**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
def can_unlock(x):
    if x % 33 == 0:
        return "YES"
    x_str = str(x)
    for i in range(len(x_str) - 1):
        reduced_x = int(x_str[:i] + x_str[i + 2:])
        if reduced_x % 33 == 0:
            return "YES"
    return "NO"
t = int(input())
results = []
for _ in range(t):
    x = int(input())
    results.append(can_unlock(x))
print("\n".join(results))

**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
3333
133333333
100000000
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
from sys import stdin

input = stdin.read
data = input().split()
t = int(data[0])
nums = list(map(int, data[1:]))

rez = []
for i in range(t):
    x = nums[i]
    if x == 0:
        rez.append('YES')
        break
    else:
        while x >= 33:
            if x % 33 == 0:  # Если делится на 33, сразу YES
                rez.append('YES')
                break
            tr = str(x).count('3')  # Считаем количество цифр "3"
            if tr >= 2:  # Если есть хотя бы две "3"
                # Реверсируем строку, удаляем первые две "3", затем снова реверсируем
                x = int(str(x)[::-1].replace('3', '', 2)[::-1])
            else:
                x %= 33  # Если "3" недостаточно, уменьшаем x до остатка от деления
        else:
            rez.append('NO')  # Если цикл завершился, а x не стало 0
print("\n".join(rez))

**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
333
3333
33333
333333
3333333
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
t= int(input())
for _ in range(t):
    n=int(input())
    s=str(n)
    l=len(s)

    odd=0
    even=0
    su=0

    for i in range(l):

        su+= int(s[i])
        if  i%2==0:
            odd+= int(s[i])
        else:
            even+= int(s[i])

    if (su%3==0) and (odd==even):
        print("YES")

    else:
        print("NO")

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

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

Think step by step.

Response:
```plaintext
3
333
666
133333332
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

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

public class A_Kevin_and_Combination_Lock {

    // Fast Input and Output
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter out = new PrintWriter(System.out);
    static StringTokenizer st;

    public static long remove33(long n) {
        String s = Long.toString(n);
        StringBuilder str = new StringBuilder("");
        int i = 0;
        while (i < s.length() - 1) {
            if (s.charAt(i) == '3' && s.charAt(i + 1) == '3') {
                i += 2;
            } else {
                str.append(s.charAt(i));
                i++;
            }
        }
        if (s.charAt(s.length() - 1) != '3') {
            str.append(s.charAt(s.length() - 1));
        }
        if (str.length() == 0) {
            return 0;
        }
        long ans = Long.parseLong(str.toString());
        return ans;
    }

    public static void main(String[] args) throws IOException {
        int t = nextInt();
        while (t-- > 0) {
            long x = nextLong();
            while (x > 0) {
                long temp = x;
                x = remove33(x);
                if (temp == x) {
                    x -= 33;
                }
            }
            if (x == 0) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }
            // System.out.println(remove33(x));
        }
        out.close();
    }

    // Fast Input Utility
    static String next() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

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

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

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

    // Utility Methods
    // 1. Bit Manipulation Utilities
    static int countSetBits(int n) {
        return Integer.bitCount(n);
    }

    static int highestOneBit(int n) {
        return Integer.highestOneBit(n);
    }

    static int lowestOneBit(int n) {
        return Integer.lowestOneBit(n);
    }

    static int leadingZeros(int n) {
        return Integer.numberOfLeadingZeros(n);
    }

    static int trailingZeros(int n) {
        return Integer.numberOfTrailingZeros(n);
    }

    static int reverseBits(int n) {
        return Integer.reverse(n);
    }

    static int rotateLeft(int n, int d) {
        return Integer.rotateLeft(n, d);
    }

    static int rotateRight(int n, int d) {
        return Integer.rotateRight(n, d);
    }

    // 2. Math Utilities
    static int gcd(int a, int b) {
        return BigInteger.valueOf(a).gcd(BigInteger.valueOf(b)).intValue();
    }

    static int absExact(int x) {
        return Math.absExact(x);
    }

    static int multiplyExact(int x, int y) {
        return Math.multiplyExact(x, y);
    }

    static int floorDiv(int x, int y) {
        return Math.floorDiv(x, y);
    }

    static BigInteger bigGCD(BigInteger a, BigInteger b) {
        return a.gcd(b);
    }

    static BigInteger modPow(BigInteger base, BigInteger exp, BigInteger mod) {
        return base.modPow(exp, mod);
    }

    // 3. Array Utilities
    static void fillArray(int[] arr, int val) {
        Arrays.fill(arr, val);
    }

    static int[] copyArray(int[] arr, int start, int end) {
        return Arrays.copyOfRange(arr, start, end);
    }

    static int arraySum(int[] arr) {
        return Arrays.stream(arr).sum();
    }

    // 4. Collection Utilities
    static <T extends Comparable<T>> T min(Collection<T> col) {
        return Collections.min(col);
    }

    static <T extends Comparable<T>> T max(Collection<T> col) {
        return Collections.max(col);
    }

    static <T> int frequency(Collection<T> col, T obj) {
        return Collections.frequency(col, obj);
    }

    static <T> boolean disjoint(Collection<T> col1, Collection<T> col2) {
        return Collections.disjoint(col1, col2);
    }

    static <T> void rotate(List<T> list, int distance) {
        Collections.rotate(list, distance);
    }

    static <T> void swap(List<T> list, int i, int j) {
        Collections.swap(list, i, j);
    }

    // 5. String Utilities
    static int indexOf(String s, int ch, int fromIndex) {
        return s.indexOf(ch, fromIndex);
    }

    static String substring(String s, int beginIndex, int endIndex) {
        return s.substring(beginIndex, endIndex);
    }

    static String replace(String s, char oldChar, char newChar) {
        return s.replace(oldChar, newChar);
    }

    static boolean matches(String s, String regex) {
        return s.matches(regex);
    }

    // 6. Priority Queue Utilities
    static PriorityQueue<Integer> minHeap() {
        return new PriorityQueue<>();
    }

    static PriorityQueue<Integer> maxHeap() {
        return new PriorityQueue<>(Collections.reverseOrder());
    }

    // 7. Deque Utilities (Useful for Sliding Window problems)
    static Deque<Integer> createDeque() {
        return new ArrayDeque<>();
    }

    // 8. TreeMap and TreeSet Utilities
    static TreeMap<Integer, Integer> createTreeMap() {
        return new TreeMap<>();
    }

    static TreeSet<Integer> createTreeSet() {
        return new TreeSet<>();
    }

    // 9. Random Utilities
    static int randomInt(int origin, int bound) {
        return ThreadLocalRandom.current().nextInt(origin, bound);
    }

    // 10. System Utilities
    static void copyArray(Object src, int srcPos, Object dest, int destPos, int length) {
        System.arraycopy(src, srcPos, dest, destPos, length);
    }

    static long nanoTime() {
        return System.nanoTime();
    }

    // Example Utility Functions for CP Problems
    static void swap(int[] arr, int i, int j) {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }

    static int gcdArray(int[] arr) {
        int result = arr[0];
        for (int i = 1; i < arr.length; i++) {
            result = gcd(result, arr[i]);
            if (result == 1)
                return 1; // No need to continue if gcd becomes 1
        }
        return result;
    }
}

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

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

Think step by step.

Response:
```plaintext
3
3333
3366
1000000000
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

