**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Update Queries
time_limit_ms: 2000
memory_limit_mb: 256
Description: Let's consider the following simple problem. You are given a string $s$ of length $n$, consisting of lowercase Latin letters, as well as an array of indices $ind$ of length $m$ ($1 \leq ind_i \leq n$) and a string $c$ of length $m$, consisting of lowercase Latin letters. Then, in order, you perform the update operations, namely, during the $i$-th operation, you set $s_{ind_i} = c_i$. Note that you perform all $m$ operations from the first to the last.

Of course, if you change the order of indices in the array $ind$ and/or the order of letters in the string $c$, you can get different results. Find the lexicographically smallest string $s$ that can be obtained after $m$ update operations, if you can rearrange the indices in the array $ind$ and the letters in the string $c$ as you like.

A string $a$ is lexicographically less than a string $b$ if and only if one of the following conditions is met:

  * $a$ is a prefix of $b$, but $a \neq b$;   * in the first position where $a$ and $b$ differ, the symbol in string $a$ is earlier in the alphabet than the corresponding symbol in string $b$.

Input: Each test consists of several sets of input data. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of sets of input data. Then follows their description.

The first line of each set of input data contains two integers $n$ and $m$ ($1 \leq n, m \leq 10^5$) — the length of the string $s$ and the number of updates.

The second line of each set of input data contains a string $s$ of length $n$, consisting of lowercase Latin letters.

The third line of each set of input data contains $m$ integers $ind_1, ind_2, \ldots, ind_m$ ($1 \leq ind_i \leq n$) — the array of indices $ind$.

The fourth line of each set of input data contains a string $c$ of length $m$, consisting of lowercase Latin letters.

It is guaranteed that the sum of $n$ over all sets of input data does not exceed $2 \cdot 10^5$. Similarly, the sum of $m$ over all sets of input data does not exceed $2 \cdot 10^5$.

Output: For each set of input data, output the lexicographically smallest string $s$ that can be obtained by rearranging the indices in the array $ind$ and the letters in the string $c$ as you like.

Examples:
input:
4
1 2
a
1 1
cb
4 4
meow
1 2 1 4
zcwz
7 4
abacaba
1 3 5 7
damn
7 10
traktor
7 6 5 4 3 2 1 6 4 2
codeforces
output:
b
cwoz
abdcmbn
ccdeefo

Note: In the first set of input data, you can leave the array $ind$ and the string $c$ unchanged and simply perform all operations in that order.

In the second set of input data, you can set the array $ind = [1, 1, 4, 2]$ and $c =$ "zczw". Then the string $s$ will change as follows: $meow \rightarrow zeow \rightarrow ceow \rightarrow ceoz \rightarrow cwoz$.

In the third set of input data, you can leave the array $ind$ unchanged and set $c = $ "admn". Then the string $s$ will change as follows: $abacaba \rightarrow abacaba \rightarrow abdcaba \rightarrow abdcmba \rightarrow abdcmbn$.

Buggy Code:
def sort_string(s):
    chars = list(s)
    n = len(chars)
    for i in range(n):
        for j in range(0, n-i-1):
            if chars[j] > chars[j+1]:
                chars[j], chars[j+1] = chars[j+1], chars[j]
    return ''.join(chars)
t = int(input())
for i in range(t):
    list1=list(map(int, input().strip().split()))
    b=input()
    list2=list(map(int, input().strip().split()))
    c=input()
    d =sort_string(c)
    k=0
    for o in range(1,len(b)+1):
        if o in list2:
            print(d[k],end="")
            k+=1
        else:
            print(b[o-1],end="")
    print('\n',end='')

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

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

Think step by step.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Update Queries
time_limit_ms: 2000
memory_limit_mb: 256
Description: Let's consider the following simple problem. You are given a string $s$ of length $n$, consisting of lowercase Latin letters, as well as an array of indices $ind$ of length $m$ ($1 \leq ind_i \leq n$) and a string $c$ of length $m$, consisting of lowercase Latin letters. Then, in order, you perform the update operations, namely, during the $i$-th operation, you set $s_{ind_i} = c_i$. Note that you perform all $m$ operations from the first to the last.

Of course, if you change the order of indices in the array $ind$ and/or the order of letters in the string $c$, you can get different results. Find the lexicographically smallest string $s$ that can be obtained after $m$ update operations, if you can rearrange the indices in the array $ind$ and the letters in the string $c$ as you like.

A string $a$ is lexicographically less than a string $b$ if and only if one of the following conditions is met:

  * $a$ is a prefix of $b$, but $a \neq b$;   * in the first position where $a$ and $b$ differ, the symbol in string $a$ is earlier in the alphabet than the corresponding symbol in string $b$.

Input: Each test consists of several sets of input data. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of sets of input data. Then follows their description.

The first line of each set of input data contains two integers $n$ and $m$ ($1 \leq n, m \leq 10^5$) — the length of the string $s$ and the number of updates.

The second line of each set of input data contains a string $s$ of length $n$, consisting of lowercase Latin letters.

The third line of each set of input data contains $m$ integers $ind_1, ind_2, \ldots, ind_m$ ($1 \leq ind_i \leq n$) — the array of indices $ind$.

The fourth line of each set of input data contains a string $c$ of length $m$, consisting of lowercase Latin letters.

It is guaranteed that the sum of $n$ over all sets of input data does not exceed $2 \cdot 10^5$. Similarly, the sum of $m$ over all sets of input data does not exceed $2 \cdot 10^5$.

Output: For each set of input data, output the lexicographically smallest string $s$ that can be obtained by rearranging the indices in the array $ind$ and the letters in the string $c$ as you like.

Examples:
input:
4
1 2
a
1 1
cb
4 4
meow
1 2 1 4
zcwz
7 4
abacaba
1 3 5 7
damn
7 10
traktor
7 6 5 4 3 2 1 6 4 2
codeforces
output:
b
cwoz
abdcmbn
ccdeefo

Note: In the first set of input data, you can leave the array $ind$ and the string $c$ unchanged and simply perform all operations in that order.

In the second set of input data, you can set the array $ind = [1, 1, 4, 2]$ and $c =$ "zczw". Then the string $s$ will change as follows: $meow \rightarrow zeow \rightarrow ceow \rightarrow ceoz \rightarrow cwoz$.

In the third set of input data, you can leave the array $ind$ unchanged and set $c = $ "admn". Then the string $s$ will change as follows: $abacaba \rightarrow abacaba \rightarrow abdcaba \rightarrow abdcmba \rightarrow abdcmbn$.

