**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
#include <iostream>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>

void solve()
{
	int n; std::cin >> n;
	std::string s, r; std::cin >> s;
	std::unordered_set<char> hs;
	for(char c: s)
	{
		if(!hs.count(c)) r += c;
		hs.insert(c);
	}

	std::sort(r.begin(), r.end());

	std::unordered_map<char, char> mp;
	for(int i = 0, j = r.size()-1; i < n; i ++, j -- )
		mp[r[i]] = r[j];

	for(int c: s)
		std::cout << mp[c];

	std::cout << '\n';
}

int main()
{
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);

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

	return 0;
}

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on edge cases and scenarios that can cause the code to fail. Here are the steps to identify such cases:

1. **Empty or Single Character Strings**: These edge cases can often reveal issues in initialization or boundary conditions.
2. **Strings with Repeated Characters**: These can expose issues in how the code handles character mappings.
3. **Strings with All Unique Characters**: These can test the symmetry and ordering of the mappings.
4. **Strings with Characters in Reverse Alphabetical Order**: These can test the sorting and mapping logic.

Given the constraints and the nature of the problem, let's create a test input that includes these edge cases:

### Test Input
```plaintext
5
1
a
3
aaa
3
abc
3
cba
6
abcabc
```

### Explanation
1. **Single Character String**:
   - `s = "a"`: This tests the simplest case where the string has only one character.
2. **String with Repeated Characters**:
   - `s = "aaa"`: This tests the case where all characters are the same, which should result in the same output.
3. **String with All Unique Characters**:
   - `s = "abc"`: This tests the case where all characters are unique and should be symmetrically mapped.
4. **String with Characters in Reverse Alphabetical Order**:
   - `s = "cba"`: This tests the case where the characters are in reverse alphabetical order, which should also be symmetrically mapped.
5. **String with Repeated and Unique Characters**:
   - `s = "abcabc"`: This tests a more complex case with repeated and unique characters.

This test input will help identify issues in the buggy code, particularly in how it handles character mappings and edge cases.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

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

#define fir first
#define sec second
#define endl "\n"

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef pair<ll, ll> pll;
const int N = 1e5 + 10, M = N * 2, mod = 1e9 + 7, inf = 0x3f3f3f3f, P = 131;

void solve()
{
    int n;
    cin >> n;
    string s;
    cin >> s;

    vector<int> cnt(26, 0);
    for(int i = 0; i < s.size(); i ++)
        cnt[s[i] - 'a'] ++;

    map<char, char> mp;
    for(int i = 0, j = 25; i < 25; i ++)
        if(cnt[i])
        {
            while(!cnt[j])
                j --;

            mp[i + 'a'] = j + 'a';
            j --;
            if(j < 0)
                j = 25;
        }

    for(int i = 0; i < s.size(); i ++)
        cout << mp[s[i]];
    cout << endl;
}

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

    int t = 1;
    cin >> t;
    while(t --)
        solve();

    return 0;
}

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

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

Think step by step.

Response:
To expose the bug in the given code, we need to focus on edge cases that might cause the algorithm to fail. The key points to consider are:

1. **Empty or Single Character Strings**: These are edge cases where the logic might break due to the lack of multiple distinct characters.
2. **Strings with All Distinct Characters**: This can test the symmetric replacement logic.
3. **Strings with Repeated Characters**: This can test the handling of multiple occurrences of the same character.
4. **Strings with Characters in Alphabetical Order**: This can test the correct formation of the auxiliary string \( r \).

Let's create a small-scale test input that includes these edge cases:

1. **Single Character String**: This should test how the code handles a string with only one character.
2. **String with All Distinct Characters**: This should test the symmetric replacement logic.
3. **String with Repeated Characters**: This should test the handling of multiple occurrences of the same character.
4. **String with Characters in Alphabetical Order**: This should test the correct formation of the auxiliary string \( r \).

Here is the test input:

```plaintext
4
1
a
5
abcde
6
aabbcc
3
abc
```

Explanation:
1. **Test Case 1**: A single character string "a". The expected output should be "a".
2. **Test Case 2**: A string with all distinct characters "abcde". The expected output should be "edcba".
3. **Test Case 3**: A string with repeated characters "aabbcc". The expected output should be "ccbbaa".
4. **Test Case 4**: A string with characters in alphabetical order "abc". The expected output should be "cba".

