**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

Buggy Code:
//package prohladenn.vko.round984;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class ProblemC {

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);

        int t = fs.nextInt();
        while (t-- > 0) {
            char[] s = fs.next().toCharArray();
            boolean[] b = new boolean[s.length];
            for (int i = 0; i < s.length; i++) {
                b[i] = s[i] == '1';
            }

            int end = endPosOf1100(b, Integer.MIN_VALUE, Integer.MAX_VALUE);

            int q = fs.nextInt();
            while (q-- > 0) {
                int i = fs.nextInt();
                boolean c = fs.nextInt() == 1;

                b[i - 1] = c;

                if (end == -1 || (i - end <= 3)) {
                    end = endPosOf1100(b, i - 4, i + 4);
                }

                out.println(end != -1 ? "YES" : "NO");
            }
        }

        out.close();
    }

    static int endPosOf1100(boolean[] b, int start, int end) {
        for (int i = Math.max(3, start); i < Math.min(b.length, end); i++) {
            if (b[i - 3] && b[i - 2] && !b[i - 1] && !b[i]) {
                return i;
            }
        }
        return -1;
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException ignored) {
                }
            return st.nextToken();
        }

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

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

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

        long[] readArrayL(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }
}

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the given buggy code, we need to focus on scenarios where the code might fail to correctly detect the presence of the substring "1100". The key is to create a sequence of operations that can cause the `endPosOf1100` function to incorrectly update the `end` variable or miss the "1100" substring.

### Steps to Generate the Test Input:
1. **Initial String**: Start with a string that does not contain "1100" but is close to it.
2. **Operations**: Perform a series of operations that gradually form "1100" or break an existing "1100" and then re-form it.
3. **Edge Cases**: Ensure the operations are at positions that can affect the detection of "1100".

### Example Test Input:
```plaintext
1
11000
5
1 0
2 1
3 1
4 0
5 1
```

### Explanation:
1. **Initial String**: "11000" — This string does not contain "1100" initially.
2. **Operations**:
   - **1 0**: Change the 1st character to '0' → "01000" (No "1100")
   - **2 1**: Change the 2nd character to '1' → "01100" (No "1100")
   - **3 1**: Change the 3rd character to '1' → "01110" (No "1100")
   - **4 0**: Change the 4th character to '0' → "01100" (No "1100")
   - **5 1**: Change the 5th character to '1' → "01101" (No "1100")

### Expected Output:
```plaintext
NO
NO
NO
NO
NO
```

### Additional Test Case:
To further challenge the code, consider a case where "1100" is formed and then broken:

```plaintext
1
0000
4
1 1
2 1
3 0
4 0
```

### Explanation:
1. **Initial String**: "0000" — This string does not contain "1100" initially.
2. **Operations**:
   - **1 1**: Change the 1st character to '1' → "1000" (No "1100")
   - **2 1**: Change the 2nd character to '1' → "1100" (Contains "1100")
   - **3 0**: Change the 3rd character to '0' → "1100" (Still contains "1100")
   - **4 0**: Change the 4th character to '0' → "1100" (Still contains "1100")

### Expected Output:
```plaintext
NO
YES
YES
YES
```

### Final Test Input:
```plaintext
1
0000
4
1 1
2 1
3 0
4 0
```

This test input should expose the bug in the code by ensuring that the "1100" substring is correctly detected and maintained through the operations.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

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

int main() {
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);

    int t;
    cin >> t;
    while (t--) {

        string input;
        int q, i;
        char v;

        cin >> input >> q;

        if (input.length() < 4) {
            while (q--) {
                cin >> i >> v;
                cout << "NO" << endl;
            }
            continue;
        }

        while (q--) {
            cin >> i >> v;
            if (input[i - 1] != v) {
                input[i - 1] = v;
            }

            if (input.find("1100") != string::npos) {
                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
1
110010
3
1 0
4 1
6 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

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

int main() {
	int t;
	cin>>t;
	while(t--) {
		string s;
		cin>>s;
		int k;
		cin>>k;
		for(int i=0; i<k; i++) {
			int a;
			char v;
			cin>>a>>v;
			s[a-1]=v;
			if(s.find("1100")!=-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
1
11001100
8
1 0
2 0
3 0
4 0
5 1
6 1
7 0
8 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

Buggy Code:
t=int(input())

for i in range(t):
    s = input()
    s_mod = list(s)

    add = s_mod

    query = int(input())

    for i in range(query):
        q = list(map(int, input().split(" ")))
        if q[0] <= len(s_mod):
            s_mod[q[0]-1] = str(q[1])
            substring = "".join(s_mod)

            if "1100" in substring:
                print("yes")
            else:
                print("no")
        else:
            print("no")

        s_mod = add

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

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

Think step by step.

Response:
```plaintext
2
1100
4
1 0
2 0
3 0
4 0
1101
4
1 0
2 0
3 0
4 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

Buggy Code:
def solve():
    s = input()
    lenS = len(s)
    n = int(input())
    # print(s)
    for i in range(n):
        x,y = input().split()
        if lenS < 4:
            print("NO")
            continue
        x = int(x)
        s = s[:x-1] +y +  s[x:]
        # print(s)
        if s.find("1100") != -1:
            print("YES")
        else:
            print("NO")

    return

if False:
    solve()
else:
    t = int(input())
    for _ in range(t):
        solve()

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

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

Think step by step.

Response:
To create a challenging test input that exposes the bug in the provided buggy code, we need to focus on scenarios that can cause the code to fail. The main issues in the buggy code are:

1. **String Manipulation Overhead**: The code uses string concatenation to modify the string `s` in each query, which can be inefficient and lead to performance issues for large inputs.
2. **Inefficient Search**: The code uses `s.find("1100")` to check for the substring "1100" after each query, which can be slow for large strings.
3. **Edge Cases**: The code may not handle edge cases correctly, such as when the string is very short or when the query positions are at the boundaries of the string.

To expose these issues, we can create a test input that includes:

1. A string that is just long enough to contain "1100" after a few queries.
2. Queries that modify the string in a way that should create or remove the "1100" substring.
3. Edge cases where the string is very short or queries are at the boundaries.

Here is a small-scale test input that meets these criteria:

```plaintext
4
1100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
```

This input includes:
1. A string "1100" with queries that modify it to check if the "1100" substring is correctly detected and removed.
2. A longer string "1100000" with queries that should create and remove the "1100" substring.
3. A string "111010" with queries that modify it to check the correct detection of "1100".
4. A short string "0100" with queries that should create and remove the "1100" substring.

This test input should effectively expose the bugs in the provided code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

Buggy Code:
import java.util.*;
public class Codeforces_R984_D3_C {
    static Scanner obj = new Scanner(System.in);

    public static void main(String[] args) {
        run();
    }

    private static void run() {
        int testcases = obj.nextInt();
        for (int i = 0; i < testcases; i++) {
            stringManipulation();
        }
    }

    private static void stringManipulation() {
        obj.nextLine();                     // upar int that and yaha string le raha hu-so that enter might come in str. iske liye
        String str = obj.nextLine();        // the string input that we will get
        int queries = obj.nextInt();        // the number of queries that will take place

        for (int i = 0; i < queries; i++) {
            char ch[] = str.toCharArray();
            int loc = obj.nextInt();
            char value = obj.next().charAt(0);

            ch[loc - 1] = value;
            str = new String(ch);           // har baar I want to show ki query ke baad hai ki nahi
            // agar end hota, toh yeh seedha end mein karta tha
            if (str.contains("1100")) System.out.println("YES");
            else System.out.println("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
1
1101
4
3 0
2 1
4 0
1 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

Buggy Code:
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int asd = sc.nextInt();
        for (int i = 0; i < asd; i++) {
            char[] s = sc.next().toCharArray();
            int dsa = sc.nextInt();
            for (int id = 0; id < dsa; id++) {
                int ii = sc.nextInt();
                int v = sc.nextInt();

                if (s.length < 4) {
                    System.out.println("no");
                    continue;
                }
                s[ii - 1] = (char) (v + '0');
                if (new String(s).contains("1100")) {
                    System.out.println("yes");
                } else {
                    System.out.println("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
1
1110
3
1 1
2 1
3 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

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

bool find11000(string &startnum,int numofqueries,int pos,char replace){
    startnum[pos-1] = replace;
    for (int j = 0; j<startnum.length()-3; j++){
      if (startnum.substr(j,4).compare("1100") == 0){
        return 1;
      }
    }
  return 0;
}
int main(){
  int n;
  cin>>n;
  for (int i = 0; i<n; i++){
    string startnum;
    int numofqueries;
    int pos;
    char replace;
    cin>>startnum;
    cin>>numofqueries;
    for (int j = 0; j<numofqueries; j++){
      cin>>pos>>replace;
      //cout << "startnum: " << startnum << endl;
      int result = find11000(startnum,numofqueries,pos,replace);
      if (result == 1){
       cout<<"YES"<<endl;
      }
      else{
       cout<<"NO"<<endl;
      }
    }
  }
}

//4
//0 1 0 1
//1 0 0 0
//0 0 0 0
//1 0 0 0

// 0 1 3 2

//5 5
//#S###
//#...#
///#.#.#
//#...#
//###G#

//6
//Input 1
//6 7
//#S#####
//#...#.#
//#.#.#.#
//#.#...G
//#...#.#
///#######
//Output 1
//8

//30
//2 9
//20 0

//9

//5 8
//########
//#.A#...#
//#.##.#B#
//#......#
//########

//Output:

//YES
//9
//LDDRRRRRU

//Sample Input1
//4 4
//@.#F
//....
//.#..
//F..&
//Sample Output1
//6

//5 5
//11000
//01111
//00100
//10111
//00010

//2

//Input 1
//5 5
//10011
//10010
//11011
//01000
//11010
//Output 1
//3

//Sample input:
//3 6
//HFDFFB
//AJHGDH
//DGAGEH
//Sample output:
//6

//5 12
//FIJIITELNWNF
//OELBCYITUAIT
//SGDGLZHPJVJF
//WBXOAUIERWEB
//ONJCDCXJCEXB

//23

**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 consider the following scenarios:

1. **Initial String with "1100"**: The initial string should contain "1100" to test if the code correctly identifies it.
2. **Modifications to "1100"**: We need to modify parts of "1100" to ensure the code correctly updates and checks the presence of "1100" after each modification.
3. **Edge Cases**: Test edge cases where the "1100" substring is at the beginning or end of the string.
4. **Multiple Queries**: Include multiple queries to ensure the code handles a series of modifications correctly.

Given these considerations, here is a small-scale test input that is complete and valid:

```plaintext
4
1100
4
1 0
2 0
3 0
4 0
1100
4
1 1
2 1
3 1
4 1
1011001
4
4 0
5 0
6 0
7 0
1011001
4
1 1
2 0
3 1
4 1
```

This test input includes:
1. A string that initially contains "1100" and then modifies each character to ensure the code correctly identifies the absence of "1100" after each modification.
2. A string that initially contains "1100" and then modifies each character to ensure the code correctly identifies the presence of "1100" after each modification.
3. A longer string that contains "1100" in the middle and modifies the "1100" substring to ensure the code correctly updates and checks the presence of "1100" after each modification.
4. A longer string that contains "1100" in the middle and modifies the "1100" substring to ensure the code correctly updates and checks the presence of "1100" after each modification.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

Buggy Code:
#include <iostream>
#include <vector>
#include <string>

using namespace std;

bool check_1100(const string &s, int start, int end) {
    for (int i = start; i <= end - 4; ++i) {
        if (s.substr(i, 4) == "1100") {
            return true;
        }
    }
    return false;
}

void solve(string &s, const vector<pair<int, int>> &queries) {
    int n = s.size();
    bool has_1100 = check_1100(s, 0, n);

    for (const auto &query : queries) {
        int i = query.first - 1;
        char v = query.second + '0';

        s[i] = v;

        int start = max(0, i - 3);
        int end = min(n, i + 4);

        if (check_1100(s, start, end)) {
            has_1100 = true;
        } else {
            has_1100 = check_1100(s, 0, n);
        }

        cout << (has_1100 ? "YES" : "NO") << endl;
    }
}

int main() {
    int t;
    cin >> t;
    while (t--) {
        string s;
        cin >> s;
        int q;
        cin >> q;
        vector<pair<int, int>> queries(q);
        for (int i = 0; i < q; ++i) {
            cin >> queries[i].first >> queries[i].second;
        }
        solve(s, queries);
    }
    return 0;
}

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

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

Think step by step.

Response:
```plaintext
1
11001
5
1 0
2 0
3 0
4 0
5 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

Buggy Code:
def isin(L, el):
    return el in ''.join(L)

n = int(input())

for _ in range(n):
    a=input()
    s = list(a)
    k = int(input())
    for _ in range(k):
        i, j = input().split()
        i=int(i)
        s[i-1] = j
        print('YES' if isin(s, '1100') 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
1
1100
4
1 0
2 0
3 0
4 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

Buggy Code:
t = int(input())

for i in range(t):
    s = list(input())
    q = int(input())

    for j in range(q):
        p, v = input().split()
        p = int(p)
        v = int(v)
        s[p-1] = str(v)
        stemp = "".join(s)

        if (stemp.find("1100") == -1): print("NO")
        else: print("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
2
11111111111111111111
2
20 0
17 1
11001100110011001100
5
1 1
4 1
7 1
10 1
13 1
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

Buggy Code:
import java.util.Scanner;

public class ElevenHundred {

    public static String returnAns(int i, int v, char[] arr) {
        if (arr.length < 4) {
            return "NO";
        }
        char new_v = '0';
        if (v == 1) {
            new_v = '1';
        }
        arr[i - 1] = new_v;
        for (int j = 0; j <= arr.length - 4; j++) {
            if (arr[j] == '1' && arr[j + 1] == '1' && arr[j + 2] == '0' && arr[j + 3] == '0') {
                return "YES";
            }
        }
        return "NO";
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) {
            String s = sc.next();
            char[] arr = s.toCharArray();
            int q = sc.nextInt();
            while (q-- > 0) {
                int i = sc.nextInt();
                int v = sc.nextInt();
                System.out.println(returnAns(i, v, arr));
            }
        }
        sc.close();
    }
}

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

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

Think step by step.

Response:
To expose the bug in the provided code, we need to focus on edge cases and scenarios where the code might fail. The code checks for the substring "1100" after each operation, but it does not efficiently handle the dynamic changes in the string. Specifically, the code does not consider the possibility that a new "1100" sequence might be created or destroyed by the update.

Here are the steps to create a challenging test input:

1. **Initial String**: Start with a string that does not contain "1100" but is close to it. For example, "11001" or "1101".
2. **Operations**: Perform operations that could potentially create or destroy the "1100" sequence.
3. **Expected Output**: Ensure that the expected output is clear and matches the expected behavior of the algorithm.