Buggy Code:
for _ in range(int(input())):
    x,y=map(int, input().split())
    a=list(input())
    ind=sorted(list(map(int, input().split())))
    b=sorted(list(input()))
    ind.append(-1)
    for i in range(y):
        if ind[i]==ind[i+1]:
            b=[*b[:i],b[-1],*b[i:-1]]
            b=list(b)
    for i in range(y):
        a[ind[i]-1]=b[i]
    print(''.join(a))

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

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

Think step by step.

Response:
```plaintext
2
5 3
abcde
1 2 2
xyz
5 5
abcde
1 2 2 3 3
wxyzq
```

2
5 3
abcde
1 2 2
xyz
5 5
abcde
1 2 2 3 3
wxyzq


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Update Queries
time_limit_ms: 2000
memory_limit_mb: 256
Description: Let's consider the following simple problem. You are given a string $s$ of length $n$, consisting of lowercase Latin letters, as well as an array of indices $ind$ of length $m$ ($1 \leq ind_i \leq n$) and a string $c$ of length $m$, consisting of lowercase Latin letters. Then, in order, you perform the update operations, namely, during the $i$-th operation, you set $s_{ind_i} = c_i$. Note that you perform all $m$ operations from the first to the last.

Of course, if you change the order of indices in the array $ind$ and/or the order of letters in the string $c$, you can get different results. Find the lexicographically smallest string $s$ that can be obtained after $m$ update operations, if you can rearrange the indices in the array $ind$ and the letters in the string $c$ as you like.

A string $a$ is lexicographically less than a string $b$ if and only if one of the following conditions is met:

  * $a$ is a prefix of $b$, but $a \neq b$;   * in the first position where $a$ and $b$ differ, the symbol in string $a$ is earlier in the alphabet than the corresponding symbol in string $b$.

Input: Each test consists of several sets of input data. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of sets of input data. Then follows their description.

The first line of each set of input data contains two integers $n$ and $m$ ($1 \leq n, m \leq 10^5$) — the length of the string $s$ and the number of updates.

The second line of each set of input data contains a string $s$ of length $n$, consisting of lowercase Latin letters.

The third line of each set of input data contains $m$ integers $ind_1, ind_2, \ldots, ind_m$ ($1 \leq ind_i \leq n$) — the array of indices $ind$.

The fourth line of each set of input data contains a string $c$ of length $m$, consisting of lowercase Latin letters.

It is guaranteed that the sum of $n$ over all sets of input data does not exceed $2 \cdot 10^5$. Similarly, the sum of $m$ over all sets of input data does not exceed $2 \cdot 10^5$.

Output: For each set of input data, output the lexicographically smallest string $s$ that can be obtained by rearranging the indices in the array $ind$ and the letters in the string $c$ as you like.

Examples:
input:
4
1 2
a
1 1
cb
4 4
meow
1 2 1 4
zcwz
7 4
abacaba
1 3 5 7
damn
7 10
traktor
7 6 5 4 3 2 1 6 4 2
codeforces
output:
b
cwoz
abdcmbn
ccdeefo

Note: In the first set of input data, you can leave the array $ind$ and the string $c$ unchanged and simply perform all operations in that order.

In the second set of input data, you can set the array $ind = [1, 1, 4, 2]$ and $c =$ "zczw". Then the string $s$ will change as follows: $meow \rightarrow zeow \rightarrow ceow \rightarrow ceoz \rightarrow cwoz$.

In the third set of input data, you can leave the array $ind$ unchanged and set $c = $ "admn". Then the string $s$ will change as follows: $abacaba \rightarrow abacaba \rightarrow abdcaba \rightarrow abdcmba \rightarrow abdcmbn$.

Buggy Code:
for t in range(int(input())):
    n,m=map(int, input().split())
    s=list(input())
    ind=list(map(int, input().split()))
    c=list(input())
    ind.sort()

    find=[]
    x=sorted(c)
    for i in ind:
        if i not in find:
            find.append(i)

    d=len(ind)-len(find)
    fc=x[:len(x)-d]

    i=0
    for j in find:
        s[j-1]=fc[i]
        i+=1

    print(''.join(s))

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

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

Think step by step.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Update Queries
time_limit_ms: 2000
memory_limit_mb: 256
Description: Let's consider the following simple problem. You are given a string $s$ of length $n$, consisting of lowercase Latin letters, as well as an array of indices $ind$ of length $m$ ($1 \leq ind_i \leq n$) and a string $c$ of length $m$, consisting of lowercase Latin letters. Then, in order, you perform the update operations, namely, during the $i$-th operation, you set $s_{ind_i} = c_i$. Note that you perform all $m$ operations from the first to the last.

Of course, if you change the order of indices in the array $ind$ and/or the order of letters in the string $c$, you can get different results. Find the lexicographically smallest string $s$ that can be obtained after $m$ update operations, if you can rearrange the indices in the array $ind$ and the letters in the string $c$ as you like.

A string $a$ is lexicographically less than a string $b$ if and only if one of the following conditions is met:

  * $a$ is a prefix of $b$, but $a \neq b$;   * in the first position where $a$ and $b$ differ, the symbol in string $a$ is earlier in the alphabet than the corresponding symbol in string $b$.

Input: Each test consists of several sets of input data. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of sets of input data. Then follows their description.

The first line of each set of input data contains two integers $n$ and $m$ ($1 \leq n, m \leq 10^5$) — the length of the string $s$ and the number of updates.

The second line of each set of input data contains a string $s$ of length $n$, consisting of lowercase Latin letters.

The third line of each set of input data contains $m$ integers $ind_1, ind_2, \ldots, ind_m$ ($1 \leq ind_i \leq n$) — the array of indices $ind$.

The fourth line of each set of input data contains a string $c$ of length $m$, consisting of lowercase Latin letters.

It is guaranteed that the sum of $n$ over all sets of input data does not exceed $2 \cdot 10^5$. Similarly, the sum of $m$ over all sets of input data does not exceed $2 \cdot 10^5$.

Output: For each set of input data, output the lexicographically smallest string $s$ that can be obtained by rearranging the indices in the array $ind$ and the letters in the string $c$ as you like.

Examples:
input:
4
1 2
a
1 1
cb
4 4
meow
1 2 1 4
zcwz
7 4
abacaba
1 3 5 7
damn
7 10
traktor
7 6 5 4 3 2 1 6 4 2
codeforces
output:
b
cwoz
abdcmbn
ccdeefo

Note: In the first set of input data, you can leave the array $ind$ and the string $c$ unchanged and simply perform all operations in that order.

In the second set of input data, you can set the array $ind = [1, 1, 4, 2]$ and $c =$ "zczw". Then the string $s$ will change as follows: $meow \rightarrow zeow \rightarrow ceow \rightarrow ceoz \rightarrow cwoz$.

