding beautiful pairs
    for(int i = 0; i < array_length-3; i++){
        for(int j = i+1; j < array_length-2; j++){
            if(triple_array[i][0]==triple_array[j][0] && triple_array[i][1]==triple_array[j][1] && triple_array[i][2]!=triple_array[j][2] || triple_array[i][0]==triple_array[j][0] && triple_array[i][1]!=triple_array[j][1] && triple_array[i][2]==triple_array[j][2] || triple_array[i][0]!=triple_array[j][0] && triple_array[i][1]==triple_array[j][1] && triple_array[i][2]==triple_array[j][2]){
                count++;
            }
        }
    }

    return count;
}

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

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

Think step by step.

Response:
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 issues in the algorithm. The main issue in the buggy code is the way it checks for beautiful pairs. The code uses a nested loop to compare each pair of triples, but it might not handle certain edge cases correctly, especially when the array has repeated elements or specific patterns.

Let's consider the following steps:

1. **Array with Repeated Elements**: An array with many repeated elements can create a large number of triples that are similar, which can lead to a high number of beautiful pairs. This can help in identifying issues with the comparison logic.

2. **Array with Specific Patterns**: Arrays with specific patterns (e.g., alternating elements, sequences) can also expose issues in the comparison logic.

3. **Array with Small Length**: Since the code uses nested loops, a small array length can help in quickly identifying the issue without overwhelming the system.

4. **Array with Different Values**: An array with a mix of different values can help in testing the comparison logic for all three positions of the triples.

Based on these considerations, let's generate a test input:

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

### Explanation:
1. **Test Case 1**: `5 1 1 2 2 1`
   - Triples: `[1, 1, 2]`, `[1, 2, 2]`, `[2, 2, 1]`
   - Beautiful pairs:
     - `[1, 1, 2]` and `[1, 2, 2]` (differ in the second position)
     - `[1, 2, 2]` and `[2, 2, 1]` (differ in the first position)
   - Expected output: `2`

2. **Test Case 2**: `6 1 2 3 2 3 1`
   - Triples: `[1, 2, 3]`, `[2, 3, 2]`, `[3, 2, 3]`, `[2, 3, 1]`
   - Beautiful pairs:
     - `[1, 2, 3]` and `[2, 3, 2]` (differ in the first position)
     - `[2, 3, 2]` and `[3, 2, 3]` (differ in the first position)
     - `[3, 2, 3]` and `[2, 3, 1]` (differ in the first and third positions)
   - Expected output: `3`

3. **Test Case 3**: `4 1 2 2 1`
   - Triples: `[1, 2, 2]`, `[2, 2, 1]`
   - Beautiful pairs:
     - `[1, 2, 2]` and `[2, 2, 1]` (differ in the first position)
   - Expected output: `1`

This test input should help in exposing any issues in the comparison logic used 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: Beautiful Triple Pairs
time_limit_ms: 4000
memory_limit_mb: 256
Description: Polycarp was given an array $a$ of $n$ integers. He really likes triples of numbers, so for each $j$ ($1 \le j \le n - 2$) he wrote down a triple of elements $[a_j, a_{j + 1}, a_{j + 2}]$.

Polycarp considers a pair of triples $b$ and $c$ beautiful if they differ in exactly one position, that is, one of the following conditions is satisfied:

  * $b_1 \ne c_1$ and $b_2 = c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 \ne c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 = c_2$ and $b_3 \ne c_3$.

Find the number of beautiful pairs of triples among the written triples $[a_j, a_{j + 1}, a_{j + 2}]$.

Input: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — the elements of the array.

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

Output: For each test case, output a single integer — the number of beautiful pairs of triples among the pairs of the form $[a_j, a_{j + 1}, a_{j + 2}]$.

Note that the answer may not fit into 32-bit data types.

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

Note: In the first example, $a = [3, 2, 2, 2, 3]$, Polycarp will write the following triples:

  1. $[3, 2, 2]$;    2. $[2, 2, 2]$;    3. $[2, 2, 3]$.

The beautiful pairs are triple $1$ with triple $2$ and triple $2$ with triple $3$.

In the third example, $a = [1, 2, 3, 2, 2, 3, 4, 2]$, Polycarp will write the following triples:

  1. $[1, 2, 3]$;    2. $[2, 3, 2]$;    3. $[3, 2, 2]$;    4. $[2, 2, 3]$;    5. $[2, 3, 4]$;    6. $[3, 4, 2]$;

The beautiful pairs are triple $1$ with triple $4$, triple $2$ with triple $5$, and triple $3$ with triple $6$.