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

/*

 */

public class Codeforces {

	public static void main(String[] subscribeToSecondThread) {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		int t = fs.nextInt();
		while(t-- > 0){
			String s = fs.next();
			if(s.equals("0")) {
				System.out.println("YES");
				return;
			}
			if(Integer.parseInt(s)>0 && Integer.parseInt(s) < 33 ) System.out.println("NO");
			else System.out.println(solve(s)?"YES":"NO");
		}

		out.flush();
		out.close();
	}

	public static boolean solve(String s){
		if(s.contains("-")) return false;
		if(s.equals("0")){
			return true;
		}

		boolean option = false;
		if(!s.equals("33") && s.contains("33")){
			// System.out.println(s.replaceFirst("33", ""));
			option = solve(s.replace("33", ""));
		}else if(Integer.parseInt(s)>=33){
			int p = Integer.parseInt(s);
			p-=33;
			// System.out.println(String.valueOf(p));
			option = solve(String.valueOf(p));
		}
		return option;

	}

	static final Random random = new Random();
	static final int mod = 1_000_000_007;

	static void ruffleSort(int[] a) {
		int n = a.length;// shuffle, then sort
		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 long add(long a, long b) {
		return (a + b) % mod;
	}

	static long sub(long a, long b) {
		return ((a - b) % mod + mod) % mod;
	}

	static long mul(long a, long b) {
		return (a * b) % mod;
	}

	static long exp(long base, long exp) {
		if (exp == 0)
			return 1;
		long half = exp(base, exp / 2);
		if (exp % 2 == 0)
			return mul(half, half);
		return mul(half, mul(half, base));
	}

	static long[] factorials = new long[2_000_001];
	static long[] invFactorials = new long[2_000_001];

	static void precompFacts() {
		factorials[0] = invFactorials[0] = 1;
		for (int i = 1; i < factorials.length; i++)
			factorials[i] = mul(factorials[i - 1], i);
		invFactorials[factorials.length - 1] = exp(factorials[factorials.length - 1], mod - 2);
		for (int i = invFactorials.length - 2; i >= 0; i--)
			invFactorials[i] = mul(invFactorials[i + 1], i + 1);
	}

	static long nCk(int n, int k) {
		return mul(factorials[n], mul(invFactorials[k], invFactorials[n - k]));
	}

	static void sort(int[] a) {
		ArrayList<Integer> l = new ArrayList<>();
		for (int i : a)
			l.add(i);
		Collections.sort(l);
		for (int i = 0; i < a.length; i++)
			a[i] = l.get(i);
	}

	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 e) {
					e.printStackTrace();
				}
			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());
		}
	}

}

**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
3333
133333333
330033
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
#include <bits/stdc++.h>
#define el "\n"
#define ll long long int
#define ull unsigned long long int
#define f(i, initializer, upper_limit) for(ll i = initializer; i < upper_limit; i++)
#define rf(i, initializer, lower_limit) for(ll i = initializer; i > lower_limit; i--)
#define YES cout<<"YES"<<el
#define NO cout<<"NO"<<el
#define deb(x) cout << #x << " = " << x << el
using namespace std;

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

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

    int t; cin>>t;
    while(t--){
        ll x; cin>>x;
        if (x%33 == 0){
            cout << "YES" << endl;
            continue;
        }
        stringstream ss;
        ss << x;
        string num = ss.str();
        ll maxl = -1, currl = 0;
        for(char ch: num){
            if(ch == '3'){
                currl++;
                maxl = max(maxl, currl);
            }
            else currl = 0;
        }
        if(maxl%2 == 0){
            // cout << maxl << endl;
            cout << "YES" << endl;  continue;
        }else{
            cout << "NO" << endl; continue;
        }
    }
    return 0;
}

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

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

Think step by step.

Response:
```plaintext
5
33
66
99
1333
333333333
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
#include <bits/stdc++.h>

#define ll long long int

using namespace std;

bool solve(ll num){
    //cout << "checking " << num << "\n";
    if(num % 3 != 0)return false;
    if(num % 33 == 0)return true;
    string num_str = to_string(num);
    for(int i=0; i<num_str.size()-1 && num_str.size() != 2; ++i){
        if(num_str[i] == '3' && num_str[i+1] == '3'){
            string s = num_str;
            s.erase(i+1);
            s.erase(i);
            if(solve(stoll(s)))return true;
        }
    }
    return false;

}

int main(){
    ll t;
    cin >> t;
    while(t--){
        ll n;
        cin >> n;
        if(solve(n))cout << "YES\n";
        else cout << "NO\n";
    }
}

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

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

Think step by step.

Response:
```plaintext
3
333
3333
33333
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
def solve():
    s = int(input())

    if s == 33:
        print("NO")
        return

    if s%33 == 0:
        print("YES")
    else:
        print("NO")

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

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

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

Think step by step.