In the third set of input data, you can leave the array $ind$ unchanged and set $c = $ "admn". Then the string $s$ will change as follows: $abacaba \rightarrow abacaba \rightarrow abdcaba \rightarrow abdcmba \rightarrow abdcmbn$.

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

int main() {
    int t;
    cin >> t;
    while (t--) {
        int n, m;
        cin >> n >> m;
        string s, c;
        cin >> s;
        multiset<int> ind_mst;
        for (int i = 0; i < m; ++i) {
            int a;
            cin >> a;
            ind_mst.insert(a - 1);
        }
        cin >> c;
        sort(c.begin(), c.end());
        int index = 0;
        /*
        multiset<char> char_mst;
        for (int i = 0; i < m; ++i) {
            char_mst.insert(c[i]);
        }
        */
        for (int i = 0; i < m; ++i) {
            if (ind_mst.count(*ind_mst.begin()) <= 1) {
                //char_mst.erase(prev(char_mst.end()));
                s[*ind_mst.begin()] = c[index];
                index++;
            }
            ind_mst.erase(ind_mst.begin());
        }
        cout << s << endl;
    }
}

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

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

Think step by step.

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

### Explanation:
1. **Test Case Description**:
   - **t = 1**: Only one set of input data.
   - **n = 5**: The length of the string `s` is 5.
   - **m = 5**: The number of update operations is 5.
   - **s = "abcde"**: The initial string.
   - **ind = [1, 2, 3, 4, 5]**: The indices for the update operations.
   - **c = "edcba"**: The string of characters to be used for the update operations.

2. **Expected Output**:
   - The lexicographically smallest string that can be obtained by rearranging the indices in `ind` and the characters in `c` is "abcde".

3. **Rationale**:
   - The buggy code has a logical error in how it handles the update operations. Specifically, it only updates the string `s` when the count of the smallest index in the multiset `ind_mst` is 1, which is not the correct approach.
   - By providing a test case where the indices and characters are already in a way that should result in the original string, we can expose the bug in the code. The correct approach should be to sort the characters in `c` and update the string `s` in the smallest possible positions to achieve the lexicographically smallest result.
   - In this test case, the correct output should be "abcde", but the buggy code might produce a different result due to its incorrect logic.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Update Queries
time_limit_ms: 2000
memory_limit_mb: 256
Description: Let's consider the following simple problem. You are given a string $s$ of length $n$, consisting of lowercase Latin letters, as well as an array of indices $ind$ of length $m$ ($1 \leq ind_i \leq n$) and a string $c$ of length $m$, consisting of lowercase Latin letters. Then, in order, you perform the update operations, namely, during the $i$-th operation, you set $s_{ind_i} = c_i$. Note that you perform all $m$ operations from the first to the last.

Of course, if you change the order of indices in the array $ind$ and/or the order of letters in the string $c$, you can get different results. Find the lexicographically smallest string $s$ that can be obtained after $m$ update operations, if you can rearrange the indices in the array $ind$ and the letters in the string $c$ as you like.

A string $a$ is lexicographically less than a string $b$ if and only if one of the following conditions is met:

  * $a$ is a prefix of $b$, but $a \neq b$;   * in the first position where $a$ and $b$ differ, the symbol in string $a$ is earlier in the alphabet than the corresponding symbol in string $b$.

Input: Each test consists of several sets of input data. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of sets of input data. Then follows their description.

The first line of each set of input data contains two integers $n$ and $m$ ($1 \leq n, m \leq 10^5$) — the length of the string $s$ and the number of updates.

The second line of each set of input data contains a string $s$ of length $n$, consisting of lowercase Latin letters.

The third line of each set of input data contains $m$ integers $ind_1, ind_2, \ldots, ind_m$ ($1 \leq ind_i \leq n$) — the array of indices $ind$.

The fourth line of each set of input data contains a string $c$ of length $m$, consisting of lowercase Latin letters.

It is guaranteed that the sum of $n$ over all sets of input data does not exceed $2 \cdot 10^5$. Similarly, the sum of $m$ over all sets of input data does not exceed $2 \cdot 10^5$.

Output: For each set of input data, output the lexicographically smallest string $s$ that can be obtained by rearranging the indices in the array $ind$ and the letters in the string $c$ as you like.

Examples:
input:
4
1 2
a
1 1
cb
4 4
meow
1 2 1 4
zcwz
7 4
abacaba
1 3 5 7
damn
7 10
traktor
7 6 5 4 3 2 1 6 4 2
codeforces
output:
b
cwoz
abdcmbn
ccdeefo

Note: In the first set of input data, you can leave the array $ind$ and the string $c$ unchanged and simply perform all operations in that order.

In the second set of input data, you can set the array $ind = [1, 1, 4, 2]$ and $c =$ "zczw". Then the string $s$ will change as follows: $meow \rightarrow zeow \rightarrow ceow \rightarrow ceoz \rightarrow cwoz$.

In the third set of input data, you can leave the array $ind$ unchanged and set $c = $ "admn". Then the string $s$ will change as follows: $abacaba \rightarrow abacaba \rightarrow abdcaba \rightarrow abdcmba \rightarrow abdcmbn$.

Buggy Code:
#include<iostream>
#include<queue>
#include<algorithm>
using namespace std;
char a[100010] = {}, b[100010] = {};
int in[100010] = {};
int n, m;
int t;
int main()
{
	int t;
	cin >> t;
	while (t--)
	{

		cin >> n >> m;
		cin >> a;
		for (int i = 1; i <= m; i++)
		{
			cin >> in[i];
		}
		cin >> b;
		sort(in + 1, in + 1 + m);
		sort(b, b + m);
		for (int i = 1; i <= m - 1; i++)
		{
			if (in[i] == in[i + 1])
			{
				for (int i2 = i; i2 <= m - 1; i2++)
				{
					in[i2] = in[i2 + 1];
				}
				b[m - 1] = '\0';
				m--;
				i--;

			}

		}

		for (int i = 1; i <= m; i++)
		{
			if (in[i] >= 0)
			{
				a[in[i] - 1] = b[i - 1];
			}
		}

		puts(a);

	}
}

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

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

Think step by step.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Update Queries
time_limit_ms: 2000
memory_limit_mb: 256
Description: Let's consider the following simple problem. You are given a string $s$ of length $n$, consisting of lowercase Latin letters, as well as an array of indices $ind$ of length $m$ ($1 \leq ind_i \leq n$) and a string $c$ of length $m$, consisting of lowercase Latin letters. Then, in order, you perform the update operations, namely, during the $i$-th operation, you set $s_{ind_i} = c_i$. Note that you perform all $m$ operations from the first to the last.

Of course, if you change the order of indices in the array $ind$ and/or the order of letters in the string $c$, you can get different results. Find the lexicographically smallest string $s$ that can be obtained after $m$ update operations, if you can rearrange the indices in the array $ind$ and the letters in the string $c$ as you like.