Let's create a test input:

```plaintext
1
1101
3
3 0
3 1
4 0
```

### Explanation:

- **Initial String**: "1101" (does not contain "1100").
- **Operations**:
  - **1st Operation**: Change the 3rd character to '0'. The string becomes "1100". The output should be "YES".
  - **2nd Operation**: Change the 3rd character back to '1'. The string becomes "1101". The output should be "NO".
  - **3rd Operation**: Change the 4th character to '0'. The string becomes "1100". The output should be "YES".

This test input is small and complete, and it should expose the bug in the code by demonstrating the dynamic nature of the string changes and the need to efficiently check for the "1100" sequence.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Anya and 1100
time_limit_ms: 3000
memory_limit_mb: 256
Description: While rummaging through things in a distant drawer, Anya found a beautiful string $s$ consisting only of zeros and ones.

Now she wants to make it even more beautiful by performing $q$ operations on it.

Each operation is described by two integers $i$ ($1 \le i \le |s|$) and $v$ ($v \in \\{0, 1\\}$) and means that the $i$-th character of the string is assigned the value $v$ (that is, the assignment $s_i = v$ is performed).

But Anya loves the number $1100$, so after each query, she asks you to tell her whether the substring "1100" is present in her string (i.e. there exist such $1 \le i \le |s| - 3$ that $s_{i}s_{i + 1}s_{i + 2}s_{i + 3} = \texttt{1100}$).

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

The first line of the test case contains the string $s$ ($1 \leq |s| \leq 2 \cdot 10^5$), consisting only of the characters "0" and "1". Here $|s|$ denotes the length of the string $s$.

The next line contains an integer $q$ ($1 \leq q \leq 2 \cdot 10^5$) — the number of queries.

The following $q$ lines contain two integers $i$ ($1 \leq i \leq |s|$) and $v$ ($v \in \\{0, 1\\}$), describing the query.

It is guaranteed that the sum of $|s|$ across all test cases does not exceed $2 \cdot 10^5$. It is also guaranteed that the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$.

Output: For each query, output "YES", if "1100" is present in Anya's string; 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:
4
100
4
1 1
2 0
2 0
3 1
1100000
3
6 1
7 1
4 1
111010
4
1 1
5 0
4 1
5 0
0100
4
3 1
1 1
2 0
2 1
output:
NO
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO

Note:

Buggy Code:
import java.util.Scanner;

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

        int t = sc.nextInt();  // Number of test cases

        // Loop through each test case
        while (t-- > 0) {
            StringBuilder s = new StringBuilder(sc.next());  // Input the binary string
            int q = sc.nextInt();  // Number of queries

            // Loop through each query
            for (int j = 0; j < q; j++) {
                int i = sc.nextInt() - 1;  // 1-based index, convert to 0-based
                char v = sc.next().charAt(0);  // New value to assign

                // Update the string at the given index
                s.setCharAt(i, v);

                // Check if "1100" exists in the string after the update
                if (s.indexOf("1100") != -1) {
                    System.out.println("YES");
                } else {
                    System.out.println("NO");
                }
            }
        }

        sc.close();
    }
}

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

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

Think step by step.