Buggy Code:
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define double long double
#define mod 1000000007

void solve(){
    int n;
    cin >> n;
    vector<int>nums(n);
    for(int i=0;i<n;i++) cin>>nums[i];

    int ans=0;
    for(int i=0;i<n-2;i++){
        for(int j=i;j<n-2;j++){
            if(nums[i]!=nums[j] && nums[i+1]==nums[j+1] && nums[i+2]==nums[j+2])ans++;
            if(nums[i]==nums[j] && nums[i+1]!=nums[j+1] && nums[i+2]==nums[j+2])ans++;
            if(nums[i]==nums[j] && nums[i+1]==nums[j+1] && nums[i+2]!=nums[j+2])ans++;
        }
    }
    cout<<ans<<endl;
}

int main(){
    #ifndef ONLINE_JUDGE
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    #endif
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int t;
    cin >> t;
    while (t--){
        solve();
    }
    return 0;
}

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

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

Think step by step.

Response:
To expose the bug in the provided code, we need to focus on the inner loop that iterates over all possible pairs of triples. The current implementation uses a nested loop, which results in a time complexity of \(O(n^2)\). This is inefficient and can lead to time limit exceeded (TLE) errors for large inputs. However, the primary issue here is the redundancy in checking pairs of triples.

A good test input to expose this inefficiency and redundancy would be an array where the number of beautiful pairs is relatively high, but the input size is still small enough to be manageable. This will force the nested loop to perform many unnecessary comparisons, making the inefficiency more apparent.

Let's consider an array where the elements are mostly the same, but with a few different elements to create beautiful pairs. This will ensure that the inner loop has to perform many comparisons, but the overall size of the array is small enough to be a valid test case.

Here's a small-scale test input that fits the criteria:

```plaintext
1
6
1 2 1 2 1 2
```

Explanation:
- The array `a = [1, 2, 1, 2, 1, 2]` has 6 elements.
- The triples formed are:
  1. `[1, 2, 1]`
  2. `[2, 1, 2]`
  3. `[1, 2, 1]`
  4. `[2, 1, 2]`
  5. `[1, 2, 1]`

- The beautiful pairs are:
  - Triple 1 with Triple 3
  - Triple 1 with Triple 5
  - Triple 3 with Triple 5
  - Triple 2 with Triple 4

This test input will force the nested loop to perform many comparisons, making the inefficiency of the current implementation more apparent.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Beautiful Triple Pairs
time_limit_ms: 4000
memory_limit_mb: 256
Description: Polycarp was given an array $a$ of $n$ integers. He really likes triples of numbers, so for each $j$ ($1 \le j \le n - 2$) he wrote down a triple of elements $[a_j, a_{j + 1}, a_{j + 2}]$.

Polycarp considers a pair of triples $b$ and $c$ beautiful if they differ in exactly one position, that is, one of the following conditions is satisfied:

  * $b_1 \ne c_1$ and $b_2 = c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 \ne c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 = c_2$ and $b_3 \ne c_3$.

Find the number of beautiful pairs of triples among the written triples $[a_j, a_{j + 1}, a_{j + 2}]$.

Input: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — the elements of the array.

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

Output: For each test case, output a single integer — the number of beautiful pairs of triples among the pairs of the form $[a_j, a_{j + 1}, a_{j + 2}]$.

Note that the answer may not fit into 32-bit data types.

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

Note: In the first example, $a = [3, 2, 2, 2, 3]$, Polycarp will write the following triples:

  1. $[3, 2, 2]$;    2. $[2, 2, 2]$;    3. $[2, 2, 3]$.

The beautiful pairs are triple $1$ with triple $2$ and triple $2$ with triple $3$.

In the third example, $a = [1, 2, 3, 2, 2, 3, 4, 2]$, Polycarp will write the following triples:

  1. $[1, 2, 3]$;    2. $[2, 3, 2]$;    3. $[3, 2, 2]$;    4. $[2, 2, 3]$;    5. $[2, 3, 4]$;    6. $[3, 4, 2]$;

The beautiful pairs are triple $1$ with triple $4$, triple $2$ with triple $5$, and triple $3$ with triple $6$.

Buggy Code:
import sys

def bro(a, n):
    count = 0
    for j in range(n - 2):
        for k in range(j + 1, n - 2):
            if (a[j] != a[k] and a[j + 1] == a[k + 1] and a[j + 2] == a[k + 2]) or \
                (a[j] == a[k] and a[j + 1] != a[k + 1] and a[j + 2] == a[k + 2]) or \
                (a[j] == a[k] and a[j + 1] == a[k + 1] and a[j + 2] != a[k + 2]):
                count += 1
    return count

t = int(sys.stdin.readline())
for _ in range(t):
    n = int(sys.stdin.readline())
    a = list(map(int, sys.stdin.readline().split()))
    print(bro(a, 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
1
6
1 2 3 1 2 3
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Beautiful Triple Pairs
time_limit_ms: 4000
memory_limit_mb: 256
Description: Polycarp was given an array $a$ of $n$ integers. He really likes triples of numbers, so for each $j$ ($1 \le j \le n - 2$) he wrote down a triple of elements $[a_j, a_{j + 1}, a_{j + 2}]$.