A string $a$ is lexicographically less than a string $b$ if and only if one of the following conditions is met:

  * $a$ is a prefix of $b$, but $a \neq b$;   * in the first position where $a$ and $b$ differ, the symbol in string $a$ is earlier in the alphabet than the corresponding symbol in string $b$.

Input: Each test consists of several sets of input data. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of sets of input data. Then follows their description.

The first line of each set of input data contains two integers $n$ and $m$ ($1 \leq n, m \leq 10^5$) — the length of the string $s$ and the number of updates.

The second line of each set of input data contains a string $s$ of length $n$, consisting of lowercase Latin letters.

The third line of each set of input data contains $m$ integers $ind_1, ind_2, \ldots, ind_m$ ($1 \leq ind_i \leq n$) — the array of indices $ind$.

The fourth line of each set of input data contains a string $c$ of length $m$, consisting of lowercase Latin letters.

It is guaranteed that the sum of $n$ over all sets of input data does not exceed $2 \cdot 10^5$. Similarly, the sum of $m$ over all sets of input data does not exceed $2 \cdot 10^5$.

Output: For each set of input data, output the lexicographically smallest string $s$ that can be obtained by rearranging the indices in the array $ind$ and the letters in the string $c$ as you like.

Examples:
input:
4
1 2
a
1 1
cb
4 4
meow
1 2 1 4
zcwz
7 4
abacaba
1 3 5 7
damn
7 10
traktor
7 6 5 4 3 2 1 6 4 2
codeforces
output:
b
cwoz
abdcmbn
ccdeefo

Note: In the first set of input data, you can leave the array $ind$ and the string $c$ unchanged and simply perform all operations in that order.

In the second set of input data, you can set the array $ind = [1, 1, 4, 2]$ and $c =$ "zczw". Then the string $s$ will change as follows: $meow \rightarrow zeow \rightarrow ceow \rightarrow ceoz \rightarrow cwoz$.

In the third set of input data, you can leave the array $ind$ unchanged and set $c = $ "admn". Then the string $s$ will change as follows: $abacaba \rightarrow abacaba \rightarrow abdcaba \rightarrow abdcmba \rightarrow abdcmbn$.

Buggy Code:
def shift(c):
    c.insert(0, c.pop())

def solve():
    n, m = map(int, input().split())
    s = list(input())
    ind = sorted(map(int, input().split()))
    c = sorted(input())

    k = set()
    for i in range(m):
        i1 = ind[i]-1

        if i1 in k:
            s[i1] = min(s[i1], c[i])
            shift(c)
        else:
            s[i1] = c[i]

        k.add(i1)

    print(*s, sep="")

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

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

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

Think step by step.

Response:
```plaintext
2
5 5
abcde
1 2 3 4 5
edcba
6 6
abcdef
1 2 3 4 5 6
fedcba
```

2
5 5
abcde
1 2 3 4 5
edcba
6 6
abcdef
1 2 3 4 5 6
fedcba


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Update Queries
time_limit_ms: 2000
memory_limit_mb: 256
Description: Let's consider the following simple problem. You are given a string $s$ of length $n$, consisting of lowercase Latin letters, as well as an array of indices $ind$ of length $m$ ($1 \leq ind_i \leq n$) and a string $c$ of length $m$, consisting of lowercase Latin letters. Then, in order, you perform the update operations, namely, during the $i$-th operation, you set $s_{ind_i} = c_i$. Note that you perform all $m$ operations from the first to the last.

Of course, if you change the order of indices in the array $ind$ and/or the order of letters in the string $c$, you can get different results. Find the lexicographically smallest string $s$ that can be obtained after $m$ update operations, if you can rearrange the indices in the array $ind$ and the letters in the string $c$ as you like.

A string $a$ is lexicographically less than a string $b$ if and only if one of the following conditions is met:

  * $a$ is a prefix of $b$, but $a \neq b$;   * in the first position where $a$ and $b$ differ, the symbol in string $a$ is earlier in the alphabet than the corresponding symbol in string $b$.

Input: Each test consists of several sets of input data. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of sets of input data. Then follows their description.

The first line of each set of input data contains two integers $n$ and $m$ ($1 \leq n, m \leq 10^5$) — the length of the string $s$ and the number of updates.

The second line of each set of input data contains a string $s$ of length $n$, consisting of lowercase Latin letters.

The third line of each set of input data contains $m$ integers $ind_1, ind_2, \ldots, ind_m$ ($1 \leq ind_i \leq n$) — the array of indices $ind$.

The fourth line of each set of input data contains a string $c$ of length $m$, consisting of lowercase Latin letters.

It is guaranteed that the sum of $n$ over all sets of input data does not exceed $2 \cdot 10^5$. Similarly, the sum of $m$ over all sets of input data does not exceed $2 \cdot 10^5$.

Output: For each set of input data, output the lexicographically smallest string $s$ that can be obtained by rearranging the indices in the array $ind$ and the letters in the string $c$ as you like.

Examples:
input:
4
1 2
a
1 1
cb
4 4
meow
1 2 1 4
zcwz
7 4
abacaba
1 3 5 7
damn
7 10
traktor
7 6 5 4 3 2 1 6 4 2
codeforces
output:
b
cwoz
abdcmbn
ccdeefo

Note: In the first set of input data, you can leave the array $ind$ and the string $c$ unchanged and simply perform all operations in that order.

In the second set of input data, you can set the array $ind = [1, 1, 4, 2]$ and $c =$ "zczw". Then the string $s$ will change as follows: $meow \rightarrow zeow \rightarrow ceow \rightarrow ceoz \rightarrow cwoz$.

In the third set of input data, you can leave the array $ind$ unchanged and set $c = $ "admn". Then the string $s$ will change as follows: $abacaba \rightarrow abacaba \rightarrow abdcaba \rightarrow abdcmba \rightarrow abdcmbn$.