Response:
```plaintext
1
1111
4
1 0
2 1
3 0
4 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Tender Carpenter
time_limit_ms: 1000
memory_limit_mb: 256
Description: In his dream, Cocoly would go on a long holiday with no worries around him. So he would try out for many new things, such as... being a carpenter. To learn it well, Cocoly decides to become an apprentice of Master, but in front of him lies a hard task waiting for him to solve.

Cocoly is given an array $$$a_1, a_2,\ldots, a_n$$$. Master calls a set of integers $$$S$$$ stable if and only if, for any possible $$$u$$$, $$$v$$$, and $$$w$$$ from the set $$$S$$$ (note that $$$u$$$, $$$v$$$, and $$$w$$$ do not necessarily have to be pairwise distinct), sticks of length $$$u$$$, $$$v$$$, and $$$w$$$ can form a non-degenerate triangle$$$^{\text{∗}}$$$.

Cocoly is asked to partition the array $$$a$$$ into several (possibly, $$$1$$$ or $$$n$$$) non-empty continuous subsegments$$$^{\text{†}}$$$, such that: for each of the subsegments, the set containing all the elements in it is stable.

Master wants Cocoly to partition $$$a$$$ in at least two different$$$^{\text{‡}}$$$ ways. You have to help him determine whether it is possible.

Input: Each test contains multiple test cases. The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 200$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \leq n \leq 200$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \leq a_i \leq 10^5$$$) — the elements in the array $$$a$$$.

Output: For each test case, print $$$\texttt{YES}$$$ if there are at least two ways to partition $$$a$$$, and $$$\texttt{NO}$$$ otherwise.

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

Examples:
input:
5
4
2 3 5 7
4
115 9 2 28
5
8 4 1 6 2
6
1 5 4 1 4 7
2
100000 100000
output:
YES
NO
NO
YES
YES

Note: In the first test case, here are two possible partitions:

- $$$[2, 3], [5, 7]$$$, since   $$$[2, 3]$$$ is stable because sticks of lengths $$$(2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3)$$$ respectively can all form non-degenerate triangles.  $$$[5, 7]$$$ is stable because sticks of lengths $$$(5, 5, 5), (5, 5, 7), (5, 7, 7), (7, 7, 7)$$$ respectively can all form non-degenerate triangles.
- and $$$[2], [3, 5], [7]$$$, since   $$$[2]$$$ is stable because sticks of lengths $$$(2, 2, 2)$$$ respectively can form a non-degenerate triangle.  $$$[3, 5]$$$ is stable because sticks of lengths $$$(3, 3, 3), (3, 3, 5), (3, 5, 5), (5, 5, 5)$$$ respectively can all form non-degenerate triangles.  $$$[7]$$$ is stable because sticks of lengths $$$(7, 7, 7)$$$ respectively can form a non-degenerate triangle.

Note that some other partitions also satisfy the constraints, such as $$$[2], [3], [5], [7]$$$ and $$$[2], [3], [5, 7]$$$.

In the second test case, Cocoly can only partition each element as a single subsegment, resulting in $$$[115], [9], [2], [28]$$$. Since we only have one possible partition, the answer is $$$\texttt{NO}$$$.

In the third test case, please note that the partition $$$[8, 4], [1], [6], [2]$$$ does not satisfy the constraints, because $$$\{8, 4\}$$$ is not a stable set: sticks of lengths $$$4$$$, $$$4$$$, and $$$8$$$ cannot form a non-degenerate triangle.

Buggy Code:
#include <iostream>
using namespace std;
int main()
{
    int t;
    cin>>t;
    while(t--){
      int n;
      cin>>n;
      int arr[n];
      for(int i=0;i<n;i++){
        cin>>arr[i];
      }int f=0;
      for(int i=0;i<n;i++){
        if(abs(arr[i]-arr[i+1])<=1){
          cout<<"YES"<<endl;
          f=1;
          break;
        }
      }
      if(f==0)cout<<"NO"<<endl;
    }
}

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the given buggy code, we need to focus on the logic that the code is incorrectly implementing. The buggy code checks if the absolute difference between consecutive elements is less than or equal to 1. This is not a correct criterion for determining whether a set of elements can form a non-degenerate triangle.

### Steps to Generate the Test Input:
1. **Identify the Bug**: The bug is in the condition `if(abs(arr[i]-arr[i+1])<=1)`. This condition only checks the difference between consecutive elements, which is not sufficient to determine if any three elements can form a non-degenerate triangle.
2. **Create a Test Case**: We need a test case where the condition `abs(arr[i]-arr[i+1]) <= 1` is true for some elements, but the array cannot be partitioned into stable subsegments in at least two different ways.
3. **Example**: Consider an array where the elements are very close to each other but still cannot form a non-degenerate triangle. For example, an array with elements `[2, 3, 4, 5, 6]`. Here, the difference between consecutive elements is 1, but not all sets of three elements can form a non-degenerate triangle.

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

### Explanation:
- **Array**: `[2, 3, 4, 5, 6]`
- **Buggy Code Behavior**: The buggy code will check the difference between consecutive elements:
  - `abs(2 - 3) = 1`
  - `abs(3 - 4) = 1`
  - `abs(4 - 5) = 1`
  - `abs(5 - 6) = 1`
  - Since all these differences are 1, the code will output `YES`.
- **Correct Behavior**: However, this array cannot be partitioned into stable subsegments in at least two different ways. For example:
  - `[2, 3, 4]` is not stable because `2 + 2 <= 4`.
  - `[3, 4, 5]` is not stable because `3 + 3 <= 5`.
  - `[4, 5, 6]` is not stable because `4 + 4 <= 6`.

Thus, the correct output should be `NO`, but the buggy code will output `YES`, exposing the bug.

This test input is small-scale, complete, and valid, and it effectively exposes the incorrect logic 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: Tender Carpenter
time_limit_ms: 1000
memory_limit_mb: 256
Description: In his dream, Cocoly would go on a long holiday with no worries around him. So he would try out for many new things, such as... being a carpenter. To learn it well, Cocoly decides to become an apprentice of Master, but in front of him lies a hard task waiting for him to solve.

Cocoly is given an array $$$a_1, a_2,\ldots, a_n$$$. Master calls a set of integers $$$S$$$ stable if and only if, for any possible $$$u$$$, $$$v$$$, and $$$w$$$ from the set $$$S$$$ (note that $$$u$$$, $$$v$$$, and $$$w$$$ do not necessarily have to be pairwise distinct), sticks of length $$$u$$$, $$$v$$$, and $$$w$$$ can form a non-degenerate triangle$$$^{\text{∗}}$$$.

Cocoly is asked to partition the array $$$a$$$ into several (possibly, $$$1$$$ or $$$n$$$) non-empty continuous subsegments$$$^{\text{†}}$$$, such that: for each of the subsegments, the set containing all the elements in it is stable.

Master wants Cocoly to partition $$$a$$$ in at least two different$$$^{\text{‡}}$$$ ways. You have to help him determine whether it is possible.

Input: Each test contains multiple test cases. The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 200$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \leq n \leq 200$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \leq a_i \leq 10^5$$$) — the elements in the array $$$a$$$.

Output: For each test case, print $$$\texttt{YES}$$$ if there are at least two ways to partition $$$a$$$, and $$$\texttt{NO}$$$ otherwise.

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

Examples:
input:
5
4
2 3 5 7
4
115 9 2 28
5
8 4 1 6 2
6
1 5 4 1 4 7
2
100000 100000
output:
YES
NO
NO
YES
YES

Note: In the first test case, here are two possible partitions:

- $$$[2, 3], [5, 7]$$$, since   $$$[2, 3]$$$ is stable because sticks of lengths $$$(2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3)$$$ respectively can all form non-degenerate triangles.  $$$[5, 7]$$$ is stable because sticks of lengths $$$(5, 5, 5), (5, 5, 7), (5, 7, 7), (7, 7, 7)$$$ respectively can all form non-degenerate triangles.
- and $$$[2], [3, 5], [7]$$$, since   $$$[2]$$$ is stable because sticks of lengths $$$(2, 2, 2)$$$ respectively can form a non-degenerate triangle.  $$$[3, 5]$$$ is stable because sticks of lengths $$$(3, 3, 3), (3, 3, 5), (3, 5, 5), (5, 5, 5)$$$ respectively can all form non-degenerate triangles.  $$$[7]$$$ is stable because sticks of lengths $$$(7, 7, 7)$$$ respectively can form a non-degenerate triangle.

Note that some other partitions also satisfy the constraints, such as $$$[2], [3], [5], [7]$$$ and $$$[2], [3], [5, 7]$$$.

In the second test case, Cocoly can only partition each element as a single subsegment, resulting in $$$[115], [9], [2], [28]$$$. Since we only have one possible partition, the answer is $$$\texttt{NO}$$$.

In the third test case, please note that the partition $$$[8, 4], [1], [6], [2]$$$ does not satisfy the constraints, because $$$\{8, 4\}$$$ is not a stable set: sticks of lengths $$$4$$$, $$$4$$$, and $$$8$$$ cannot form a non-degenerate triangle.

Buggy Code:
#include <iostream>
#include <vector>
using namespace std;
int main()
{
	int t;
	cin >> t;
	while(t--){
		int n;
		int count = 0;
		cin >> n;
		vector <int> arr(n);
		for (int i = 0; i<n; i++)
			cin >> arr[i];

		int i = 0;
		int j = i+ 1;
		while(j < n){
			int x = max(arr[i],arr[j]);
			int y = min(arr[i],arr[j]);
			if (count >= 2){
				cout << "NO" << endl;
				break;
			}
			if (y+y <= x){
				i = j;
				j = i+1;
				count++;
			}
			else{
				i = j+1;
				j++;
			}
		}
		if (count < 2)
			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
5
4
1 1 1 2
4
2 2 2 3
4
1 2 3 6
4
1 1 1 3
4
2 2 2 4
```

### Explanation:
1. **Test Case 1:**
   - Array: `[1, 1, 1, 2]`
   - This array can be partitioned in multiple ways:
     - `[1, 1], [1, 2]`
     - `[1], [1], [1, 2]`
   - Both partitions are valid, so the output should be `YES`.

2. **Test Case 2:**
   - Array: `[2, 2, 2, 3]`
   - This array can also be partitioned in multiple ways:
     - `[2, 2], [2, 3]`
     - `[2], [2], [2, 3]`
   - Both partitions are valid, so the output should be `YES`.

3. **Test Case 3:**
   - Array: `[1, 2, 3, 6]`
   - This array can only be partitioned in a single way:
     - `[1], [2], [3], [6]`
   - Any other partition would include a subarray that is not stable (e.g., `[1, 2, 3]` is not stable because 1 + 2 = 3). Therefore, the output should be `NO`.

4. **Test Case 4:**
   - Array: `[1, 1, 1, 3]`
   - This array can be partitioned in multiple ways:
     - `[1, 1], [1, 3]`
     - `[1], [1], [1, 3]`
   - Both partitions are valid, so the output should be `YES`.

5. **Test Case 5:**
   - Array: `[2, 2, 2, 4]`
   - This array can only be partitioned in a single way:
     - `[2], [2], [2], [4]`
   - Any other partition would include a subarray that is not stable (e.g., `[2, 2, 4]` is not stable because 2 + 2 = 4). Therefore, the output should be `NO`.

These test cases are designed to expose the bug in the buggy code by providing scenarios where the code's logic for determining the number of valid partitions fails.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Tender Carpenter
time_limit_ms: 1000
memory_limit_mb: 256
Description: In his dream, Cocoly would go on a long holiday with no worries around him. So he would try out for many new things, such as... being a carpenter. To learn it well, Cocoly decides to become an apprentice of Master, but in front of him lies a hard task waiting for him to solve.

Cocoly is given an array $$$a_1, a_2,\ldots, a_n$$$. Master calls a set of integers $$$S$$$ stable if and only if, for any possible $$$u$$$, $$$v$$$, and $$$w$$$ from the set $$$S$$$ (note that $$$u$$$, $$$v$$$, and $$$w$$$ do not necessarily have to be pairwise distinct), sticks of length $$$u$$$, $$$v$$$, and $$$w$$$ can form a non-degenerate triangle$$$^{\text{∗}}$$$.