This test input should help identify any issues in the given buggy code, particularly in handling edge cases and the symmetric replacement logic.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
#include <iostream>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <map>
using namespace std;
const int N = 1e6;
typedef pair<int, int> PII;
PII a[N];
int main()
{
    int t;
    scanf("%d", &t);
    while(t--)
    {
        int n;
        scanf("%d", &n);
        string s;
        cin >> s;
        map<char,bool>st;
        map<char,char>mp;
        for(int i = 0 ;i<s.length();i++)
        {
            st[s[i]]=true;
        }
        auto p = st.end();
        p--;
        auto q = st.begin();
        while(q!=p)
        {
            mp[q->first]=p->first;
            mp[p->first]=q->first;
            ++q,--p;
        }
        mp[p->first]=q->first;
        for(int i =0 ;i<n;i++)
        {
            cout << mp[s[i]];
        }
        puts("");
    }
}

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

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

Think step by step.

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

1. **Understand the Bug**: The buggy code has a potential issue with the way it maps characters in the symmetric encoding. Specifically, the code may not correctly handle the middle character in strings with an odd number of distinct characters.

2. **Focus on Edge Cases**:
   - **Single Character**: A string with a single character.
   - **Two Characters**: A string with two distinct characters.
   - **Odd Number of Distinct Characters**: A string with an odd number of distinct characters.
   - **Even Number of Distinct Characters**: A string with an even number of distinct characters.

3. **Generate Test Input**:
   - **Single Character**: This should be straightforward.
   - **Two Characters**: This should also be straightforward.
   - **Odd Number of Distinct Characters**: This is a critical case to test the middle character mapping.
   - **Even Number of Distinct Characters**: This should be straightforward as well.

Let's create a small-scale test input that includes these cases:

```plaintext
4
1
a
2
ab
3
abc
4
abcd
```

This test input includes:
- A single character string "a".
- A two-character string "ab".
- A three-character string "abc" (odd number of distinct characters).
- A four-character string "abcd" (even number of distinct characters).

These cases should help expose any issues with the symmetric encoding and decoding process 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: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
for _ in range(int(input())):
    n = int(input())
    s = input()
    arr = set()
    dict1 = {}
    ans = ''
    for i in range(n):
        arr.add(s[i])
    arr = list(arr)
    arr.sort()
    for i in range(1,n//2+2):
        dict1[arr[i-1]] = arr[-i]
        dict1[arr[-i]] = arr[i-1]
    for i in s:
        ans += dict1[i]
    print(ans)

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the given buggy code, we need to focus on edge cases and scenarios that might cause the code to fail. Here are the key points to consider:

1. **Empty or Single Character Strings**: The code should handle these cases correctly.
2. **Strings with Repeated Characters**: The code should correctly handle strings where some characters are repeated.
3. **Strings with All Unique Characters**: The code should handle strings where all characters are unique.
4. **Strings with Characters Not in the Alphabetical Order**: The code should handle strings where the characters are not in alphabetical order.
5. **Strings with Characters Not Present in the Original String**: The code should handle cases where the input string contains characters that were not present in the original string.

Given these points, let's construct a test input that covers these scenarios:

```plaintext
5
1
a
3
aaa
5
abcde
7
abcdeba
11
aabbccddeff
```

Explanation:
- The first test case (`1 a`) checks the handling of a single character string.
- The second test case (`3 aaa`) checks the handling of a string with repeated characters.
- The third test case (`5 abcde`) checks the handling of a string with all unique characters.
- The fourth test case (`7 abcdeba`) checks the handling of a string where the characters are not in alphabetical order.
- The fifth test case (`11 aabbccddeff`) checks the handling of a string with repeated characters and a mix of unique and repeated characters.

This test input should help expose any issues in the buggy code.