Buggy Code:
import java.util.Arrays;
import java.util.Collection;
import java.util.HashSet;
import java.util.Scanner;
import java.util.TreeSet;

public class Solution2 {

    public static String sortString(String inputString)
    {
        char tempArray[] = inputString.toCharArray();

        Arrays.sort(tempArray);

        return new String(tempArray);
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int t = sc.nextInt();

        while(t-- > 0)
        {
            int len = sc.nextInt();
            int arr_len = sc.nextInt();

            String str = sc.next();

            int[] arr = new int[arr_len];

            for(int i = 0; i < arr_len; i++)
            {
                arr[i] = sc.nextInt();
            }

            String characters = sc.next();

            // put arrays into treeset
            TreeSet<Integer> treeSet = new TreeSet<>();

            for(int i = 0; i < arr_len; i++)
            {
                treeSet.add(arr[i]);
            }

            // sort the characters string in lexicographically order
            characters = sortString(characters);

            // replace character to lexicographically minimum character of chracters string in the str string at index of treeSet
            int k = 0;
            for(int i : treeSet)
            {
                char c = characters.charAt(k++);

                if(i == 1)
                {
                    str = c + str.substring(1);
                }
                else if(i == len)
                {
                    str = str.substring(0, len-1) + c;
                }
                else
                {
                    str = str.substring(0, i-1) + c + str.substring(i);
                }
            }

            System.out.println(str);
        }
    }
}

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

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

Think step by step.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Update Queries
time_limit_ms: 2000
memory_limit_mb: 256
Description: Let's consider the following simple problem. You are given a string $s$ of length $n$, consisting of lowercase Latin letters, as well as an array of indices $ind$ of length $m$ ($1 \leq ind_i \leq n$) and a string $c$ of length $m$, consisting of lowercase Latin letters. Then, in order, you perform the update operations, namely, during the $i$-th operation, you set $s_{ind_i} = c_i$. Note that you perform all $m$ operations from the first to the last.

Of course, if you change the order of indices in the array $ind$ and/or the order of letters in the string $c$, you can get different results. Find the lexicographically smallest string $s$ that can be obtained after $m$ update operations, if you can rearrange the indices in the array $ind$ and the letters in the string $c$ as you like.

A string $a$ is lexicographically less than a string $b$ if and only if one of the following conditions is met:

  * $a$ is a prefix of $b$, but $a \neq b$;   * in the first position where $a$ and $b$ differ, the symbol in string $a$ is earlier in the alphabet than the corresponding symbol in string $b$.

Input: Each test consists of several sets of input data. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of sets of input data. Then follows their description.

The first line of each set of input data contains two integers $n$ and $m$ ($1 \leq n, m \leq 10^5$) — the length of the string $s$ and the number of updates.

The second line of each set of input data contains a string $s$ of length $n$, consisting of lowercase Latin letters.

The third line of each set of input data contains $m$ integers $ind_1, ind_2, \ldots, ind_m$ ($1 \leq ind_i \leq n$) — the array of indices $ind$.

The fourth line of each set of input data contains a string $c$ of length $m$, consisting of lowercase Latin letters.

It is guaranteed that the sum of $n$ over all sets of input data does not exceed $2 \cdot 10^5$. Similarly, the sum of $m$ over all sets of input data does not exceed $2 \cdot 10^5$.

Output: For each set of input data, output the lexicographically smallest string $s$ that can be obtained by rearranging the indices in the array $ind$ and the letters in the string $c$ as you like.

Examples:
input:
4
1 2
a
1 1
cb
4 4
meow
1 2 1 4
zcwz
7 4
abacaba
1 3 5 7
damn
7 10
traktor
7 6 5 4 3 2 1 6 4 2
codeforces
output:
b
cwoz
abdcmbn
ccdeefo

Note: In the first set of input data, you can leave the array $ind$ and the string $c$ unchanged and simply perform all operations in that order.

In the second set of input data, you can set the array $ind = [1, 1, 4, 2]$ and $c =$ "zczw". Then the string $s$ will change as follows: $meow \rightarrow zeow \rightarrow ceow \rightarrow ceoz \rightarrow cwoz$.

In the third set of input data, you can leave the array $ind$ unchanged and set $c = $ "admn". Then the string $s$ will change as follows: $abacaba \rightarrow abacaba \rightarrow abdcaba \rightarrow abdcmba \rightarrow abdcmbn$.

Buggy Code:
import java.util.*;

public class problem3 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();

        while (t-- > 0) {
            int n = sc.nextInt();
            int m = sc.nextInt();
            sc.nextLine();
            String s = sc.nextLine();
            int[] ind = new int[m];
            for (int i = 0; i < m; i++) {
                ind[i] = sc.nextInt();
            }
            sc.nextLine();
            String c = sc.nextLine();

            solve(n, m, s, ind, c);
        }
        sc.close();
    }

    public static void solve(int n, int m, String s, int[] ind, String c) {
        Set<Integer> st = new TreeSet<>();
        for (int i : ind) {
            st.add(i);
        }

        char[] cChars = c.toCharArray();
        Arrays.sort(cChars);
        String sortedT = new String(cChars);

        int j = 0;
        for (int i : st) {
            if (j < sortedT.length()) {
                s = s.substring(0, i - 1) + sortedT.charAt(j) + s.substring(i);
                j++;
            }
        }
        System.out.println(s);
    }

}

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

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

Think step by step.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

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

int main() {
    int t;
    cin >> t;
    while (t--) {
        int n;
        cin>>n;
        vector<int> con(n);
        bool allZero = true, hasMiddleZero = false;
        for (int i=0; i<n; i++) {
            cin >> con[i];
            if (con[i]!=0) {
                allZero = false;
            }
            if (con[i]==0 && i>0 && i<n - 1) {
                hasMiddleZero = true;
            }
        }
        if(allZero) {
            cout<<0<<endl;
        }else if(hasMiddleZero) {
            cout<<2<<endl;
        }else{
            cout<<1<<endl;
        }
    }
    return 0;
}

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

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

Think step by step.

Response:
```plaintext
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
5
1 2 3 4 5
```

This test input includes a variety of cases to challenge the buggy code:

1. **Case with a single non-zero element**: This case is straightforward and should work correctly with the buggy code.
2. **Case with all zeros**: This case is also straightforward and should work correctly.
3. **Case with a mix of zeros and non-zeros**: This case is designed to test the logic for handling zeros in the middle of the array.
4. **Case with a sequence of consecutive integers**: This case is designed to test the logic for handling a subarray where the MEX can be calculated correctly.
5. **Case with large numbers**: This case is designed to test the logic for handling large numbers and ensuring the MEX calculation is correct.
6. **Case with a mix of zeros and large numbers**: This case is designed to test the logic for handling a mix of zeros and large numbers.
7. **Case with a single zero**: This case is straightforward and should work correctly.
8. **Case with a small array**: This case is straightforward and should work correctly.
9. **Case with a sequence of consecutive integers starting from 1**: This case is designed to test the logic for handling a subarray where the MEX is 0.
10. **Case with a sequence of consecutive integers starting from 1 and ending with a non-zero number**: This case is designed to test the logic for handling a subarray where the MEX is 0.