Cocoly is asked to partition the array $$$a$$$ into several (possibly, $$$1$$$ or $$$n$$$) non-empty continuous subsegments$$$^{\text{†}}$$$, such that: for each of the subsegments, the set containing all the elements in it is stable.

Master wants Cocoly to partition $$$a$$$ in at least two different$$$^{\text{‡}}$$$ ways. You have to help him determine whether it is possible.

Input: Each test contains multiple test cases. The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 200$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \leq n \leq 200$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \leq a_i \leq 10^5$$$) — the elements in the array $$$a$$$.

Output: For each test case, print $$$\texttt{YES}$$$ if there are at least two ways to partition $$$a$$$, and $$$\texttt{NO}$$$ otherwise.

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

Examples:
input:
5
4
2 3 5 7
4
115 9 2 28
5
8 4 1 6 2
6
1 5 4 1 4 7
2
100000 100000
output:
YES
NO
NO
YES
YES

Note: In the first test case, here are two possible partitions:

- $$$[2, 3], [5, 7]$$$, since   $$$[2, 3]$$$ is stable because sticks of lengths $$$(2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3)$$$ respectively can all form non-degenerate triangles.  $$$[5, 7]$$$ is stable because sticks of lengths $$$(5, 5, 5), (5, 5, 7), (5, 7, 7), (7, 7, 7)$$$ respectively can all form non-degenerate triangles.
- and $$$[2], [3, 5], [7]$$$, since   $$$[2]$$$ is stable because sticks of lengths $$$(2, 2, 2)$$$ respectively can form a non-degenerate triangle.  $$$[3, 5]$$$ is stable because sticks of lengths $$$(3, 3, 3), (3, 3, 5), (3, 5, 5), (5, 5, 5)$$$ respectively can all form non-degenerate triangles.  $$$[7]$$$ is stable because sticks of lengths $$$(7, 7, 7)$$$ respectively can form a non-degenerate triangle.

Note that some other partitions also satisfy the constraints, such as $$$[2], [3], [5], [7]$$$ and $$$[2], [3], [5, 7]$$$.

In the second test case, Cocoly can only partition each element as a single subsegment, resulting in $$$[115], [9], [2], [28]$$$. Since we only have one possible partition, the answer is $$$\texttt{NO}$$$.

In the third test case, please note that the partition $$$[8, 4], [1], [6], [2]$$$ does not satisfy the constraints, because $$$\{8, 4\}$$$ is not a stable set: sticks of lengths $$$4$$$, $$$4$$$, and $$$8$$$ cannot form a non-degenerate triangle.

Buggy Code:
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
void solve(){
    int k;
    cin >> k;
    vector<int> a;
    for(int i = 0; i < k; i++){
        int num;
        cin >> num;
        a.push_back(num);
    }
    sort(a.begin(), a.end());
    int min = a[1] - a[0];
    int now = 0;
    for(int i = 1; i < k - 1; i++){
        if(a[i + 1] - a[i] < min) now = i;
    }
    if(a[now] * 2 > a[now + 1]) cout << "YES" << endl;
    else cout << "NO" << 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:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on edge cases where the code's logic might fail. The key issue in the buggy code is the incorrect logic for determining if a partition is stable. The code checks if the difference between consecutive elements is minimal and if the smaller element is more than half of the larger element. However, this does not correctly determine the stability of the entire subsegment.

Let's consider a few edge cases:

1. **All elements are the same**: This should always be a stable set.
2. **Elements form a sequence where the sum of the two smallest elements is not greater than the largest element**: This should not be a stable set.
3. **Elements where the difference between consecutive elements is minimal but the set is still not stable**.

A good test case to expose the bug is a sequence where the elements are close but not all elements form a stable set. For example, a sequence where the sum of the two smallest elements is not greater than the largest element.

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

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

Explanation:
- The array `[1, 1, 2, 3]` should not be partitioned into stable subsegments in multiple ways.
- The subsegment `[1, 1, 2]` is not stable because `1 + 1 = 2` (not greater than 2).
- The subsegment `[1, 2, 3]` is not stable because `1 + 2 = 3` (not greater than 3).
- Therefore, the correct output should be `NO`.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Tender Carpenter
time_limit_ms: 1000
memory_limit_mb: 256
Description: In his dream, Cocoly would go on a long holiday with no worries around him. So he would try out for many new things, such as... being a carpenter. To learn it well, Cocoly decides to become an apprentice of Master, but in front of him lies a hard task waiting for him to solve.

Cocoly is given an array $$$a_1, a_2,\ldots, a_n$$$. Master calls a set of integers $$$S$$$ stable if and only if, for any possible $$$u$$$, $$$v$$$, and $$$w$$$ from the set $$$S$$$ (note that $$$u$$$, $$$v$$$, and $$$w$$$ do not necessarily have to be pairwise distinct), sticks of length $$$u$$$, $$$v$$$, and $$$w$$$ can form a non-degenerate triangle$$$^{\text{∗}}$$$.

Cocoly is asked to partition the array $$$a$$$ into several (possibly, $$$1$$$ or $$$n$$$) non-empty continuous subsegments$$$^{\text{†}}$$$, such that: for each of the subsegments, the set containing all the elements in it is stable.

Master wants Cocoly to partition $$$a$$$ in at least two different$$$^{\text{‡}}$$$ ways. You have to help him determine whether it is possible.

Input: Each test contains multiple test cases. The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 200$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \leq n \leq 200$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \leq a_i \leq 10^5$$$) — the elements in the array $$$a$$$.

Output: For each test case, print $$$\texttt{YES}$$$ if there are at least two ways to partition $$$a$$$, and $$$\texttt{NO}$$$ otherwise.

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

Examples:
input:
5
4
2 3 5 7
4
115 9 2 28
5
8 4 1 6 2
6
1 5 4 1 4 7
2
100000 100000
output:
YES
NO
NO
YES
YES

Note: In the first test case, here are two possible partitions:

- $$$[2, 3], [5, 7]$$$, since   $$$[2, 3]$$$ is stable because sticks of lengths $$$(2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3)$$$ respectively can all form non-degenerate triangles.  $$$[5, 7]$$$ is stable because sticks of lengths $$$(5, 5, 5), (5, 5, 7), (5, 7, 7), (7, 7, 7)$$$ respectively can all form non-degenerate triangles.
- and $$$[2], [3, 5], [7]$$$, since   $$$[2]$$$ is stable because sticks of lengths $$$(2, 2, 2)$$$ respectively can form a non-degenerate triangle.  $$$[3, 5]$$$ is stable because sticks of lengths $$$(3, 3, 3), (3, 3, 5), (3, 5, 5), (5, 5, 5)$$$ respectively can all form non-degenerate triangles.  $$$[7]$$$ is stable because sticks of lengths $$$(7, 7, 7)$$$ respectively can form a non-degenerate triangle.

Note that some other partitions also satisfy the constraints, such as $$$[2], [3], [5], [7]$$$ and $$$[2], [3], [5, 7]$$$.

In the second test case, Cocoly can only partition each element as a single subsegment, resulting in $$$[115], [9], [2], [28]$$$. Since we only have one possible partition, the answer is $$$\texttt{NO}$$$.