Response:
```plaintext
3
33
66
133333332
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
def test_number(n: int) -> bool:
    while '33' in str(n):
        n = int(str(n).replace('33', '', 1))

    return n % 33 == 0

def main() -> None:
    T = int(input())
    for _ in range(T):
        num = int(input())
        if test_number(num):
            print("YES")
        else:
            print("NO")

if __name__ == "__main__":
    main()

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

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

Think step by step.

Response:
```plaintext
3
3333
6666
133332
```

**Explanation:**
1. **3333**: This input tests the scenario where the number consists entirely of the digit '3'. The correct output should be "YES" because Kevin can remove the consecutive '33' pairs until the number becomes 0. However, the buggy code might get stuck in an infinite loop if it doesn't handle the replacement correctly.

2. **6666**: This input tests the scenario where the number is a multiple of 33 but does not contain the digit '3'. The correct output should be "YES" because Kevin can repeatedly subtract 33 until the number becomes 0. The buggy code might fail if it doesn't correctly handle the subtraction operation.

3. **133332**: This input tests the scenario where the number contains consecutive '33' pairs that can be removed, followed by a valid subtraction to reach 0. The correct output should be "YES" because Kevin can first remove the '33' pairs to get 12, and then subtract 33 to get 0. The buggy code might fail if it doesn't correctly handle the combination of removal and subtraction operations.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
import java.util.*;
public class Main
{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		while(t!=0)
		{
		    int x=sc.nextInt();
		    String str=String.valueOf(x);
		    int flag=0;
		    while(x>=0)
		    {
		        if(str.contains("33")) {str=str.replace("33",""); x=Integer.valueOf(str);}
		        else x=x-33;
		        if(x==0) {flag=1; break;}
		    }
		    if(flag==1) System.out.println("yes");
		    else System.out.println("no");
		    /*for(int i=1;i<str.length();i++)
		    {
		        if(str[i]=='3' && str[i-1]=='3')
		        {
		            str=str.replace()
		        }
		    }*/

		    t--;
		}
	}
}

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

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

Think step by step.

Response:
```plaintext
3
333
1333
333333333
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
import java.util.*;

public class Cf_99 {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int testCases = scanner.nextInt();
        StringBuilder output = new StringBuilder();

        while (testCases-- > 0) {
            long number = scanner.nextLong();
            if (canUnlock(number)) {
                output.append("YES\n");
            } else {
                output.append("NO\n");
            }
        }

        System.out.print(output);
    }

    public static boolean canUnlock(long number) {
        while (number >= 33) {
            if (number % 33 == 0) {
                number -= 33; // Subtract 33 if divisible
            } else {
                // Check if "33" exists as a substring
                long temp = number;
                boolean found = false;
                long factor = 1;
                while (temp > 0) {
                    if (temp % 100 == 33) { // Check last two digits
                        found = true;
                        break;
                    }
                    temp /= 10;
                    factor *= 10;
                }
                if (found) {
                    number -= (33 * factor / 100); // Remove "33" by simulating subtraction
                } else {
                    return false; // No valid moves left
                }
            }
        }

        return number == 0; // Check if reduced to zero
    }
}

**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
3333
6666
133333333
999999999
123456789
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

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

bool canUnlock(int x) {
    while (x >= 33) {
        x -= 33;
    }

    std::string xStr = std::to_string(x);
    while (xStr.find("33") != std::string::npos) {
        size_t pos = xStr.find("33");
        xStr.erase(pos, 2);
    }

    return (xStr == "0");
}

int main() {
    int t;
    std::cin >> t;
    while (t--) {
        int x;
        std::cin >> x;
        if (canUnlock(x)) {
            std::cout << "Yes" << std::endl;
        } else {
            std::cout << "No" << std::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
5
333
666
1333
1000000000
3333333333
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
#include <iostream>
#include <queue>
#include <unordered_set>
#include <string>
using namespace std;
#define ll long long

int main(){
    ios::sync_with_stdio(false);cin.tie(NULL);
    int t;cin>>t;
    while(t--){
        ll x;cin>>x;
        if(!x){cout<<"YES\n";continue;}
        queue<ll>q;unordered_set<ll>v;
        q.push(x);v.insert(x);
        bool ok=false;
        while(!q.empty()){
            ll y=q.front();q.pop();
            if(!y){ok=true;break;}
            if(y>=33){
                ll z=y-33;
                if(!z){ok=true;break;}
                if(!v.count(z)){v.insert(z);q.push(z);}
            }
            string s=to_string(y);
            for(size_t pos=s.find("33");pos!=string::npos;pos=s.find("33",pos+1)){
                string ns=s.substr(0,pos)+s.substr(pos+2);
                ll z=ns.empty()?0:stoll(ns);
                if(!z){ok=true;break;}
                if(!v.count(z)){v.insert(z);q.push(z);}
            }
            if(ok) break;
        }
        cout<<(ok?"YES\n":"NO\n");
    }
}

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

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

Think step by step.

Response:
```plaintext
3
333
1332
133333333
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
def can_unlock(x):
    while x > 0:

        if x >= 33:
            x -= 33

        else:

            str_x = str(x)

            if '33' in str_x:
                x = int(str_x.replace('33', '', 1))
            else:

                if x % 3 == 0:
                    return False
                break
    return x == 0

t = int(input())

for _ in range(t):
    x = int(input())
    if can_unlock(x):
        print("YES")
    else:
        print("NO")

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

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

Think step by step.

Response:
```plaintext
5
333
366
1333
33333
133333333
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
def can_escape(x):
    while x > 0:
        if x == 33:
            return "YES"
        elif x < 33:
            # Check for consecutive '3's in the digits
            if str(x).count('3') < 2:
                return "NO"
            # Remove consecutive '3's
            x_str = str(x)
            x_str = x_str.replace('33', '', 1)
            x = int(x_str) if x_str else 0
        else:
            x -= 33
    return "YES" if x == 0 else "NO"

def main():
    t = int(input())
    results = []
    for _ in range(t):
        x = int(input())
        results.append(can_escape(x))
    print("\n".join(results))

if __name__ == "__main__":
    main()

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

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

Think step by step.