The last case, `5 1 2 3 4 5`, is particularly challenging because it should require only one operation to convert the entire array to zeros, but the buggy code might incorrectly output 2 due to the presence of zeros in the middle of the array.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

Buggy Code:
#include<iostream>

using namespace std;

int main(){
    // problem: https://codeforces.com/contest/2049/problem/A
    int t;
    cin >> t;
    while(t--){
        int n;
        cin >> n;
        int arr[n];
        for(int i = 0; i < n; i++){
            cin >> arr[i];
        }

        // if there is only one element in the array
        // if((n == 1 && arr[0] == 0) || (n == 2 && arr[0] == 0 && arr[1] == 0)){
        //     cout << 0 << endl;
        //     continue;
        // }
        // else if(n == 1 && arr[0] != 0) {
        //     cout << 1 << endl;
        //     continue;
        // }

        // find the number of zeros in the array
        int count = 0;
        for(int i = 0; i < n; i++){
            if(arr[i] == 0){
                count++;
            }
        }

        if(n == count) {
            cout << 0 << endl;
        }
        else if(count > 2) {
            cout << 2 << endl;
        }
        else if(count == 2) {
            if(arr[0] == 0 && arr[n-1] == 0)
                cout << 1 << endl;
            else
                cout << 2 << endl;
        }
        else if(count == 1) {
            if(arr[0] == 0 || arr[n-1] == 0)
                cout << 1 << endl;
            else
                cout << 2 << endl;
        }
        else {
            cout << 1 << endl;
        }

    }

    return 0 ;
}

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

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

Think step by step.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

Buggy Code:
#include<iostream>

using namespace std;

int a[501];

int main()
{
	int n;
	cin >> n;
	for (int x = 0; x < n; x++)
	{
		int  y;//测试样例
		cin >> y;
		for (int i = 0; i < y; i++)
		{
			cin >> a[i];
		}
		int temp = 0, TEMP = 0;
		for (int m = 0; m < y; m++)
		{
			if (a[m] != 0) { TEMP++; }
		}
		for (int j = 0; j < y; j++)
		{
			if (a[j] == 0) { temp++; }
		}
		if (TEMP == y) { cout << "1" << endl; continue; }
		if (temp == y) { cout << "0" << endl; continue; }

		int biao = 0;//0表示中间没0，1表示中间有0
		for (int i1 = 1; i1 < y-1; i1++)
		{
			if (a[i1] == 0) { biao = 1; break; }
		}

		if (biao == 0) { cout << "1"<<endl; continue; }
		if (biao == 1) { cout << "2"<<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:
To generate a challenging test input that exposes the bug in the provided code, we need to consider the following:

1. **Edge Cases**: Test cases where the array contains a mix of zeros and non-zeros in specific patterns that the code might not handle correctly.
2. **Boundary Conditions**: Test cases with the smallest and largest possible input sizes.
3. **Special Patterns**: Test cases with specific patterns that might cause the code to fail, such as arrays with all zeros, arrays with all non-zeros, and arrays with zeros in the middle.

Let's break down the test input:

1. **All Zeros**: This is a simple case where the array contains only zeros.
2. **All Non-Zeros**: This is a simple case where the array contains only non-zeros.
3. **Zeros in the Middle**: This is a more complex case where the array has zeros in the middle.
4. **Zeros at the Ends**: This is a case where the array has zeros at the ends but non-zeros in the middle.
5. **Mixed Values**: This is a case where the array has a mix of zeros and non-zeros in a more random pattern.

Here is a small-scale test input that includes these cases:

```plaintext
5
5
0 0 0 0 0
5
1 2 3 4 5
5
1 0 2 0 3
5
0 1 2 3 0
5
0 1 2 3 4
```

Explanation:
1. **First Test Case**: All zeros. Expected output: 0.
2. **Second Test Case**: All non-zeros. Expected output: 1.
3. **Third Test Case**: Zeros in the middle. Expected output: 2.
4. **Fourth Test Case**: Zeros at the ends. Expected output: 2.
5. **Fifth Test Case**: Mixed values. Expected output: 2.

This test input should help expose the bug in the provided code, particularly in how it handles arrays with zeros in the middle and mixed values.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

Buggy Code:
ct = int(input())

for w in range(ct):
    l = int(input())

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

    if sum(v) == 0:
        print(0)

    elif 0 not in v:
        print(1)

    else:
        if v[0] > 0:

            c = 1
        else:
            c = 0

        for i in range(len(v)):
            if i > 0:
                if (v[i] == 0 and v[i-1] > 0) and sum(v[i:]) > 0:
                    c +=1

        if c > 1:
            print(2)
        else:
            print(1)

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

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

Think step by step.

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

1. **Cases where the array already contains only zeros**: The code correctly handles this case.
2. **Cases where the array does not contain any zeros**: The code correctly handles this case.
3. **Cases where the array contains zeros but the logic for counting operations is incorrect**: This is where the code might fail.

The buggy code has a specific issue with how it counts the number of operations needed when there are zeros in the array. It seems to incorrectly count the number of transitions from a positive number to zero and from zero to a positive number.

Let's construct a test case that will expose this issue:

- An array with a pattern that alternates between positive numbers and zeros, but in a way that should require more than 2 operations to convert all elements to zero.

Here's a test case that should expose the bug:

```plaintext
1
10
1 0 1 0 1 0 1 0 1 0
```

Explanation:
- The array `[1, 0, 1, 0, 1, 0, 1, 0, 1, 0]` alternates between 1 and 0.
- The correct number of operations needed to convert this array to all zeros is 5, because each subarray of `[1, 0]` needs to be replaced with 0, and there are 5 such subarrays.
- The buggy code, however, will incorrectly count the number of operations as 2, which is not correct.

This test case should help 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: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

Buggy Code:
def main():
    t = int(input())
    for case in range(t):
        n = int(input())
        arr = []
        arr = list(map(int, input().split()))
        if max(arr) == 0:
            print(0)
            continue
        flag = False
        for i in range(1, len(arr)-1):
            if arr[i] == 0:
                flag2 = False
                for j in range(i+1, len(arr)):
                    if arr[j]!=0:
                        flag = True
                        flag2 = True
                        break
                if flag2:
                    break
        if flag is False:
            print(1)
        else:
            print(2)

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
4
0 1 2 0
5
1 0 1 0 2
6
0 1 2 3 4 0
7
0 0 1 2 3 0 0
8
1 0 1 0 1 2 3 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

Buggy Code:
import java.util.*;
public class cf994a {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for (int i = 0; i < t; i++) {
            int n = sc.nextInt();
            int a[]= new int[n];
            int f=0,s=0;
            for (int j = 0; j < n; j++) {
                a[j] = sc.nextInt();
                s=s+a[j];
            }
            for (int j = 1; j < n-1; j++) {
                if(a[j]==0){
                    f=2;
                    break;
                }
            }
            if (s==0){
                f=0;
            }
            else if (f==0){
                f=1;
            }
            System.out.println(f);
        }
    }
}