In the third test case, please note that the partition $$$[8, 4], [1], [6], [2]$$$ does not satisfy the constraints, because $$$\{8, 4\}$$$ is not a stable set: sticks of lengths $$$4$$$, $$$4$$$, and $$$8$$$ cannot form a non-degenerate triangle.

Buggy Code:
def solve():
    t = int(input())
    results = []
    for _ in range(t):
        n = int(input())
        a = list(map(int, input().split()))
        if len(set(a)) == 1:
            results.append("YES")
            continue
        a.sort()
        stable = False
        for i in range(n - 2):
            if a[i] + a[i + 1] > a[i + 2]:
                stable = True
                break
        if stable and not (n == 5 and a == [1, 2, 4, 6, 8]):
            results.append("YES")
        else:
            results.append("NO")
    print("\n".join(results))
solve()

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

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

Think step by step.

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

### Explanation:
1. **Test Case 1: [2, 3, 4, 5]**
   - This array can be partitioned in multiple ways, such as `[2, 3], [4, 5]` and `[2], [3, 4], [5]`. Both partitions are valid, so the expected output is `YES`.

2. **Test Case 2: [1, 1, 1, 1]**
   - This array can only be partitioned into single-element subsegments, so the expected output is `NO`.

3. **Test Case 3: [1, 2, 3, 4, 5]**
   - This array can be partitioned in multiple ways, such as `[1, 2, 3], [4, 5]` and `[1, 2], [3, 4], [5]`. Both partitions are valid, so the expected output is `YES`.

4. **Test Case 4: [1, 2, 2, 3, 3, 4]**
   - This array can be partitioned in multiple ways, such as `[1, 2, 2], [3, 3, 4]` and `[1, 2], [2, 3], [3, 4]`. Both partitions are valid, so the expected output is `YES`.

5. **Test Case 5: [1, 2]**
   - This array can only be partitioned into single-element subsegments, so the expected output is `NO`.

These test cases are designed to cover a variety of scenarios, including arrays with repeated elements, arrays that can be partitioned in multiple ways, and arrays that cannot be partitioned in more than one way. The buggy code's logic for checking stability and the special case for `n == 5 and a == [1, 2, 4, 6, 8]` is tested in these cases.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Tender Carpenter
time_limit_ms: 1000
memory_limit_mb: 256
Description: In his dream, Cocoly would go on a long holiday with no worries around him. So he would try out for many new things, such as... being a carpenter. To learn it well, Cocoly decides to become an apprentice of Master, but in front of him lies a hard task waiting for him to solve.

Cocoly is given an array $$$a_1, a_2,\ldots, a_n$$$. Master calls a set of integers $$$S$$$ stable if and only if, for any possible $$$u$$$, $$$v$$$, and $$$w$$$ from the set $$$S$$$ (note that $$$u$$$, $$$v$$$, and $$$w$$$ do not necessarily have to be pairwise distinct), sticks of length $$$u$$$, $$$v$$$, and $$$w$$$ can form a non-degenerate triangle$$$^{\text{∗}}$$$.

Cocoly is asked to partition the array $$$a$$$ into several (possibly, $$$1$$$ or $$$n$$$) non-empty continuous subsegments$$$^{\text{†}}$$$, such that: for each of the subsegments, the set containing all the elements in it is stable.

Master wants Cocoly to partition $$$a$$$ in at least two different$$$^{\text{‡}}$$$ ways. You have to help him determine whether it is possible.

Input: Each test contains multiple test cases. The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 200$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \leq n \leq 200$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \leq a_i \leq 10^5$$$) — the elements in the array $$$a$$$.

Output: For each test case, print $$$\texttt{YES}$$$ if there are at least two ways to partition $$$a$$$, and $$$\texttt{NO}$$$ otherwise.

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

Examples:
input:
5
4
2 3 5 7
4
115 9 2 28
5
8 4 1 6 2
6
1 5 4 1 4 7
2
100000 100000
output:
YES
NO
NO
YES
YES

Note: In the first test case, here are two possible partitions:

- $$$[2, 3], [5, 7]$$$, since   $$$[2, 3]$$$ is stable because sticks of lengths $$$(2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3)$$$ respectively can all form non-degenerate triangles.  $$$[5, 7]$$$ is stable because sticks of lengths $$$(5, 5, 5), (5, 5, 7), (5, 7, 7), (7, 7, 7)$$$ respectively can all form non-degenerate triangles.
- and $$$[2], [3, 5], [7]$$$, since   $$$[2]$$$ is stable because sticks of lengths $$$(2, 2, 2)$$$ respectively can form a non-degenerate triangle.  $$$[3, 5]$$$ is stable because sticks of lengths $$$(3, 3, 3), (3, 3, 5), (3, 5, 5), (5, 5, 5)$$$ respectively can all form non-degenerate triangles.  $$$[7]$$$ is stable because sticks of lengths $$$(7, 7, 7)$$$ respectively can form a non-degenerate triangle.

Note that some other partitions also satisfy the constraints, such as $$$[2], [3], [5], [7]$$$ and $$$[2], [3], [5, 7]$$$.

In the second test case, Cocoly can only partition each element as a single subsegment, resulting in $$$[115], [9], [2], [28]$$$. Since we only have one possible partition, the answer is $$$\texttt{NO}$$$.

In the third test case, please note that the partition $$$[8, 4], [1], [6], [2]$$$ does not satisfy the constraints, because $$$\{8, 4\}$$$ is not a stable set: sticks of lengths $$$4$$$, $$$4$$$, and $$$8$$$ cannot form a non-degenerate triangle.

Buggy Code:
for _ in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    if n == 2:
        if a[-2]*2 > a[-1] or a[-1]*2 > a[-2]:
            print('YES')
        else:
            print('NO')
    else:
        ans = 'NO'
        for i in range(2, n):
            x = a[i-2]
            y = a[i-1]
            z = a[i]
            if x+y > z and x+z > y and z+y > x:
                ans = 'YES'
                break
        print(ans)

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

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

Think step by step.

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

**Explanation:**
1. **Test Case 1:**
   - Input: `4 1 2 3 4`
   - Expected Output: `NO`
   - Reason: The only stable subsegments are `[1]`, `[2]`, `[3]`, and `[4]`. Any other combination of these elements does not form a stable set.

2. **Test Case 2:**
   - Input: `5 1 2 3 4 5`
   - Expected Output: `NO`
   - Reason: Similar to the first test case, the only stable subsegments are `[1]`, `[2]`, `[3]`, `[4]`, and `[5]`. Any other combination of these elements does not form a stable set.

3. **Test Case 3:**
   - Input: `6 1 1 2 3 5 8`
   - Expected Output: `NO`
   - Reason: The only stable subsegments are `[1]`, `[1]`, `[2]`, `[3]`, `[5]`, and `[8]`. Any other combination of these elements does not form a stable set.

These test cases are designed to challenge the buggy code by providing inputs where the elements are in increasing order and do not easily form stable sets, thus exposing the logic errors in the code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Tender Carpenter
time_limit_ms: 1000
memory_limit_mb: 256
Description: In his dream, Cocoly would go on a long holiday with no worries around him. So he would try out for many new things, such as... being a carpenter. To learn it well, Cocoly decides to become an apprentice of Master, but in front of him lies a hard task waiting for him to solve.

Cocoly is given an array $$$a_1, a_2,\ldots, a_n$$$. Master calls a set of integers $$$S$$$ stable if and only if, for any possible $$$u$$$, $$$v$$$, and $$$w$$$ from the set $$$S$$$ (note that $$$u$$$, $$$v$$$, and $$$w$$$ do not necessarily have to be pairwise distinct), sticks of length $$$u$$$, $$$v$$$, and $$$w$$$ can form a non-degenerate triangle$$$^{\text{∗}}$$$.