5
1
a
3
aaa
5
abcde
7
abcdeba
11
aabbccddeff


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
def solve():
    n = int(input())
    b = list(input())
    uniq = sorted(list(set(b)))
    ans = []
    hmap = {}
    for i in range((n//2)):
        hmap[uniq[i]] = uniq[len(uniq)-1-i]
        hmap[uniq[len(uniq)-1-i]] = uniq[i]

    if len(uniq)%2 !=0:
        hmap[uniq[len(uniq)//2 ]] = uniq[len(uniq)//2 ]

    for c in b:
        ans.append(hmap[c])
    print("".join(ans))

def test():
    t = int(input())
    for i in range(t):
        solve()

# solve()
test()

**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 edge cases and scenarios:

1. **Single Character String**: This tests the simplest case where the string has only one unique character.
2. **String with All Unique Characters**: This tests the case where all characters in the string are unique.
3. **String with Repeated Characters**: This tests the case where some characters are repeated.
4. **String with Symmetric Characters**: This tests the case where the string has characters that are symmetric in the auxiliary string.
5. **String with Odd and Even Lengths**: This tests the case where the length of the string is both odd and even.

Let's construct a test input that includes these scenarios:

```plaintext
5
1
a
3
abc
5
aabbcc
7
abacaba
8
abcabcde
```

### Explanation:
1. **Test Case 1**:
   - `n = 1`
   - `b = "a"`
   - This tests the single character string case. The expected output is `"a"`.

2. **Test Case 2**:
   - `n = 3`
   - `b = "abc"`
   - This tests the string with all unique characters. The expected output is `"cba"`.

3. **Test Case 3**:
   - `n = 5`
   - `b = "aabbcc"`
   - This tests the string with repeated characters. The expected output is `"ccbbcc"`.

4. **Test Case 4**:
   - `n = 7`
   - `b = "abacaba"`
   - This tests the string with symmetric characters. The expected output is `"abacaba"`.

5. **Test Case 5**:
   - `n = 8`
   - `b = "abcabcde"`
   - This tests the string with odd and even lengths. The expected output is `"edcbabcd"`.

These test cases should help expose any issues in the buggy code, particularly in how it handles different lengths and character distributions.

5
1
a
3
abc
5
aabbcc
7
abacaba
8
abcabcde


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
import sys

t=int(sys.stdin.readline().strip())
for i in range(t):
    l=int(sys.stdin.readline().strip())
    si=sys.stdin.readline().strip()
    if l == 1:
        print(si)
    else:
        nov=set()
        for j in si:
            nov.add(ord(j))
        nov=list(nov)
        li=len(nov)
        dic=dict()
        if li % 2 == 0:
            for k in range(li//2):
                dic[nov[k]]=chr(nov[li-k-1])
                dic[nov[li-k-1]]=chr(nov[k])
        else:
            for k in range((li-1)//2):
                dic[nov[k]]=chr(nov[li-k-1])
                dic[nov[li-k-1]]=chr(nov[k])
            dic[nov[(li-1)//2]]=chr(nov[(li-1)//2])
        for k in si:
            print(dic[ord(k)],end='')
        print()

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

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

Think step by step.

Response:
To create a challenging test input that exposes the bug in the given buggy code, we need to focus on edge cases and scenarios that are likely to cause issues. Here are the steps to identify and construct such a test input:

1. **Single Character String**: This is already handled correctly in the buggy code, so it's not a good candidate for exposing the bug.

2. **Strings with All Unique Characters**: This is a good candidate because the buggy code might have issues with the symmetry when all characters are unique.

3. **Strings with Repeated Characters**: The buggy code might have issues if the same character appears multiple times in the string.

4. **Strings with Odd and Even Lengths**: The buggy code might handle these cases differently, so both should be tested.

5. **Strings with Characters in Alphabetical Order**: This can help verify if the code correctly handles the symmetric replacement.

6. **Strings with Characters in Reverse Alphabetical Order**: This can also help verify the symmetric replacement logic.

Based on these considerations, let's construct a small-scale test input that includes these edge cases:

```plaintext
6
5
abcde
5
edcba
5
aabbcc
5
ccbbba
5
abcba
5
abcde
```

### Explanation:
1. **abcde**: All unique characters in alphabetical order.
2. **edcba**: All unique characters in reverse alphabetical order.
3. **aabbcc**: Repeated characters with even length.
4. **ccbbba**: Repeated characters with odd length.
5. **abcba**: Symmetric string with odd length.
6. **abcde**: Repeated for consistency and to ensure the code handles repeated test cases correctly.