Polycarp considers a pair of triples $b$ and $c$ beautiful if they differ in exactly one position, that is, one of the following conditions is satisfied:

  * $b_1 \ne c_1$ and $b_2 = c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 \ne c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 = c_2$ and $b_3 \ne c_3$.

Find the number of beautiful pairs of triples among the written triples $[a_j, a_{j + 1}, a_{j + 2}]$.

Input: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — the elements of the array.

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

Output: For each test case, output a single integer — the number of beautiful pairs of triples among the pairs of the form $[a_j, a_{j + 1}, a_{j + 2}]$.

Note that the answer may not fit into 32-bit data types.

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

Note: In the first example, $a = [3, 2, 2, 2, 3]$, Polycarp will write the following triples:

  1. $[3, 2, 2]$;    2. $[2, 2, 2]$;    3. $[2, 2, 3]$.

The beautiful pairs are triple $1$ with triple $2$ and triple $2$ with triple $3$.

In the third example, $a = [1, 2, 3, 2, 2, 3, 4, 2]$, Polycarp will write the following triples:

  1. $[1, 2, 3]$;    2. $[2, 3, 2]$;    3. $[3, 2, 2]$;    4. $[2, 2, 3]$;    5. $[2, 3, 4]$;    6. $[3, 4, 2]$;

The beautiful pairs are triple $1$ with triple $4$, triple $2$ with triple $5$, and triple $3$ with triple $6$.

Buggy Code:
import sys
from collections import defaultdict
input = sys.stdin.readline

############ ---- Input Functions ---- ############
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return(map(int,input().split()))

for _ in range(inp()):
    n = inp()
    a = inlt()

    c = 0

    d_12 = {}
    d_13 = {}
    d_23 = {}

    for i in range(n-2):
        if (a[i], a[i + 1]) in d_12:
            for x in d_12[(a[i], a[i + 1])]:
                if x != a[i + 2]:
                    c += 1
        if (a[i], a[i + 2]) in d_13:
            for x in d_13[(a[i], a[i + 2])]:
                if x != a[i + 1]:
                    c += 1
        if (a[i + 1], a[i + 2]) in d_23:
            for x in d_23[(a[i + 1], a[i + 2])]:
                if x != a[i]:
                    c += 1

        if (a[i], a[i + 1]) not in d_12:
            d_12[(a[i], a[i + 1])] = []
        if (a[i], a[i + 2]) not in d_13:
            d_13[(a[i], a[i + 2])] = []
        if (a[i+1], a[i + 2]) not in d_23:
            d_23[(a[i + 1], a[i + 2])] = []

        d_12[(a[i], a[i + 1])].append(a[i + 2])
        d_13[(a[i], a[i + 2])].append(a[i + 1])
        d_23[(a[i + 1], a[i + 2])].append(a[i])

    print(c)

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

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

Think step by step.

Response:
```plaintext
1
6
1 1 1 2 2 2
```

**Explanation:**

1. **Understanding the Bug**: The buggy code incorrectly handles the case where the same pair of elements is repeated in the array, leading to potential over-counting or under-counting of beautiful pairs.

2. **Test Input Design**:
   - We need an array where the same pairs of elements are repeated multiple times to expose the bug.
   - The array `[1, 1, 1, 2, 2, 2]` has repeated pairs:
     - Pairs `(1, 1)`, `(1, 2)`, and `(2, 2)` are repeated.
   - This should create multiple beautiful pairs, but the buggy code might not handle the repeated pairs correctly.

3. **Expected Output**:
   - The correct number of beautiful pairs for this input is `3`:
     - `[1, 1, 1]` and `[1, 1, 2]` (different in the third position)
     - `[1, 1, 2]` and `[1, 2, 2]` (different in the second position)
     - `[1, 2, 2]` and `[2, 2, 2]` (different in the first position)

This test input should help expose the bug 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: Beautiful Triple Pairs
time_limit_ms: 4000
memory_limit_mb: 256
Description: Polycarp was given an array $a$ of $n$ integers. He really likes triples of numbers, so for each $j$ ($1 \le j \le n - 2$) he wrote down a triple of elements $[a_j, a_{j + 1}, a_{j + 2}]$.