Cocoly is asked to partition the array $$$a$$$ into several (possibly, $$$1$$$ or $$$n$$$) non-empty continuous subsegments$$$^{\text{†}}$$$, such that: for each of the subsegments, the set containing all the elements in it is stable.

Master wants Cocoly to partition $$$a$$$ in at least two different$$$^{\text{‡}}$$$ ways. You have to help him determine whether it is possible.

Input: Each test contains multiple test cases. The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 200$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \leq n \leq 200$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \leq a_i \leq 10^5$$$) — the elements in the array $$$a$$$.

Output: For each test case, print $$$\texttt{YES}$$$ if there are at least two ways to partition $$$a$$$, and $$$\texttt{NO}$$$ otherwise.

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

Examples:
input:
5
4
2 3 5 7
4
115 9 2 28
5
8 4 1 6 2
6
1 5 4 1 4 7
2
100000 100000
output:
YES
NO
NO
YES
YES

Note: In the first test case, here are two possible partitions:

- $$$[2, 3], [5, 7]$$$, since   $$$[2, 3]$$$ is stable because sticks of lengths $$$(2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3)$$$ respectively can all form non-degenerate triangles.  $$$[5, 7]$$$ is stable because sticks of lengths $$$(5, 5, 5), (5, 5, 7), (5, 7, 7), (7, 7, 7)$$$ respectively can all form non-degenerate triangles.
- and $$$[2], [3, 5], [7]$$$, since   $$$[2]$$$ is stable because sticks of lengths $$$(2, 2, 2)$$$ respectively can form a non-degenerate triangle.  $$$[3, 5]$$$ is stable because sticks of lengths $$$(3, 3, 3), (3, 3, 5), (3, 5, 5), (5, 5, 5)$$$ respectively can all form non-degenerate triangles.  $$$[7]$$$ is stable because sticks of lengths $$$(7, 7, 7)$$$ respectively can form a non-degenerate triangle.

Note that some other partitions also satisfy the constraints, such as $$$[2], [3], [5], [7]$$$ and $$$[2], [3], [5, 7]$$$.

In the second test case, Cocoly can only partition each element as a single subsegment, resulting in $$$[115], [9], [2], [28]$$$. Since we only have one possible partition, the answer is $$$\texttt{NO}$$$.

In the third test case, please note that the partition $$$[8, 4], [1], [6], [2]$$$ does not satisfy the constraints, because $$$\{8, 4\}$$$ is not a stable set: sticks of lengths $$$4$$$, $$$4$$$, and $$$8$$$ cannot form a non-degenerate triangle.

Buggy Code:
t = int(input())
for _ in range(t):
    n = int(input())
    numbers = [0]
    numbers.extend(list(map(int, input().split())))
    numbers.append(float('inf'))
    found = 'NO'

    for i in range(0, n):
        number = numbers[i]
        next_number = numbers[i + 1]
        prev_number = numbers[i - 1]

        if (
                (number == next_number or number == prev_number) or
                (number < next_number < number * 2) or
                (number < prev_number < number * 2)
        ):
            found = 'YES'
            break

    print(found)

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

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

Think step by step.

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

### Explanation:
1. **Test Case 1:**
   - Input: `3 1 2 3`
   - This case checks if the code can handle a small array where the elements are in increasing order. The only possible partition is `[1], [2], [3]`, which does not satisfy the condition of having at least two different ways to partition the array. The expected output should be `NO`.

2. **Test Case 2:**
   - Input: `4 2 2 2 2`
   - This case checks if the code can handle an array with all elements being the same. The array can be partitioned in multiple ways, such as `[2, 2], [2, 2]` or `[2], [2], [2], [2]`. The expected output should be `YES`.

3. **Test Case 3:**
   - Input: `5 1 2 2 3 4`
   - This case checks if the code can handle a slightly more complex array with repeated elements. The array can be partitioned in multiple ways, such as `[1, 2], [2, 3], [4]` or `[1], [2, 2], [3, 4]`. The expected output should be `YES`.

These test cases are designed to expose potential issues in the buggy code, particularly in handling arrays with repeated elements and ensuring that the partitioning is done correctly.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Tender Carpenter
time_limit_ms: 1000
memory_limit_mb: 256
Description: In his dream, Cocoly would go on a long holiday with no worries around him. So he would try out for many new things, such as... being a carpenter. To learn it well, Cocoly decides to become an apprentice of Master, but in front of him lies a hard task waiting for him to solve.

Cocoly is given an array $$$a_1, a_2,\ldots, a_n$$$. Master calls a set of integers $$$S$$$ stable if and only if, for any possible $$$u$$$, $$$v$$$, and $$$w$$$ from the set $$$S$$$ (note that $$$u$$$, $$$v$$$, and $$$w$$$ do not necessarily have to be pairwise distinct), sticks of length $$$u$$$, $$$v$$$, and $$$w$$$ can form a non-degenerate triangle$$$^{\text{∗}}$$$.

Cocoly is asked to partition the array $$$a$$$ into several (possibly, $$$1$$$ or $$$n$$$) non-empty continuous subsegments$$$^{\text{†}}$$$, such that: for each of the subsegments, the set containing all the elements in it is stable.

Master wants Cocoly to partition $$$a$$$ in at least two different$$$^{\text{‡}}$$$ ways. You have to help him determine whether it is possible.

Input: Each test contains multiple test cases. The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 200$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \leq n \leq 200$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \leq a_i \leq 10^5$$$) — the elements in the array $$$a$$$.

Output: For each test case, print $$$\texttt{YES}$$$ if there are at least two ways to partition $$$a$$$, and $$$\texttt{NO}$$$ otherwise.

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

Examples:
input:
5
4
2 3 5 7
4
115 9 2 28
5
8 4 1 6 2
6
1 5 4 1 4 7
2
100000 100000
output:
YES
NO
NO
YES
YES

Note: In the first test case, here are two possible partitions:

- $$$[2, 3], [5, 7]$$$, since   $$$[2, 3]$$$ is stable because sticks of lengths $$$(2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3)$$$ respectively can all form non-degenerate triangles.  $$$[5, 7]$$$ is stable because sticks of lengths $$$(5, 5, 5), (5, 5, 7), (5, 7, 7), (7, 7, 7)$$$ respectively can all form non-degenerate triangles.
- and $$$[2], [3, 5], [7]$$$, since   $$$[2]$$$ is stable because sticks of lengths $$$(2, 2, 2)$$$ respectively can form a non-degenerate triangle.  $$$[3, 5]$$$ is stable because sticks of lengths $$$(3, 3, 3), (3, 3, 5), (3, 5, 5), (5, 5, 5)$$$ respectively can all form non-degenerate triangles.  $$$[7]$$$ is stable because sticks of lengths $$$(7, 7, 7)$$$ respectively can form a non-degenerate triangle.

Note that some other partitions also satisfy the constraints, such as $$$[2], [3], [5], [7]$$$ and $$$[2], [3], [5, 7]$$$.

In the second test case, Cocoly can only partition each element as a single subsegment, resulting in $$$[115], [9], [2], [28]$$$. Since we only have one possible partition, the answer is $$$\texttt{NO}$$$.

In the third test case, please note that the partition $$$[8, 4], [1], [6], [2]$$$ does not satisfy the constraints, because $$$\{8, 4\}$$$ is not a stable set: sticks of lengths $$$4$$$, $$$4$$$, and $$$8$$$ cannot form a non-degenerate triangle.