This test input should help expose any issues in the buggy code, particularly with handling unique characters and repeated characters.

6
5
abcde
5
edcba
5
aabbcc
5
ccbbba
5
abcba
5
abcde


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
import java.util.*;

public class Main {
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        while(n-- > 0){
            int count = scan.nextInt();
            StringBuilder str = new StringBuilder(scan.next());
            int[] a = new int[26];
            for (int i = 0; i < count; i++) {
                int t = str.charAt(i) - 'a';
                if(a[t] == 0){
                    a[t] = 1;
                }
            }

            int t1 = 0,t2 = a.length-1;
            while(t1 < t2){
                while(a[t1] == 0) t1++;
                while(a[t2] == 0) t2--;
                a[t1] = t2;
                a[t2] = t1++;
                t2--;
            }

            for (int i = 0; i < count; i++) {
                str.replace(i,i,""+(char)(a[str.charAt(i)-'a']+'a'));
                str.deleteCharAt(i+1);
            }
            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:
To generate a challenging test input that exposes the bug in the provided buggy code, let's consider the following steps:

1. **Understand the Bug**: The buggy code has a logical error in the way it handles the symmetric replacement. Specifically, the code incorrectly updates the array `a` and the string `str` during the replacement process.

2. **Edge Cases**:
   - **Single Character String**: A string with a single character.
   - **String with All Unique Characters**: A string where all characters are unique.
   - **String with Repeated Characters**: A string where characters are repeated.
   - **String with All Identical Characters**: A string where all characters are the same.

3. **Challenging Input**:
   - **Single Character String**: This should be straightforward and should work correctly.
   - **String with All Unique Characters**: This should test the symmetric replacement logic.
   - **String with Repeated Characters**: This should test the consistency of the replacement.
   - **String with All Identical Characters**: This should test the edge case where the symmetric replacement should be trivial.

Given these considerations, let's create a small-scale test input that includes these edge cases:

```plaintext
4
1
a
3
abc
6
abccba
3
aaa
```

This input includes:
- A single character string "a".
- A string with all unique characters "abc".
- A string with repeated characters "abccba".
- A string with all identical characters "aaa".

This should help in exposing the bug in the buggy code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
import java.util.*;

public class main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    int myInt = scanner.nextInt();
    scanner.nextLine();
    for (int i = 0; i < myInt; i++) {
      int n = scanner.nextInt();
      char[] s = new char[n];
      char[] new_s = new char[n];
      String sc = scanner.next();
      for (int j = 0; j < n; j++) {
        char c = sc.charAt(j);
        s[j] = c;
        new_s[j] = c;
      }
      // System.out.println("s: " + Arrays.toString(s));
      // System.out.println("new s: " + Arrays.toString(new_s));
      if (n == 1) {
        System.out.println(s[0]);
      } else {
        Arrays.sort(s);
        HashMap<Character, Character> hm = new HashMap<>();
        int l = 0, r = n - 1;
        while (l < r) {
          // System.out.println("while: " + s[l] + "--" + s[r]);
          while (l > 0 && s[l] == s[l - 1]) {
            l++;
          }
          while (r < n - 1 && s[r] == s[r + 1]) {
            r--;
          }
          // System.out.println(s[l] + " / " + s[r]);
          hm.put(s[r], s[l]);
          hm.put(s[l], s[r]);
          l++;
          r--;
        }
        if (n % 2 == 1) {
          int p = (n / 2);
          if (!hm.containsValue(s[p])) {
            hm.put(s[p], s[p]);
          }
        }
        // System.out.println("sorted s: " + Arrays.toString(s));
        // System.out.println("new s: " + Arrays.toString(new_s));
        // System.out.println(hm);

        for (int j = 0; j < n; j++) {
          new_s[j] = hm.get(new_s[j]);
        }
        // System.out.print("RESULT: ");
        System.out.println(new_s);
      }
    }
    scanner.close();
  }
}

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on edge cases and scenarios that could maximize the failure probability. Here are the steps to consider:

1. **Single Character Strings**: Test cases where the input string has only one character. The code should handle this case correctly by outputting the same character.