Response:
```plaintext
5
333
3333
33333
333333
3333333
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
import java.util.Scanner;

public class CombinationLock {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt(); // Number of test cases
        StringBuilder result = new StringBuilder();

        while (t-- > 0) {
            long x = scanner.nextLong(); // Input number x for the test case

            // Check if x can be reduced to 0
            if (canUnlock(x)) {
                result.append("YES\n");
            } else {
                result.append("NO\n");
            }
        }

        // Print all results
        System.out.print(result);
    }

    private static boolean canUnlock(long x) {
        // If x >= 33, we can reduce it by subtracting 33 repeatedly.
        while (x >= 33) {
            x -= 33;
        }

        // If x < 33, check if it contains two consecutive digits '3'.
        String strX = Long.toString(x);
        return x == 0 || strX.contains("33");
    }
}

**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
333
66
1333
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Kevin and Combination Lock
time_limit_ms: 1000
memory_limit_mb: 256
Description: Kevin is trapped in Lakeside Village by Grace. At the exit of the village, there is a combination lock that can only be unlocked if Kevin solves it.

The combination lock starts with an integer $$$ x $$$. Kevin can perform one of the following two operations zero or more times:

1. If $$$ x \neq 33 $$$, he can select two consecutive digits $$$ 3 $$$ from $$$ x $$$ and remove them simultaneously. For example, if $$$ x = 13\,323 $$$, he can remove the second and third $$$ 3 $$$, changing $$$ x $$$ to $$$ 123 $$$.
2. If $$$ x \geq 33 $$$, he can change $$$ x $$$ to $$$ x - 33 $$$. For example, if $$$ x = 99 $$$, he can choose this operation to change $$$ x $$$ to $$$ 99 - 33 = 66 $$$.

When the value of $$$ x $$$ on the combination lock becomes $$$ 0 $$$, Kevin can unlock the lock and escape from Lakeside Village. Please determine whether it is possible for Kevin to unlock the combination lock and escape.

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

The only line of each test case contains a positive integer $$$x$$$ ($$$1\leq x\leq 10^9$$$).

Output: For each test case, output "YES" or "NO" (without quotes) in one line, representing whether Kevin can unlock the combination lock and escape. 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:
5
165
6369
666
114514
133333332
output:
YES
YES
NO
NO
YES

Note: For the first test case, $$$165\xrightarrow{-33}132\xrightarrow{-33}99\xrightarrow{-33}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the second test case, $$$6369\xrightarrow{-33}6{\color{red}{33}}6\xrightarrow{\text{remove "33"}}66\xrightarrow{-33}33\xrightarrow{-33}0$$$.

For the third test case, it can be proven that, regardless of the operations performed, $$$666$$$ cannot be transformed into $$$0$$$.

Buggy Code:
import java.util.Scanner;

public class KevinAndPermutation {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();
        scanner.nextLine();
        for (int i = 0; i < t; i++) {
            int a = scanner.nextInt();
            scanner.nextLine();
            boolean isValid = false;
            while (a > 0) {
                if (a % 33 == 0) {
                    isValid = true;
                    System.out.println("YES");
                    break;
                }
                a -= 33;
            }
            if (!isValid) {
                System.out.println("NO");
            }
        }
        scanner.close();
    }
}

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

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

Think step by step.

Response:
```plaintext
3
33
66
1333
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Turtle and Good Strings
time_limit_ms: 1000
memory_limit_mb: 256
Description: Turtle thinks a string $s$ is a good string if there exists a sequence of strings $t_1, t_2, \ldots, t_k$ ($k$ is an arbitrary integer) such that:

  * $k \ge 2$.    * $s = t_1 + t_2 + \ldots + t_k$, where $+$ represents the concatenation operation. For example, $\texttt{abc} = \texttt{a} + \texttt{bc}$.    * For all $1 \le i < j \le k$, the first character of $t_i$ isn't equal to the last character of $t_j$.

Turtle is given a string $s$ consisting of lowercase Latin letters. Please tell him whether the string $s$ is a good string!

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

The first line of each test case contains a single integer $n$ ($2 \le n \le 100$) — the length of the string.

The second line of each test case contains a string $s$ of length $n$, consisting of lowercase Latin letters.

Output: For each test case, output "YES" if the string $s$ is a good string, and "NO" otherwise.

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
2
aa
3
aba
4
abcb
12
abcabcabcabc
output:
No
nO
Yes
YES

Note: In the first test case, the sequence of strings $\texttt{a}, \texttt{a}$ satisfies the condition $s = t_1 + t_2 + \ldots + t_k$, but the first character of $t_1$ is equal to the last character of $t_2$. It can be seen that there doesn't exist any sequence of strings which satisfies all of the conditions, so the answer is "NO".

In the third test case, the sequence of strings $\texttt{ab}, \texttt{cb}$ satisfies all of the conditions.

In the fourth test case, the sequence of strings $\texttt{abca}, \texttt{bcab}, \texttt{cabc}$ satisfies all of the conditions.