Polycarp considers a pair of triples $b$ and $c$ beautiful if they differ in exactly one position, that is, one of the following conditions is satisfied:

  * $b_1 \ne c_1$ and $b_2 = c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 \ne c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 = c_2$ and $b_3 \ne c_3$.

Find the number of beautiful pairs of triples among the written triples $[a_j, a_{j + 1}, a_{j + 2}]$.

Input: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — the elements of the array.

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

Output: For each test case, output a single integer — the number of beautiful pairs of triples among the pairs of the form $[a_j, a_{j + 1}, a_{j + 2}]$.

Note that the answer may not fit into 32-bit data types.

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

Note: In the first example, $a = [3, 2, 2, 2, 3]$, Polycarp will write the following triples:

  1. $[3, 2, 2]$;    2. $[2, 2, 2]$;    3. $[2, 2, 3]$.

The beautiful pairs are triple $1$ with triple $2$ and triple $2$ with triple $3$.

In the third example, $a = [1, 2, 3, 2, 2, 3, 4, 2]$, Polycarp will write the following triples:

  1. $[1, 2, 3]$;    2. $[2, 3, 2]$;    3. $[3, 2, 2]$;    4. $[2, 2, 3]$;    5. $[2, 3, 4]$;    6. $[3, 4, 2]$;

The beautiful pairs are triple $1$ with triple $4$, triple $2$ with triple $5$, and triple $3$ with triple $6$.

Buggy Code:
import java.util.*;

public class Solution3 {
    static Scanner input=new Scanner(System.in);
    public static void retAns(){
        int n=input.nextInt();
        int[] arr=new int[n];
        for(int i=0;i<n;i++){
            arr[i]=input.nextInt();
        }
        int count=0;
        Map<ArrayList<Integer>,Integer> map=new HashMap<>();
        for(int i=0;i<n-2;i++){
            ArrayList<Integer> inner=new ArrayList<>();
            // inner.add(arr[i]);
            for(int j=0;j<3;j++){
                inner.add(arr[i+j]);
            }
            // if(map.containsKey(inner)){
            //     continue;
            // }
            int whole=map.getOrDefault(inner, 0);
            for(int j=0;j<3;j++){
                int temp=inner.get(j);
                inner.set(j,-1);
                if(map.containsKey(inner)){
                    int prev=map.get(inner);
                    map.put(inner,prev+1);
                    count+=prev-whole;

                }
                else{
                    ArrayList<Integer> newArr=new ArrayList<>(inner);
                    map.put(newArr,1);

                }
                inner.set(j,temp);

            }
            // System.out.println(inner);

            map.put(inner,whole+1);

        }
        // System.out.println(map);
        System.out.println(count);

    }
    public static void main(String[] args) {
        int t=input.nextInt();
        for(int i=0;i<t;i++){
            retAns();
        }
    }

}

**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 focus on edge cases or scenarios that can maximize the failure probability. The key issues in the code include:

1. **Incorrect handling of the map and the count of beautiful pairs**.
2. **Potential issues with the way the map is updated and queried**.

Given these points, a good test input should:

- Include repeated elements to test the logic for counting beautiful pairs.
- Have a length that is not too large but still sufficient to cause issues if the logic is incorrect.
- Include sequences that can create multiple beautiful pairs to ensure the counting logic is correct.

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

```plaintext
1
6
1 2 2 2 1 1
```

This input will create the following triples:
1. `[1, 2, 2]`
2. `[2, 2, 2]`
3. `[2, 2, 1]`
4. `[2, 1, 1]`

The beautiful pairs are:
- Triple 1 with triple 2 (differ in the first position)
- Triple 2 with triple 3 (differ in the first position)
- Triple 3 with triple 4 (differ in the second position)

Thus, the correct output should be `3`.

This input is small enough to be manageable and should help in identifying the issues 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: Beautiful Triple Pairs
time_limit_ms: 4000
memory_limit_mb: 256
Description: Polycarp was given an array $a$ of $n$ integers. He really likes triples of numbers, so for each $j$ ($1 \le j \le n - 2$) he wrote down a triple of elements $[a_j, a_{j + 1}, a_{j + 2}]$.

Polycarp considers a pair of triples $b$ and $c$ beautiful if they differ in exactly one position, that is, one of the following conditions is satisfied:

  * $b_1 \ne c_1$ and $b_2 = c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 \ne c_2$ and $b_3 = c_3$;    * $b_1 = c_1$ and $b_2 = c_2$ and $b_3 \ne c_3$.

Find the number of beautiful pairs of triples among the written triples $[a_j, a_{j + 1}, a_{j + 2}]$.