**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
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
```

This test input is designed to cover a variety of edge cases and typical scenarios to ensure the buggy code is thoroughly tested. The cases include arrays that are already all zeros, arrays with a single element, and arrays with mixed values that require multiple operations to convert to all zeros. The goal is to expose the issues in the buggy code, particularly the incorrect handling of subarray operations and the `mex` function.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

Buggy Code:
import java.util.*;
public class MEXDestruction {
    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();
            int[] arr = new int[n];
            int cnt=0;
            for(int j=0;j<n;j++){
                arr[j] = in.nextInt();
                if(arr[j]==0){
                    cnt++;
                }
            }
            if(arr.length==1 && arr[0]==0){
                System.out.println(0);
            }else if(cnt==0){
                System.out.println(1);
            }
            else if(cnt==1){
                if(arr[0]==0 || arr[n-1]==0){
                    System.out.println(1);
                }else{
                    System.out.println(2);
                }
            }else if(cnt==n){
                System.out.println(0);
            }else if(cnt==2){
                if(arr[0]==0 && arr[n-1]==0){
                    System.out.println(1);
                }else{
                    System.out.println(2);
                }
            }else{
                System.out.println(2);
            }
        }
    }
}

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

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

Think step by step.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

Buggy Code:
#include<iostream>
using namespace std;
int main(){
	int t;
	cin>>t;
	while(t--){
		int n;
		cin>>n;
		int a[n+5];
		int fl0=0,fl1=0;
		for(int i=1;i<=n;i++){
			cin>>a[i];
			if(a[i]==0) fl0=1;
			else fl1=1;
		}
		if(fl0&&!fl1){
			printf("0\n");
		}
		else if(!fl0&&fl1){
			printf("1\n");
		}
		else if(fl0&&fl1){
			int flag=0;
			for(int i=1;i<=n;i++){
				if(i!=1&&i!=n&&a[i]==0&&a[i+1]!=0&&a[i-1]!=0) flag=1;
			}
			if(flag) printf("2\n");
			else printf("1\n");
		}
	}

	return 0;
}

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

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

Think step by step.

Response:
```plaintext
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
```

This test input includes a variety of cases to ensure the code is thoroughly tested:

1. A case where a single operation can reduce the array to zeros (e.g., `0 1 2 3`).
2. A case where the array is already all zeros (e.g., `0 0 0 0 0 0`).
3. A case where multiple operations are needed (e.g., `1 0 1 0 1`).
4. A case with a large range of numbers (e.g., `9 100 0 89 12 2 3`).
5. A case where the array has a mix of zeros and non-zeros, but can be reduced in one operation (e.g., `3 2 1 0`).
6. A case with a mix of zeros and non-zeros, requiring two operations (e.g., `0 7 0 2 0 7 0`).
7. A case with a single element (e.g., `0`).
8. A case with two elements, one of which is zero (e.g., `0 1`).

These cases should help expose any issues in the buggy code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

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

using namespace std;
using namespace __gnu_pbds;

typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pbds; // find_by_order, order_of_key
#define int long long
#define pii pair<int,int>
#define ll long long
#define endl '\n'
const int MOD = 1e9+7;

void solve()
{
    int n; cin>>n;
    vector<int> v(n);
    int cnt=0;
    for(int i=0;i<n;i++){
        cin>>v[i];
        if(v[i]==0){
            cnt++;
        }
    }

    if(cnt==n){
        cout<<0<<endl;
        return;
    }else if(cnt==0){
        cout<<1<<endl;
        return;
    }

    for(int i=1;i<n-1;i++){
        if(v[i]==0 and v[i-1]!=0 and v[i+1]!=0){
            cout<<2<<endl;
            return;
        }
    }
    cnt=0;
    for(int i=1;i<(n-1);i++){
        if(v[i]!=0 and v[i-1]==0 and v[i+1]==0){
            cnt++;
        }
    }

    if(cnt>1){
        cout<<2<<endl;
    }else{

    cout<<1<<endl;
    }

}
int32_t main()
{

    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);

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

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on scenarios that are not correctly handled by the current logic. The buggy code has several issues, including:

1. Incorrect handling of subarrays with more than one zero.
2. Incorrect handling of subarrays with multiple non-zero elements.
3. Incorrect logic for determining the minimum number of operations.

Let's consider a test case that maximizes the failure probability:

- A test case where the array has a mix of zeros and non-zero elements, but the current logic incorrectly determines the number of operations.

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

```plaintext
3
5
1 0 1 0 1
5
1 2 0 2 1
5
0 1 2 1 0
```

Explanation:
1. **Test Case 1: [1, 0, 1, 0, 1]**
   - The current logic might incorrectly determine that this requires 2 operations, but it actually requires 1 operation (replace the entire subarray with its MEX, which is 2, and then replace 2 with 0).
2. **Test Case 2: [1, 2, 0, 2, 1]**
   - The current logic might incorrectly determine that this requires 2 operations, but it actually requires 1 operation (replace the entire subarray with its MEX, which is 0).
3. **Test Case 3: [0, 1, 2, 1, 0]**
   - The current logic might incorrectly determine that this requires 1 operation, but it actually requires 2 operations (replace the subarray [1, 2, 1] with its MEX, which is 0, and then replace the remaining non-zero elements with 0).

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

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

int main(){
	int t;
	cin >> t;
	while(t--){
		int n;
		cin >> n;
		vector<int>v(n);
		int zero_cnt = 0;
		for(int i=0 ; i<n ; i++){
			cin >> v[i];
			if(v[i] == 0) zero_cnt++;
		}
		if(zero_cnt == v.size()){
			cout << 0 << endl;
			continue;
		}
		if(zero_cnt == 0){
			cout << 1 << endl;
			continue;
		}
		int x = 0;
		int NoOfSubarray = 0;
		for(int i=0 ; i<n ; i++){
			if(v[i] != 0){
				x++;
			}
			if(x == 1){
				NoOfSubarray++;
			}
			if(v[i] == 0){
				x = 0;
			}
		}
		if(NoOfSubarray == 1){
			cout << 1 << endl;
		}
		else{
			cout << 2 << endl;
		}
	}
}

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

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

Think step by step.

Response:
```plaintext
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
5
1 2 3 4 5
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

Buggy Code:
def code(num):
    for i in range(num):
        len = int(input())
        inp = input()
        lst = [int(n) for n in inp.split(" ")]
        count = 0
        for i in range(len):
            if lst[i] == 0:
                count += 1
        if count == len:
            print(0)
        elif count == 0:
            print(1)
        elif lst[0] == 0:
            if lst[len-1] == 0:
                if count > 2:
                    print(2)
                else:
                    print(1)
            elif count > 1:
                print(2)
            else:
                print(1)
        elif lst[len-1] == 0:
            if count > 1:
                print(2)
            else:
                print(1)
        else:
            print(2)

code(int(input()))

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

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

Think step by step.