Buggy Code:
#include <bits/stdc++.h>
#define file(s) if (fopen(s".in", "r")) freopen(s".in", "r", stdin), freopen(s".out", "w", stdout)
#define int long long
using namespace std;
const int NN=2e3+60,N=1e5+70,MOD=1e9+7,inf=1e18+7,pr1=420,K=sqrt(1e7);
int binpow (int num,int pw,int MOD1){
    if (pw==0) return 1;
    int x=binpow(num,pw/2,MOD1); x=x*x%MOD1;
    if (pw%2==1) x=x*num%MOD1;
    return x%MOD1;}
void junk(){
	int n;
	cin>>n;
	string s;
	cin>>s;
    bool check=0;
    for (int i=1;i<n-1;i++) {
        if (s[i]!=s[0] && s[i+1]!=s[n-1]) {
            check=true;
        }
	}if (check)cout<<"YES\n";
	else cout<<"NO\n";

}
signed main(/*ITS OVER ANAKIN. I HAVE A HIGH GROUND*/){//file("");
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
int Test=1;cin>>Test;
while(Test--){junk();}
/*YOU UNDERESTIMATE MY POWER*/
}

**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 where the code might fail. The buggy code checks if there exists an index `i` such that `s[i]` is not equal to `s[0]` and `s[i+1]` is not equal to `s[n-1]`. However, this logic is flawed because it doesn't correctly handle the requirement that the first character of `t_i` should not be equal to the last character of `t_j` for all `1 <= i < j <= k`.

### Steps to Generate the Test Input

1. **Edge Case: Single Character Repeated**:
   - A string with a single character repeated, such as "aa", should be a "NO" because no valid sequence `t_1, t_2, ..., t_k` can be formed.

2. **Edge Case: String with All Unique Characters**:
   - A string with all unique characters, such as "abcd", should be a "YES" because any partition will satisfy the condition.

3. **Edge Case: String with Repeating Patterns**:
   - A string like "abab" should be a "YES" because it can be partitioned as "ab" + "ab".

4. **Edge Case: String with a Single Middle Character Different**:
   - A string like "aabb" should be a "NO" because the first character of "aa" is equal to the last character of "bb".

5. **Edge Case: String with a Single Different Character in the Middle**:
   - A string like "abca" should be a "YES" because it can be partitioned as "abc" + "a".

### Chosen Test Input

Let's choose a test input that includes these edge cases to maximize the chance of exposing the bug.

```plaintext
5
2
aa
4
abcd
4
abab
4
aabb
4
abca
```

### Explanation

- **Test Case 1**: "aa" should be "NO" because no valid sequence can be formed.
- **Test Case 2**: "abcd" should be "YES" because any partition will satisfy the condition.
- **Test Case 3**: "abab" should be "YES" because it can be partitioned as "ab" + "ab".
- **Test Case 4**: "aabb" should be "NO" because the first character of "aa" is equal to the last character of "bb".
- **Test Case 5**: "abca" should be "YES" because it can be partitioned as "abc" + "a".

This test input will help identify the bug in the provided code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Turtle and Good Strings
time_limit_ms: 1000
memory_limit_mb: 256
Description: Turtle thinks a string $s$ is a good string if there exists a sequence of strings $t_1, t_2, \ldots, t_k$ ($k$ is an arbitrary integer) such that:

  * $k \ge 2$.    * $s = t_1 + t_2 + \ldots + t_k$, where $+$ represents the concatenation operation. For example, $\texttt{abc} = \texttt{a} + \texttt{bc}$.    * For all $1 \le i < j \le k$, the first character of $t_i$ isn't equal to the last character of $t_j$.

Turtle is given a string $s$ consisting of lowercase Latin letters. Please tell him whether the string $s$ is a good string!

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

The first line of each test case contains a single integer $n$ ($2 \le n \le 100$) — the length of the string.

The second line of each test case contains a string $s$ of length $n$, consisting of lowercase Latin letters.

Output: For each test case, output "YES" if the string $s$ is a good string, and "NO" otherwise.

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
2
aa
3
aba
4
abcb
12
abcabcabcabc
output:
No
nO
Yes
YES

Note: In the first test case, the sequence of strings $\texttt{a}, \texttt{a}$ satisfies the condition $s = t_1 + t_2 + \ldots + t_k$, but the first character of $t_1$ is equal to the last character of $t_2$. It can be seen that there doesn't exist any sequence of strings which satisfies all of the conditions, so the answer is "NO".

In the third test case, the sequence of strings $\texttt{ab}, \texttt{cb}$ satisfies all of the conditions.

In the fourth test case, the sequence of strings $\texttt{abca}, \texttt{bcab}, \texttt{cabc}$ satisfies all of the conditions.

Buggy Code:
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <numeric>
#include <bitset>
#include <set>
#include <map>
#include <queue>
#include <climits>
#include <cmath>

const int MOD = 1e9+7;

bool issame(std::string &str) {
	for (int i = 1; i < str.size(); i++) {
		if (str[i] != str[i-1]) return false;
	}
	return true;
}

int main() {
	std::ios_base::sync_with_stdio(false), std::cin.tie(nullptr), std::cout.tie(nullptr);
	int _; std::cin >> _; while (_--) {
		int n; std::cin >> n;
		std::string str; std::cin >> str;

		if (n < 4) {
			std::cout << "No\n";
			continue;
		}

		if (issame(str)) {
			std::cout << "No\n";
			continue;
		}

		std::cout << "Yes\n";
	}
}

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

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

Think step by step.