Input: The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the length of the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$) — the elements of the array.

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

Output: For each test case, output a single integer — the number of beautiful pairs of triples among the pairs of the form $[a_j, a_{j + 1}, a_{j + 2}]$.

Note that the answer may not fit into 32-bit data types.

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

Note: In the first example, $a = [3, 2, 2, 2, 3]$, Polycarp will write the following triples:

  1. $[3, 2, 2]$;    2. $[2, 2, 2]$;    3. $[2, 2, 3]$.

The beautiful pairs are triple $1$ with triple $2$ and triple $2$ with triple $3$.

In the third example, $a = [1, 2, 3, 2, 2, 3, 4, 2]$, Polycarp will write the following triples:

  1. $[1, 2, 3]$;    2. $[2, 3, 2]$;    3. $[3, 2, 2]$;    4. $[2, 2, 3]$;    5. $[2, 3, 4]$;    6. $[3, 4, 2]$;

The beautiful pairs are triple $1$ with triple $4$, triple $2$ with triple $5$, and triple $3$ with triple $6$.

Buggy Code:
/*
ID: epicpla1
LANG: JAVA
TASK: beautifulpairs
*/

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

public class beautifulPairs {
    public void run() throws Exception {
        //FastScannerbeautifulPairs f = new FastScannerbeautifulPairs("beautifulPairs".toLowerCase() + ".in");
        FastScannerbeautifulPairs f = new FastScannerbeautifulPairs();

        //PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("beautifulPairs".toLowerCase() + ".out")));
        PrintWriter out = new PrintWriter(System.out);

        int cases = f.nextInt();

        while(cases-- > 0){
            HashMap<Long, Integer> map = new HashMap<>();

            int length = f.nextInt();

            int[] line = new int[length];
            for (int i = 0; i < length; i++) line[i] = f.nextInt();

            long answer = 0L;
            for (int i = 0; i < length-2; i++){
                long trip = line[i]*1_000_000_000_000L+line[i+1]*1_000_000L+line[i+2];

                long hash1 = line[i]*1_000_000_000_000L+line[i+1]*1_000_000L;
                long hash2 = line[i]*1_000_000_000_000L+line[i+2];
                long hash3 = line[i+1]*1_000_000L+line[i+2];

                if (!map.containsKey(trip)) map.put(trip, 1);
                else map.put(trip, map.get(trip)+1);

                if (!map.containsKey(hash1)) map.put(hash1, 1);
                else{
                    answer += map.get(hash1) - (map.get(trip)-1);
                    map.put(hash1, map.get(hash1)+1);
                }

                if (!map.containsKey(hash2)) map.put(hash2, 1);
                else{
                    answer += map.get(hash2) - (map.get(trip)-1);
                    map.put(hash2, map.get(hash2)+1);
                }

                if (!map.containsKey(hash3)) map.put(hash3, 1);
                else{
                    answer += map.get(hash3) - (map.get(trip)-1);
                    map.put(hash3, map.get(hash3)+1);
                }
            }
            out.println(answer);
        }

        out.flush();
    }

    public static void main(String[] args) throws Exception {
        new beautifulPairs().run();
    }
}

class FastScannerbeautifulPairs {
    BufferedReader br;
    StringTokenizer st;

    public FastScannerbeautifulPairs() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public FastScannerbeautifulPairs(String fileName) throws FileNotFoundException {
        br = new BufferedReader(new FileReader(fileName));
    }

    String next() {
        while (st == null || !st.hasMoreTokens()) {
            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 != null && st.hasMoreTokens()) {
                str = st.nextToken("\n");
            } else {
                str = br.readLine();
            }
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}
//Property of the One and Only KoKoa_Bean

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

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

Think step by step.

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

1. **Understand the Bug**: The code uses a hash map to count occurrences of triples and partial hashes. The bug might be related to how it calculates and updates the counts for these hashes.

2. **Edge Cases**:
   - **Repetitive Elements**: If the array has many repetitive elements, the hash map might not correctly count the beautiful pairs.
   - **Small Array**: A small array can help identify issues more easily.
   - **Distinct Elements**: An array with distinct elements can test the hash map's ability to handle unique triples.

3. **Maximize Failure Probability**:
   - Use a small array with repetitive elements to maximize the likelihood of the bug being exposed.
   - Ensure the array length is within the constraints but small enough to be manageable.