2. **Strings with Repeated Characters**: Test cases where the input string has repeated characters. The code should handle this case correctly by ensuring that the mapping is consistent.

3. **Strings with All Unique Characters**: Test cases where the input string has all unique characters. The code should handle this case correctly by performing the symmetric encoding and decoding.

4. **Strings with Specific Patterns**: Test cases where the input string has specific patterns that could expose issues in the logic, such as strings with alternating characters or strings that are already symmetrically encoded.

5. **Maximum Length Strings**: Test cases where the input string is at the maximum length (200,000 characters) to ensure the code handles large inputs efficiently.

Given the constraints, we will generate a small-scale test input that includes a mix of these cases to ensure the code is thoroughly tested.

Here is the test input:

```plaintext
5
1
a
3
aaa
9
abcdefgfe
1
z
15
hnndledmnhlttin
```

This test input includes:
- A single character string (`"a"`).
- A string with repeated characters (`"aaa"`).
- A string with all unique characters (`"abcdefgfe"`).
- A single character string with a different character (`"z"`).
- A string with a specific pattern (`"hnndledmnhlttin"`).

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

5
1
a
3
aaa
9
abcdefgfe
1
z
15
hnndledmnhlttin


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

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

using namespace std;
void findDistinct(string &s) {
    for(int i = 1; i < s.length(); i++) {
        for(int j = 1; j < s.length(); j++) {
            if(s[j] < s[j-1]) {
                char temp = s[j];
                s[j] = s[j-1];
                s[j-1] = temp;
            }
        }
    }
    int i = 1;
    while(i <= s.length()) {
        if(s[i] == s[i-1]) {
            s.erase(i, 1);
        }
        else i++;
    }
}

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

    while(t--) {
        int n;
        cin >> n;
        string s, b;
        getline(cin >> ws, s);
        b = s;
        findDistinct(s);
        for(int i = 0; i < b.length(); i++) {
            for(int j = 0; j < s.length(); j++) {
                if(b[i] == s[j]){
                    b[i] = s[s.length() - 1 - j];
                    break;
                }
            }
        }
        cout << b << endl;

    }

    return 0;
}

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

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

Think step by step.

Response:
```plaintext
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
```

### Explanation:
1. **Test Case 1:**
   - **Input:** `serofedsoc`
   - **Output:** `codeforces`
   - This is a standard test case to check the basic functionality.

2. **Test Case 2:**
   - **Input:** `ttf`
   - **Output:** `fft`
   - This test case includes repeated characters to ensure the algorithm handles them correctly.

3. **Test Case 3:**
   - **Input:** `tlrhgmaoi`
   - **Output:** `algorithm`
   - This test case has a longer string with a mix of characters to ensure the algorithm works for more complex inputs.

4. **Test Case 4:**
   - **Input:** `w`
   - **Output:** `w`
   - This is a single-character test case to check the edge case where the string length is 1.

5. **Test Case 5:**
   - **Input:** `hnndledmnhlttin`
   - **Output:** `meetinthemiddle`
   - This test case has a longer string with repeated characters and a more complex structure to ensure the algorithm handles it correctly.

### Rationale:
- **Edge Cases:**
  - Single character: Ensures the algorithm handles strings of length 1.
  - Repeated characters: Ensures the algorithm correctly handles and decodes strings with repeated characters.
- **Complexity:**
  - Longer strings: Ensures the algorithm can handle strings of varying lengths and complexities.
- **Standard Cases:**
  - Mixed characters: Ensures the algorithm works for a variety of input strings.

This set of test cases should help expose any bugs in the provided buggy code.