Response:
```plaintext
3
2
aa
4
abba
6
abcabc
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Turtle and Good Strings
time_limit_ms: 1000
memory_limit_mb: 256
Description: Turtle thinks a string $s$ is a good string if there exists a sequence of strings $t_1, t_2, \ldots, t_k$ ($k$ is an arbitrary integer) such that:

  * $k \ge 2$.    * $s = t_1 + t_2 + \ldots + t_k$, where $+$ represents the concatenation operation. For example, $\texttt{abc} = \texttt{a} + \texttt{bc}$.    * For all $1 \le i < j \le k$, the first character of $t_i$ isn't equal to the last character of $t_j$.

Turtle is given a string $s$ consisting of lowercase Latin letters. Please tell him whether the string $s$ is a good string!

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

The first line of each test case contains a single integer $n$ ($2 \le n \le 100$) — the length of the string.

The second line of each test case contains a string $s$ of length $n$, consisting of lowercase Latin letters.

Output: For each test case, output "YES" if the string $s$ is a good string, and "NO" otherwise.

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
2
aa
3
aba
4
abcb
12
abcabcabcabc
output:
No
nO
Yes
YES

Note: In the first test case, the sequence of strings $\texttt{a}, \texttt{a}$ satisfies the condition $s = t_1 + t_2 + \ldots + t_k$, but the first character of $t_1$ is equal to the last character of $t_2$. It can be seen that there doesn't exist any sequence of strings which satisfies all of the conditions, so the answer is "NO".

In the third test case, the sequence of strings $\texttt{ab}, \texttt{cb}$ satisfies all of the conditions.

In the fourth test case, the sequence of strings $\texttt{abca}, \texttt{bcab}, \texttt{cabc}$ satisfies all of the conditions.

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

void cf(){

    int n;
    cin>>n;
    string s;
    cin>>s;
    int k = 0;
    for(int i=1;i<n;i++){
        if(s[i]!=s[i-1]) k++;
    }
    if(k>2){
        cout<<"Yes"<<endl;
        return;
    }
    cout<<"No"<<endl;
}
int main(){
    int t;
    cin>>t;
    while(t--){
       cf();
    }
    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 given buggy code, we need to focus on edge cases where the code might fail. The bug in the code is that it only checks if there are more than two positions where consecutive characters are different. However, the problem requires that the string can be split into at least two substrings such that the first character of any substring is not equal to the last character of any other substring.

Here are the steps to generate a challenging test input:

1. **Edge Case with Consecutive Characters:**
   - A string where all characters are the same, such as "aaaaa". This should return "NO" because it cannot be split into valid substrings.

2. **Edge Case with Alternating Characters:**
   - A string with alternating characters, such as "ababab". This should return "YES" because it can be split into valid substrings like "ab" and "ab".

3. **Edge Case with a Single Different Character:**
   - A string like "aaba". This should return "YES" because it can be split into valid substrings like "aa" and "ba".

4. **Edge Case with a Small String:**
   - A string like "ab". This should return "NO" because it cannot be split into at least two substrings.

5. **Edge Case with a Long String:**
   - A string like "abcabcabcabc". This should return "YES" because it can be split into valid substrings like "abc", "abc", "abc", and "abc".

Based on these considerations, here is a small-scale test input that includes various edge cases:

```plaintext
5
5
aaaaa
6
ababab
4
aaba
2
ab
12
abcabcabcabc
```

This test input will help expose the bug in the given buggy code by covering different scenarios.

5
5
aaaaa
6
ababab
4
aaba
2
ab
12
abcabcabcabc


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Turtle and Good Strings
time_limit_ms: 1000
memory_limit_mb: 256
Description: Turtle thinks a string $s$ is a good string if there exists a sequence of strings $t_1, t_2, \ldots, t_k$ ($k$ is an arbitrary integer) such that:

  * $k \ge 2$.    * $s = t_1 + t_2 + \ldots + t_k$, where $+$ represents the concatenation operation. For example, $\texttt{abc} = \texttt{a} + \texttt{bc}$.    * For all $1 \le i < j \le k$, the first character of $t_i$ isn't equal to the last character of $t_j$.

Turtle is given a string $s$ consisting of lowercase Latin letters. Please tell him whether the string $s$ is a good string!

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

The first line of each test case contains a single integer $n$ ($2 \le n \le 100$) — the length of the string.

The second line of each test case contains a string $s$ of length $n$, consisting of lowercase Latin letters.

Output: For each test case, output "YES" if the string $s$ is a good string, and "NO" otherwise.

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
2
aa
3
aba
4
abcb
12
abcabcabcabc
output:
No
nO
Yes
YES

Note: In the first test case, the sequence of strings $\texttt{a}, \texttt{a}$ satisfies the condition $s = t_1 + t_2 + \ldots + t_k$, but the first character of $t_1$ is equal to the last character of $t_2$. It can be seen that there doesn't exist any sequence of strings which satisfies all of the conditions, so the answer is "NO".

In the third test case, the sequence of strings $\texttt{ab}, \texttt{cb}$ satisfies all of the conditions.

In the fourth test case, the sequence of strings $\texttt{abca}, \texttt{bcab}, \texttt{cabc}$ satisfies all of the conditions.

Buggy Code:
def solve():
    t = int(input())

    for _ in range(t):
        n = int(input())
        s = input()

        is_good = False

        # Check every possible valid subsequence split
        for i in range(n - 1):
            for j in range(i + 2, n):
                if s[i] != s[j]:
                    is_good = True
                    break
            if is_good:
                break

        if is_good:
            print("YES")
        else:
            print("NO")

# Run the solve function to process all test cases
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
4
2
ab
3
abc
4
abca
6
abacba
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Turtle and Good Strings
time_limit_ms: 1000
memory_limit_mb: 256
Description: Turtle thinks a string $s$ is a good string if there exists a sequence of strings $t_1, t_2, \ldots, t_k$ ($k$ is an arbitrary integer) such that:

  * $k \ge 2$.    * $s = t_1 + t_2 + \ldots + t_k$, where $+$ represents the concatenation operation. For example, $\texttt{abc} = \texttt{a} + \texttt{bc}$.    * For all $1 \le i < j \le k$, the first character of $t_i$ isn't equal to the last character of $t_j$.

Turtle is given a string $s$ consisting of lowercase Latin letters. Please tell him whether the string $s$ is a good string!

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

The first line of each test case contains a single integer $n$ ($2 \le n \le 100$) — the length of the string.

The second line of each test case contains a string $s$ of length $n$, consisting of lowercase Latin letters.

Output: For each test case, output "YES" if the string $s$ is a good string, and "NO" otherwise.

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
2
aa
3
aba
4
abcb
12
abcabcabcabc
output:
No
nO
Yes
YES

Note: In the first test case, the sequence of strings $\texttt{a}, \texttt{a}$ satisfies the condition $s = t_1 + t_2 + \ldots + t_k$, but the first character of $t_1$ is equal to the last character of $t_2$. It can be seen that there doesn't exist any sequence of strings which satisfies all of the conditions, so the answer is "NO".

In the third test case, the sequence of strings $\texttt{ab}, \texttt{cb}$ satisfies all of the conditions.

In the fourth test case, the sequence of strings $\texttt{abca}, \texttt{bcab}, \texttt{cabc}$ satisfies all of the conditions.

Buggy Code:
import bisect
import heapq
import sys, threading
import math
import itertools
from fractions import Fraction
from collections import Counter
# sys.setrecursionlimit(20005)
# threading.stack_size(10**7)

def read(typ):
    return [typ(x) for x in input().split()]

def solve():
    n, = read(int)
    s = input()
    head = s[0]
    tail = s[n - 1]
    if head == tail:
        print("No")
        return
    for i in range(1, n - 2):
        if s[i] != head and s[i + 1] != tail and s[i] != s[i + 1]:
            print("Yes")
            return
    print("No")

def main():
    t = 1
    t = int(input())
    for ts in range(t):
        solve()

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

if __name__ == "__main__":
    # threading.Thread(target = main).start()
    main()

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on edge cases and scenarios that are likely to cause the code to fail. The buggy code checks if the first character of the string is equal to the last character and if there exists a pair of characters that satisfy certain conditions. However, it does not correctly handle all edge cases.

### Step-by-Step Analysis:

1. **First and Last Character Check:**
   - The code checks if the first character is equal to the last character. If they are equal, it immediately returns "No".
   - This is a valid check, but it doesn't cover all cases.

2. **Internal Character Check:**
   - The code then iterates through the string to find a pair of characters that satisfy the conditions.
   - It checks if `s[i] != head`, `s[i + 1] != tail`, and `s[i] != s[i + 1]`.
   - This check is not comprehensive and can miss valid sequences.

### Challenging Test Case:
To expose the bug, we need a string where the first and last characters are different, but the internal characters do not satisfy the conditions as checked by the code.

### Example Test Case:
Consider the string "abcba". Here, the first character is 'a' and the last character is 'a', but the internal characters are 'b', 'c', and 'b'. The sequence "abc" and "ba" should satisfy the conditions, but the code might miss this.

### Test Input:
```plaintext
1
5
abcba
```

### Explanation:
- The string "abcba" has a length of 5.
- The first character is 'a' and the last character is 'a', so the code will not immediately return "No".
- The internal characters are 'b', 'c', and 'b'.
- The sequence "abc" and "ba" satisfies the conditions, but the code might not correctly identify this.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Turtle and Good Strings
time_limit_ms: 1000
memory_limit_mb: 256
Description: Turtle thinks a string $s$ is a good string if there exists a sequence of strings $t_1, t_2, \ldots, t_k$ ($k$ is an arbitrary integer) such that:

  * $k \ge 2$.    * $s = t_1 + t_2 + \ldots + t_k$, where $+$ represents the concatenation operation. For example, $\texttt{abc} = \texttt{a} + \texttt{bc}$.    * For all $1 \le i < j \le k$, the first character of $t_i$ isn't equal to the last character of $t_j$.

Turtle is given a string $s$ consisting of lowercase Latin letters. Please tell him whether the string $s$ is a good string!

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

The first line of each test case contains a single integer $n$ ($2 \le n \le 100$) — the length of the string.

The second line of each test case contains a string $s$ of length $n$, consisting of lowercase Latin letters.

Output: For each test case, output "YES" if the string $s$ is a good string, and "NO" otherwise.

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
2
aa
3
aba
4
abcb
12
abcabcabcabc
output:
No
nO
Yes
YES

Note: In the first test case, the sequence of strings $\texttt{a}, \texttt{a}$ satisfies the condition $s = t_1 + t_2 + \ldots + t_k$, but the first character of $t_1$ is equal to the last character of $t_2$. It can be seen that there doesn't exist any sequence of strings which satisfies all of the conditions, so the answer is "NO".

In the third test case, the sequence of strings $\texttt{ab}, \texttt{cb}$ satisfies all of the conditions.

In the fourth test case, the sequence of strings $\texttt{abca}, \texttt{bcab}, \texttt{cabc}$ satisfies all of the conditions.

Buggy Code:
answerpool = []
for i in range(int(input())):
    n = int(input())
    st = str(input())
    if len(st)<=3:
        if st[0] == st[len(st) -1]:
            answerpool.append('NO')
        else:
            answerpool.append('YES')
    else:
        for i in range(2,n+1):
            if n%i >=2 or n%i ==0:
                if st[i -1] !=st[:]:
                    answerpool.append('YES')
                    break
for i in answerpool:
    print(i)

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

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

Think step by step.

Response:
```plaintext
5
2
aa
3
aba
4
abcb
5
abcba
6
abcabc
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Turtle and Good Strings
time_limit_ms: 1000
memory_limit_mb: 256
Description: Turtle thinks a string $s$ is a good string if there exists a sequence of strings $t_1, t_2, \ldots, t_k$ ($k$ is an arbitrary integer) such that:

  * $k \ge 2$.    * $s = t_1 + t_2 + \ldots + t_k$, where $+$ represents the concatenation operation. For example, $\texttt{abc} = \texttt{a} + \texttt{bc}$.    * For all $1 \le i < j \le k$, the first character of $t_i$ isn't equal to the last character of $t_j$.

Turtle is given a string $s$ consisting of lowercase Latin letters. Please tell him whether the string $s$ is a good string!

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

The first line of each test case contains a single integer $n$ ($2 \le n \le 100$) — the length of the string.

The second line of each test case contains a string $s$ of length $n$, consisting of lowercase Latin letters.

Output: For each test case, output "YES" if the string $s$ is a good string, and "NO" otherwise.