Given these considerations, let's create a test input that is small and contains repetitive elements:

```plaintext
1
5
2 2 2 2 2
```

This test input will help expose any issues in the code's handling of repetitive elements and the calculation of beautiful pairs. The expected output for this test input should be `0` because there are no beautiful pairs in an array where all elements are the same.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

Buggy Code:
#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
int a[50];
int main()
{
    int t;
    cin >> t;
    while (t-- > 0)
    {
        int n, cnt = 0;
        cin  >> n;
        for (int i = 0 ; i <  n ; i ++)
        {
            cin >> a[i];
        }
        for (int i = 0 ; i  < n - 1; i ++)
        {
            if (a[i] == a[i+1])continue;

            if (abs(a[i] - a[i+1])  != 5 && abs(a[i] - a[i+1]) != 7)
            {
                cout << "NO" << endl;
                cnt = 1;
                break;
            }

        }
        if (cnt == 0)
        cout << "YES" << 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
2
127 122
3
120 127 122
4
10 15 10 15
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

Buggy Code:
//In the name of ALLAH

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

typedef long long ll;
#define endl '\n'
#define mem(a,b) memset(a, b, sizeof(a) )
#define optimize() ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define fraction() cout.unsetf(ios::floatfield); cout.precision(10); cout.setf(ios::fixed,ios::floatfield);
 int arr[50];

int main()
{
    optimize();
    int t;
    cin>>t;
    while(t--){
        int n;
        cin>>n;
        int cnt=0;
        for(int i=0;i<n;i++) cin>>arr[i];
        for(int i=0;i<n;i++){
            int ans=abs(arr[i]-arr[i+1]);

            if(ans==5 || ans==7){
                cnt++;
            }
            }

        if(cnt==n-1) cout<<"YES"<<endl;
            else cout <<"NO"<<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
2
127 122
3
127 122 117
4
127 122 117 112
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

Buggy Code:
#include<stdio.h>
#include<math.h>
int main()
{
    int t;
    scanf("%d",&t);
    int n[51],cha[10000];
    for(int i=0;i<t;i++)
    {
        int a=0;
        scanf("%d",&n[i]);
        for(int j=0;j<n[i];j++)
        {
            scanf("%d",&cha[j]);
        }
        for(int k=1;k<n[i];k++)
        {
            if((abs(cha[k]-cha[k-1])==5)||(abs(cha[k]-cha[k-1])==7)) a=1;
            else
            {
                a=0;
                break;
            }
        }
        if(a) printf("YES\n");
        else printf("NO\n");
    }
    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
2
114 109
3
76 83 88
5
63 58 65 58 65
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

Buggy Code:
def is_perfect_melody(notes):
    return "YES" if all(abs(notes[i] - notes[i + 1]) in (5, 7) for i in range(len(notes) - 1)) else "NO"

def main():
    # Multi-line string simulating input
    input_data = """8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75"""

    # Splitting the input data into lines
    lines = input_data.strip().split('\n')

    t = int(lines[0])  # Number of melodies
    results = []

    index = 1
    for _ in range(t):
        n = int(lines[index])  # Number of notes
        notes = list(map(int, lines[index + 1].split()))
        result = is_perfect_melody(notes)
        results.append(result)
        index += 2  # Move to the next melody input

    print("\n".join(results))

if __name__ == "__main__":
    main()

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

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

Think step by step.

Response:
To create a challenging test input that exposes the bug in the provided code, we need to focus on edge cases and scenarios that maximize the probability of failure. Here are some considerations:

1. **Edge Cases:**
   - Melodies with the minimum number of notes (2 notes).
   - Melodies with the maximum number of notes (50 notes).
   - Melodies where the interval between notes is exactly 5 or 7 semitones.
   - Melodies where the interval between notes is not 5 or 7 semitones.

2. **Complex Scenarios:**
   - Melodies with repeated notes.
   - Melodies with a mix of intervals (some 5 semitones and some 7 semitones).
   - Melodies with a single interval that is not 5 or 7 semitones.

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

```plaintext
5
2
0 5
3
0 7 14
5
10 15 22 27 34
4
5 12 17 22
8
10 15 20 15 10 15 20 25
```

Explanation:
- The first melody has 2 notes with an interval of 5 semitones.
- The second melody has 3 notes with intervals of 7 semitones.
- The third melody has 5 notes with intervals of 5 and 7 semitones.
- The fourth melody has 4 notes with intervals of 7 and 5 semitones.
- The fifth melody has 8 notes with a mix of intervals, including some that are not 5 or 7 semitones.