Buggy Code:
import java.util.*;

public class Main {
    static final int MOD = 1000000007;

    public static void main(String[] args) {
        //initCode();
        Scanner scanner = new Scanner(System.in);
        int testCases = scanner.nextInt();
        while (testCases-- > 0) {
            solve(scanner);
        }
        scanner.close();
    }

    static void solve(Scanner scanner) {
        int n = scanner.nextInt();
        int[] array = new int[n];
        for (int i = 0; i < n; i++) {
            array[i] = scanner.nextInt();
        }
        Arrays.sort(array);

        int count = 0;
        for (int i = 0; i < n - 1; i++) {
            if (2 * array[i] <= array[i + 1]) {
                count++;
            }
        }

        if (count >= n / 2) {
            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
3
1 2 3
4
1 2 3 4
5
1 1 2 3 5
```

**Explanation:**

1. **Test Case 1:**
   - **Array:** `[1, 2, 3]`
   - **Expected Output:** `NO`
   - **Reason:** The only way to partition this array into stable subsegments is `[1], [2], [3]`. There are no other valid partitions.

2. **Test Case 2:**
   - **Array:** `[1, 2, 3, 4]`
   - **Expected Output:** `YES`
   - **Reason:** There are multiple valid partitions, such as `[1], [2, 3], [4]` and `[1, 2], [3, 4]`.

3. **Test Case 3:**
   - **Array:** `[1, 1, 2, 3, 5]`
   - **Expected Output:** `NO`
   - **Reason:** The only way to partition this array into stable subsegments is `[1], [1], [2], [3], [5]`. There are no other valid partitions.

These test cases are designed to expose the bug in the faulty code by focusing on edge cases where the number of valid partitions is either exactly one or more than one. The buggy code incorrectly counts the number of valid partitions and may fail to handle these edge cases correctly.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Tender Carpenter
time_limit_ms: 1000
memory_limit_mb: 256
Description: In his dream, Cocoly would go on a long holiday with no worries around him. So he would try out for many new things, such as... being a carpenter. To learn it well, Cocoly decides to become an apprentice of Master, but in front of him lies a hard task waiting for him to solve.

Cocoly is given an array $$$a_1, a_2,\ldots, a_n$$$. Master calls a set of integers $$$S$$$ stable if and only if, for any possible $$$u$$$, $$$v$$$, and $$$w$$$ from the set $$$S$$$ (note that $$$u$$$, $$$v$$$, and $$$w$$$ do not necessarily have to be pairwise distinct), sticks of length $$$u$$$, $$$v$$$, and $$$w$$$ can form a non-degenerate triangle$$$^{\text{∗}}$$$.

Cocoly is asked to partition the array $$$a$$$ into several (possibly, $$$1$$$ or $$$n$$$) non-empty continuous subsegments$$$^{\text{†}}$$$, such that: for each of the subsegments, the set containing all the elements in it is stable.

Master wants Cocoly to partition $$$a$$$ in at least two different$$$^{\text{‡}}$$$ ways. You have to help him determine whether it is possible.

Input: Each test contains multiple test cases. The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 200$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \leq n \leq 200$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \leq a_i \leq 10^5$$$) — the elements in the array $$$a$$$.

Output: For each test case, print $$$\texttt{YES}$$$ if there are at least two ways to partition $$$a$$$, and $$$\texttt{NO}$$$ otherwise.

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

Examples:
input:
5
4
2 3 5 7
4
115 9 2 28
5
8 4 1 6 2
6
1 5 4 1 4 7
2
100000 100000
output:
YES
NO
NO
YES
YES

Note: In the first test case, here are two possible partitions:

- $$$[2, 3], [5, 7]$$$, since   $$$[2, 3]$$$ is stable because sticks of lengths $$$(2, 2, 2), (2, 2, 3), (2, 3, 3), (3, 3, 3)$$$ respectively can all form non-degenerate triangles.  $$$[5, 7]$$$ is stable because sticks of lengths $$$(5, 5, 5), (5, 5, 7), (5, 7, 7), (7, 7, 7)$$$ respectively can all form non-degenerate triangles.
- and $$$[2], [3, 5], [7]$$$, since   $$$[2]$$$ is stable because sticks of lengths $$$(2, 2, 2)$$$ respectively can form a non-degenerate triangle.  $$$[3, 5]$$$ is stable because sticks of lengths $$$(3, 3, 3), (3, 3, 5), (3, 5, 5), (5, 5, 5)$$$ respectively can all form non-degenerate triangles.  $$$[7]$$$ is stable because sticks of lengths $$$(7, 7, 7)$$$ respectively can form a non-degenerate triangle.

Note that some other partitions also satisfy the constraints, such as $$$[2], [3], [5], [7]$$$ and $$$[2], [3], [5, 7]$$$.

In the second test case, Cocoly can only partition each element as a single subsegment, resulting in $$$[115], [9], [2], [28]$$$. Since we only have one possible partition, the answer is $$$\texttt{NO}$$$.

In the third test case, please note that the partition $$$[8, 4], [1], [6], [2]$$$ does not satisfy the constraints, because $$$\{8, 4\}$$$ is not a stable set: sticks of lengths $$$4$$$, $$$4$$$, and $$$8$$$ cannot form a non-degenerate triangle.

Buggy Code:
import java.util.*;
import java.io.*;
public class TenderCarpenter  {
    static FastReader in = new FastReader();
    static FastWriter out = new FastWriter();
    static final Random random=new Random();
    static long mod=1000000007L;
    static HashMap<String,Integer>map=new HashMap<>();

    static int max(int a, int b)
    {
        if(a<b)
            return b;
        return a;
    }

    static void ruffleSort(int[] a) {
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

//    static < E > void print(E res)
//    {
//        System.out.println(res);
//    }

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

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

    static int abs(int a)
    {
        if(a<0)
            return -1*a;
        return a;
    }

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

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

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt()
        {
            return Integer.parseInt(next());
        }

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

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }

        int [] readintarray(int n) {
            int res [] = new int [n];
            for(int i = 0; i<n; i++)res[i] = nextInt();
            return res;
        }
        long [] readlongarray(int n) {
            long res [] = new long [n];
            for(int i = 0; i<n; i++)res[i] = nextLong();
            return res;
        }
    }

    static class FastWriter {
        private final BufferedWriter bw;

        public FastWriter() {
            this.bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }

        public void print(Object object) throws IOException {
            bw.append("" + object);
        }

        public void println(Object object) throws IOException {
            print(object);
            bw.append("\n");
        }

        public void close() throws IOException {
            bw.close();
        }
    }

    /************ Main functions starts here *********************/

    public static void main(String args[]) throws IOException {
        int t = in.nextInt();
        while (t-- > 0) {
            int n = in.nextInt();
            int a[] = in.readintarray(n);
            int c = 0;

            for (int j = 0; j < n; j+=1) {
                for (int i = j; i < n-2; i+=3) {
                    if (c > 0)
                        break;
                    if (a[i] + a[i + 1] > a[i + 2] && a[i] + a[i + 2] > a[i + 1] && a[i + 1] + a[i + 2] > a[i])
                        c++;
                }
            }

            if(c<1) {
                for (int j = 0; j < n; j++) {
                    for (int i = j; i < n - 1; i += 2) {
                        if (c > 0)
                            break;
                        if (2 * a[i] > a[i + 1] && 2 * a[i + 1] > a[i]) {
                            c++;
                        }
                    }
                }
            }

            if(c>0)
                System.out.println("Yes");
            else
                System.out.println("No");

        }
        out.close();

    }

}

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

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

Think step by step.

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