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
2
aa
3
aba
4
abcb
12
abcabcabcabc
output:
No
nO
Yes
YES

Note: In the first test case, the sequence of strings $\texttt{a}, \texttt{a}$ satisfies the condition $s = t_1 + t_2 + \ldots + t_k$, but the first character of $t_1$ is equal to the last character of $t_2$. It can be seen that there doesn't exist any sequence of strings which satisfies all of the conditions, so the answer is "NO".

In the third test case, the sequence of strings $\texttt{ab}, \texttt{cb}$ satisfies all of the conditions.

In the fourth test case, the sequence of strings $\texttt{abca}, \texttt{bcab}, \texttt{cabc}$ satisfies all of the conditions.

Buggy Code:
//package codeforces;
import java.util.*;
public class contest {

    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        for(int i=0;i<t;i++){
            int n = in.nextInt();
            String s = in.next();
            if(n <= 2){
                System.out.println("NO");
                continue;
            }
            if(s.charAt(0) != s.charAt(n-1)){
                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:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on the logic of the code. The buggy code checks only if the first and last characters of the string are different to determine if the string is a good string. This is incorrect because it doesn't consider the conditions for the sequence of strings \( t_1, t_2, \ldots, t_k \) where the first character of \( t_i \) is not equal to the last character of \( t_j \) for all \( 1 \le i < j \le k \).

### Steps to Generate the Test Input:
1. **Edge Case 1: Short Strings** - Test with strings of length 2 to ensure the code handles short strings correctly.
2. **Edge Case 2: Strings with Identical First and Last Characters** - Test with strings where the first and last characters are the same, but the string can still be a good string.
3. **Edge Case 3: Strings with Different First and Last Characters** - Test with strings where the first and last characters are different, but the string cannot be a good string.
4. **Edge Case 4: Long Strings** - Test with longer strings to ensure the code handles longer inputs correctly.

### Challenging Test Input:
```plaintext
5
2
aa
3
aba
4
abcb
5
abcba
6
abcabc
```

### Explanation:
1. **Test Case 1:**
   - Input: `2 aa`
   - Expected Output: `NO`
   - Reason: The string "aa" cannot be split into two or more non-empty substrings where the first character of one substring is not equal to the last character of another.

2. **Test Case 2:**
   - Input: `3 aba`
   - Expected Output: `NO`
   - Reason: The string "aba" cannot be split into two or more non-empty substrings where the first character of one substring is not equal to the last character of another.

3. **Test Case 3:**
   - Input: `4 abcb`
   - Expected Output: `YES`
   - Reason: The string "abcb" can be split into "ab" and "cb", where the first character of "ab" (a) is not equal to the last character of "cb" (b).

4. **Test Case 4:**
   - Input: `5 abcba`
   - Expected Output: `NO`
   - Reason: The string "abcba" cannot be split into two or more non-empty substrings where the first character of one substring is not equal to the last character of another.

5. **Test Case 5:**
   - Input: `6 abcabc`
   - Expected Output: `YES`
   - Reason: The string "abcabc" can be split into "abc" and "abc", where the first character of "abc" (a) is not equal to the last character of "abc" (c).

This test input should effectively expose the bug in the provided code by including cases where the first and last characters are the same but the string can still be a good string, and cases where the first and last characters are different but the string cannot be a good string.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Turtle and Good Strings
time_limit_ms: 1000
memory_limit_mb: 256
Description: Turtle thinks a string $s$ is a good string if there exists a sequence of strings $t_1, t_2, \ldots, t_k$ ($k$ is an arbitrary integer) such that:

  * $k \ge 2$.    * $s = t_1 + t_2 + \ldots + t_k$, where $+$ represents the concatenation operation. For example, $\texttt{abc} = \texttt{a} + \texttt{bc}$.    * For all $1 \le i < j \le k$, the first character of $t_i$ isn't equal to the last character of $t_j$.

Turtle is given a string $s$ consisting of lowercase Latin letters. Please tell him whether the string $s$ is a good string!

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

The first line of each test case contains a single integer $n$ ($2 \le n \le 100$) — the length of the string.

The second line of each test case contains a string $s$ of length $n$, consisting of lowercase Latin letters.

Output: For each test case, output "YES" if the string $s$ is a good string, and "NO" otherwise.

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
2
aa
3
aba
4
abcb
12
abcabcabcabc
output:
No
nO
Yes
YES

Note: In the first test case, the sequence of strings $\texttt{a}, \texttt{a}$ satisfies the condition $s = t_1 + t_2 + \ldots + t_k$, but the first character of $t_1$ is equal to the last character of $t_2$. It can be seen that there doesn't exist any sequence of strings which satisfies all of the conditions, so the answer is "NO".

In the third test case, the sequence of strings $\texttt{ab}, \texttt{cb}$ satisfies all of the conditions.

In the fourth test case, the sequence of strings $\texttt{abca}, \texttt{bcab}, \texttt{cabc}$ satisfies all of the conditions.

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

public class Main {
    private static final FastIO sc = new FastIO();

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

    static void solve() {
       int n=sc.nextInt();
       String s=sc.next();
      int i=0,f=0;
       for(i=1;i<n-1;i++)
       {
            if(s.charAt(i)!=s.charAt(0) && s.charAt(i+1)!=s.charAt(n-1))
            {
                f=1;
                break;
            }
       }
       if(f==1)
       System.out.println("YES");
       else
       System.out.println("NO");
    }
}

class FastIO extends PrintWriter {
    private BufferedReader br;
    private StringTokenizer st;

    public FastIO() {
        this(System.in, System.out);
    }

    public FastIO(InputStream in, OutputStream out) {
        super(out);
        br = new BufferedReader(new InputStreamReader(in));
    }

    public FastIO(String input, String output) throws FileNotFoundException {
        super(output);
        br = new BufferedReader(new FileReader(input));
    }

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

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

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

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

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

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

Think step by step.

Response:
```plaintext
3
2
ab
3
aba
4
abca
```