This test input should help expose any issues in the buggy code, particularly with handling different interval patterns and edge cases.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

Buggy Code:
t = int(input())

for _ in range(t):
    n = int(input())
    a = list(map(int, input().split()))
    b = [0 for i in range(n)]

    for i in range(1, n):
        b[i] = abs(a[i] - a[i-1])

    if len(set(b)) <= 3:
        print('YES')
    else:
        print('NO')

**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
0 5 10
4
0 5 10 15
5
0 5 10 15 20
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

Buggy Code:
for _ in range(int(input())):
    lenlis=int(input())
    lis=list(map(int,input().split()))
    i=0
    while (abs(lis[i]-lis[i+1])==5 or abs(lis[i]-lis[i+1])==7) and i<lenlis-2:
        i=i+1
    if i==lenlis-2:
        print("YES")
    else:
        print("NO")

**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
10 15
3
10 15 20
4
10 15 20 25
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

Buggy Code:
import java.util.Scanner;
import java.lang.Math;

public class NewClass1 {
  public static void main(String[] args){

    Scanner sc = new Scanner(System.in);
    int num = sc.nextInt(), i = 1, j=1;
    sc.nextLine();
    boolean perfect=true;
    while (i<=num){

      int num2 = sc.nextInt(); sc.nextLine();
      int a = sc.nextInt();
      while (j<=num2-1){

        int b = sc.nextInt();
        int dif = Math.abs(a-b);
        if (!(dif==5 || dif==7)){
          perfect=false;
          break;
        }
        a=b;
        j++;
      }
      sc.nextLine();

      System.out.println(perfect?"YES":"NO");
      i++;
      perfect = true;
    }

  }

}

**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
109 104
2
109 104
5
109 104 109 104 109
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

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

public class Quintomania2036A {

    public static void main(String[] args) {
        MyScanner scanner = new MyScanner();
        int n = scanner.nextInt();

        for (int i = 0; i < n; i++) {
            int a = scanner.nextInt();

            int[] arr = new int[a];
            for (int j = 0; j < a; j++) {
                int d = scanner.nextInt();
                arr[j] = d;
            }
            boolean res = func(arr);
            System.out.println(res == true ? "YES" : "NO");
        }
    }

    private static boolean func(int[] arr) {

        for (int i = 1; i < arr.length; i++) {
            int absValue = Math.abs(arr[i] - arr[i - 1]);
            if (absValue < 5 || absValue > 7) {
                return false;
            }
        }

        return true;
    }

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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 {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
}

**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
114 109
3
76 83 88
5
63 58 65 58 65
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

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

void solve() {
    int n;
    cin >> n;
    vector<int> v(n);
    for (int i = 0; i < n; i++) {
        cin >> v[i];
    }
    for (int i = 0; i < n - 1; i++) {
        int diff = abs(v[i] - v[i + 1]);
        if (diff < 5 || diff > 7) {
            cout << "NO" << endl;
            return;
        }
    }
    cout << "YES" << endl;
}

int main() {
    int t;
    cin >> t;
    while (t--) {
        solve();
    }
    return 0;
}

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

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

Think step by step.

Response:
```plaintext
3
2
10 15
3
10 15 20
5
10 15 22 27 32
```

### Explanation:
1. **First Test Case:**
   - Melody: `10 15`
   - Intervals: `|10 - 15| = 5`
   - Expected Output: `YES` (All intervals are 5 semitones)

2. **Second Test Case:**
   - Melody: `10 15 20`
   - Intervals: `|10 - 15| = 5`, `|15 - 20| = 5`
   - Expected Output: `YES` (All intervals are 5 semitones)

3. **Third Test Case:**
   - Melody: `10 15 22 27 32`
   - Intervals: `|10 - 15| = 5`, `|15 - 22| = 7`, `|22 - 27| = 5`, `|27 - 32| = 5`
   - Expected Output: `NO` (The interval between 15 and 22 is 7 semitones, which is allowed, but the interval between 22 and 27 is 5 semitones, which is allowed, and the interval between 27 and 32 is 5 semitones, which is allowed. However, the code will incorrectly identify this as a valid interval because it only checks if the interval is 5 or 7, not if it alternates correctly.)

This test input is designed to expose the bug in the code where the intervals between notes are not checked for the correct alternation pattern of 5 and 7 semitones. The third test case, in particular, is crafted to show that the code will incorrectly output `NO` when it should output `YES` because the intervals alternate correctly.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

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

int main() {
    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        vector<int> arr(n);  // Declare the array with size n
        for (int i = 0; i < n; i++) {
            cin >> arr[i];
        }

        if (n % 2 == 0) {  // If n is even
            int maxi = 0;
            for (int i = 1; i < n; i++) {
                maxi = max(maxi,abs( arr[i] - arr[i - 1]));
            }
            if (maxi == 5 || maxi == 7) {
                cout << "Yes" << endl;
            } else {
                cout << "No" << endl;
            }
        } else {
            int maxii = 0;
            for (int i = 2; i < n; i++) {
                maxii = max(maxii, abs(arr[i] - arr[i - 1]));

            }
            maxii = min(arr[0],maxii);

            int maxiii = 0;
            for (int i = 1; i < n - 1; i++) {
                maxiii = max(maxiii, abs(arr[i] - arr[i - 1]));
            }
            maxiii = min(maxiii,arr[n-1]);

            if (maxii == 5 || maxiii == 5 || maxii == 7 || maxiii == 7) {
                cout << "Yes" << endl;
            } else {
                cout << "No" << endl;
            }
        }
    }

    return 0;
}

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

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

Think step by step.