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


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

Buggy Code:
mod = 1000000007

test_cases = int(input())
for _ in range(test_cases):
    size = int(input())
    arr = list(map(int, input().split()))
    zero_count = arr.count(0)

    if zero_count == size:
        print(0)
    else:
        if zero_count == 1 and (arr[0] == 0 or arr[-1] == 0):
            print(1)
        elif zero_count == 2 and (arr[0] == 0 and arr[-1] == 0):
            print(1)
        elif zero_count == 0:
            print(1)
        else:
            print(2)

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

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

Think step by step.

Response:
```plaintext
3
5
1 0 1 0 1
4
0 3 9 0
7
0 7 0 2 0 7 0
```


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

Buggy Code:
import java.util.*;
public class A {
    public static void main(String[] args) {
      Scanner sc=new Scanner(System.in);
      int cases=sc.nextInt();
      while(cases-->0){
       int n=sc.nextInt();
       int[] arr=new int[n];
       int count=0;
       for(int i=0;i<n;i++){
        arr[i]=sc.nextInt();
        if(arr[i]==0){
          count++;
        }
       }
       if(count==n){
        System.out.println(0);
       }else if(count==0||check(arr)){
        System.out.println(1);
       }else{
        if(arr[0]==0&&count==1||arr[n-1]==0&&count==1||(arr[0]==0&&arr[n-1]==0&&count==2)){
          System.out.println(1);
        }else{
          System.out.println(2);
        }
       }

      }
      sc.close();

    }
    public static boolean check(int[] arr) {

      // Extract meaningful non-zero numbers for sequence validation
      int previous = -1;

      for (int num : arr) {
          if (num != 0) {
              if (previous != -1 && Math.abs(num - previous) != 1) {
                  return false; // Sequence is broken
              }
              previous = num; // Update the last valid non-zero number
          }
      }

      return true;
  }

}

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on edge cases where the code's logic might fail. The key areas to consider are:

1. **Arrays with only zeros**: The code correctly handles these cases.
2. **Arrays with a single non-zero element**: The code should handle these correctly.
3. **Arrays where the non-zero elements are not consecutive and the `check` function might fail**: The `check` function checks if the non-zero elements form a sequence where the difference between consecutive elements is 1. We need to create a case where this check fails but the minimum number of operations is still 1.
4. **Arrays with a specific pattern of zeros and non-zeros that might confuse the logic**.

Let's construct a test case that fits the third scenario:

```plaintext
1
5
0 2 0 1 0
```

Explanation:
- The array is `[0, 2, 0, 1, 0]`.
- The non-zero elements are `2` and `1`, which are not consecutive.
- The `check` function will return `false` because `2` and `1` are not consecutive.
- However, the correct answer is `1` because we can choose the subarray `[2, 0, 1]` and replace it with `0`, resulting in the array `[0, 0, 0, 0]`.

This test case should expose the bug in the `check` function and the logic that follows it.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: MEX Destruction
time_limit_ms: 1000
memory_limit_mb: 256
Description: Evirir the dragon snuck into a wizard's castle and found a mysterious contraption, and their playful instincts caused them to play with (destroy) it...

Evirir the dragon found an array $$$a_1, a_2, \ldots, a_n$$$ of $$$n$$$ non-negative integers.

In one operation, they can choose a non-empty subarray$$$^{\text{∗}}$$$ $$$b$$$ of $$$a$$$ and replace it with the integer $$$\operatorname{mex}(b)$$$$$$^{\text{†}}$$$. They want to use this operation any number of times to make $$$a$$$ only contain zeros. It can be proven that this is always possible under the problem constraints.

What is the minimum number of operations needed?

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 50$$$), the length of $$$a$$$.

The second line of each test case contains $$$n$$$ space-separated integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 100$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$500$$$.

Output: For each test case, output a single integer on a line, the minimum number of operations needed to make $$$a$$$ contain only zeros.

Examples:
input:
10
4
0 1 2 3
6
0 0 0 0 0 0
5
1 0 1 0 1
5
3 1 4 1 5
4
3 2 1 0
7
9 100 0 89 12 2 3
4
0 3 9 0
7
0 7 0 2 0 7 0
1
0
2
0 1
output:
1
0
2
1
1
2
1
2
0
1

Note: In the first test case, Evirir can choose the subarray $$$b = [1, 2, 3]$$$ and replace it with $$$\operatorname{mex}(1, 2, 3) = 0$$$, changing $$$a$$$ from $$$[0, \underline{1, 2, 3}]$$$ to $$$[0, 0]$$$ (where the chosen subarray is underlined). Therefore, the answer is $$$1$$$.

In the second test case, $$$a$$$ already contains only $$$0$$$s, so no operation is needed.

In the third test case, Evirir can change $$$a$$$ as follows: $$$[1, \underline{0, 1, 0, 1}] \to [\underline{1, 2}] \to [0]$$$. Here, $$$\operatorname{mex}(0, 1, 0, 1) = 2$$$ and $$$\operatorname{mex}(1, 2) = 0$$$.

In the fourth test case, Evirir can choose $$$b$$$ to be the entire array $$$a$$$, changing $$$a$$$ from $$$[\underline{3, 1, 4, 1, 5}]$$$ to $$$[0]$$$.

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

public class A_MEX_Destruction {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

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

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

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

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

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

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

    static FastReader vt = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        try {
            int testCases = vt.nextInt();
            // int testCases = 1;
            while (testCases-- > 0) {
                // write code here
                solve();
            }
            out.flush();
        } catch (Exception e) {
            return;
        }
    }

    static void solve() {
        int n = vt.nextInt();
        int[] ar = new int[n];
        for (int i = 0; i < n; i++) {
            ar[i] = vt.nextInt();
        }
        int id = -1;
        int left = 0;
        int right = 0;
        for (int i = 0; i < n; i++) {
            if (ar[i] == 0 && left > 0) {
                id = i;
                break;
            } else if (ar[i] > 0) {
                left++;
            }
        }
        if (id == -1 && left != 0) {
            out.println(1);
            return;
        }
        int l = 0;
        int r = 0;
        for (int i = 0; i < id; i++) {
            if (ar[i] > 0) {
                l++;
                break;
            }
        }
        for (int i = n - 1; i > id; i--) {
            if (ar[i] > 0) {
                r++;
            } else {
                right++;
            }
        }
        if (l == 0 && r == 0) {
            out.println(0);
        } else if (l == 0 || r == 0) {
            if (right > 0) {
                out.println(2);
                return;
            }
            out.println(1);
        } else {
            out.println(2);
        }
    }
}

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

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

Think step by step.

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