Response:
To expose the bug in the provided code, we need to focus on the logic that checks whether a melody is perfect. The buggy code has a flawed approach to determining the intervals between notes. Specifically, it uses the maximum interval to decide if the melody is perfect, which is incorrect. The correct approach should check if all intervals between adjacent notes are either 5 or 7 semitones.

Let's construct a test input that highlights this issue:

1. **Melody with an even number of notes (n is even):**
   - The code incorrectly checks if the maximum interval is 5 or 7.
   - We can create a melody where the intervals are mixed but still contain both 5 and 7 semitones.

2. **Melody with an odd number of notes (n is odd):**
   - The code incorrectly checks the maximum interval and then applies a min operation, which is not the correct way to determine if all intervals are 5 or 7 semitones.
   - We can create a melody where the intervals are mixed but still contain both 5 and 7 semitones.

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

```plaintext
3
4
100 105 100 105
5
100 105 112 105 112
6
100 105 112 105 112 107
```

Explanation:
1. **First Melody (n = 4):**
   - Notes: 100, 105, 100, 105
   - Intervals: 5, 5, 5
   - Expected output: YES (since all intervals are 5 semitones)

2. **Second Melody (n = 5):**
   - Notes: 100, 105, 112, 105, 112
   - Intervals: 5, 7, 7, 7
   - Expected output: YES (since all intervals are either 5 or 7 semitones)

3. **Third Melody (n = 6):**
   - Notes: 100, 105, 112, 105, 112, 107
   - Intervals: 5, 7, 7, 7, 5
   - Expected output: YES (since all intervals are either 5 or 7 semitones)

The provided test input should highlight the issues with the buggy code's logic for checking intervals.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

Buggy Code:
for _ in range(int(input())):
    a=input()
    b=list(map(int,input().split()))
    k=True
    for i in range(1,len(b)):
        if abs(b[i-1]-b[i])!=5 and abs(b[i-1]-b[i])!=7 and b[i-1]-b[i]!=0:
            k=False
    if k==True:
        print('YES')
    else:
        print('NO')

**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
10 15
3
20 25 30
4
35 42 47 54
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

Buggy Code:
for _ in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    ans = True
    for i in range(n-2):
        ans &= abs(a[i]-a[i+1]) in (5,7)
    print("YES" if ans else "NO")

**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
70 75 80
3
70 75 82
3
70 75 87
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

Buggy Code:
/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;
public class Main
{
    public int melody(int[] a)
    {
        int x=a.length;
        for(int k=0;k<x-2;k++)
        {
            boolean b=((Math.abs(a[k+1]-a[k])==5)||(Math.abs(a[k+1]-a[k])==7));
            if(b==false)
            {
                return 0;
            }
        }
        return 1;
    }

    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[] arr;
            arr=new int[n];
            for(int j=0;j<n;j++)
            {
                arr[j]=sc.nextInt();
            }
            Main m=new Main();
            int val=m.melody(arr);
            if(val==0)
            {
                System.out.println("no");
            }
            else
                {
                    System.out.println("yes");
                }

        }
    }
}

**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
114 109
3
76 83 88
4
38 45 52 59
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Quintomania
time_limit_ms: 1000
memory_limit_mb: 256
Description: Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input: The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output: For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Examples:
input:
8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75
output:
YES
YES
YES
NO
YES
NO
YES
YES

Note:

Buggy Code:
import java.util.*;
public class Main{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for(int i=1;i<=t;i++){
            int n = sc.nextInt();
            int arr[] = new int[n];
            for(int j=0;j<n;j++){
                arr[j] = sc.nextInt();
            }
            int k = 1;
            StringBuilder result = new StringBuilder("Yes");
            while(k<n-1){
                if(arr[k]-arr[k+1]!=5 && arr[k]-arr[k+1]!=-5 && arr[k]-arr[k+1]!=7 && arr[k]-arr[k+1]!=-7){
                    result.delete(0, 3) ;
                    result.append("No");
                    break;
                }
                k++;
            }
            System.out.println(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
127 122
3
0 7 12
4
5 10 15 20
```