5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
#include<bits/stdc++.h>
using namespace std;
char b[200010], s[200010], ans[20010];
int main()
{
	int t;
	cin >> t;
	int cnt[26];
	while (t--)
	{
		memset(cnt, 0, sizeof(cnt));
		memset(b, 0, sizeof(b));
		memset(s, 0, sizeof(s));
		memset(ans, 0, sizeof(ans));
		int n;
		cin >> n;
		cin >> b;
		for (int i = 0; i < strlen(b); i++)
			cnt[b[i] - 'a']++;
		int j = 0;
		for (int i = 0; i < 26; i++)
			if (cnt[i] > 0) s[j++] = 'a' + i;
		for (int i = 0; i < strlen(s); i++)
			ans[s[i] - 'a'] = s[strlen(s) - i - 1];
		for (int i = 0; i < strlen(b); i++)
			b[i] = ans[b[i] - 'a'];
		cout << b << endl;
	}
	return 0;
}

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

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

Think step by step.

Response:
To expose the bug in the provided buggy code, we need to focus on edge cases and scenarios that might cause issues in the symmetric encoding and decoding process. Here are some key considerations:

1. **Single Character Strings**: The code should handle strings of length 1 correctly.
2. **Strings with Repeated Characters**: The code should handle strings where some characters are repeated.
3. **Strings with All Unique Characters**: The code should handle strings where all characters are unique.
4. **Strings with Special Patterns**: The code should handle strings with specific patterns that might cause issues in the symmetric mapping.

Given these considerations, let's create a test input that includes these scenarios:

```plaintext
5
1
a
3
aaa
5
abcde
7
abacaba
10
serofedsoc
```

This test input includes:
1. A single character string "a".
2. A string with repeated characters "aaa".
3. A string with all unique characters "abcde".
4. A string with a special pattern "abacaba".
5. A known test case "serofedsoc" to ensure the expected behavior.

This input should help expose any issues in the symmetric encoding and decoding process.

5
1
a
3
aaa
5
abcde
7
abacaba
10
serofedsoc


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
from functools import cache
t = int(input())

@cache
def ret(a):
    return k[-k.index(a) - 1]

for _ in range(t):
    ret.cache_clear()
    ans = ""
    n = int(input())
    s = input()
    k = list(set(s))
    k.sort()
    for i in s:
        ans += ret(i)
    print(ans)

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

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

Think step by step.

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

1. The use of `@cache` and `ret.cache_clear()` can lead to incorrect results if the same characters appear in different test cases.
2. The set of characters `k` is sorted, but if the same character appears multiple times, it can lead to incorrect mappings.

Let's consider a test input that includes repeated characters and different test cases to highlight these issues:

```plaintext
3
5
aaaaa
7
abcdeff
11
abracadabra
```

### Explanation:
1. **Test Case 1: "aaaaa"**
   - The string `s` consists of only one unique character 'a'.
   - The set `k` will be `['a']`.
   - The encoded string should be the same as the original string, but the buggy code might handle this incorrectly due to the cache.

2. **Test Case 2: "abcdeff"**
   - The string `s` contains a repeated character 'f'.
   - The set `k` will be `['a', 'b', 'c', 'd', 'e', 'f']`.
   - The encoded string should be "fedcbaa", but the buggy code might handle the repeated character incorrectly.

3. **Test Case 3: "abracadabra"**
   - The string `s` contains multiple repeated characters.
   - The set `k` will be `['a', 'b', 'c', 'd', 'r']`.
   - The encoded string should be "rddcadaddbr", but the buggy code might handle the repeated characters incorrectly.

This test input is designed to challenge the buggy code by including edge cases with repeated characters and multiple test cases.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
for _ in range(int(input())):

    n = int(input())

    s = input()

    arr = [0] * 26

    h_map = {}

    temp = list(set(s))
    temp.sort()
    r = "".join(temp)

    count = 0
    for c in r:
        h_map[c] = count
        count += 1

    res = ""
    for c in s:

        idx = h_map[c]

        res += r[-1 - idx]

    print(res)

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the given buggy code, we need to consider edge cases and scenarios that can cause the algorithm to fail. Here are the steps to identify such a test input:

1. **Empty or Single Character String**: Test cases with very short strings can reveal issues in how the code handles minimal input.
2. **All Characters are the Same**: This can expose issues in how the code handles a string with a single unique character.
3. **All Distinct Characters**: A string with all distinct characters can test the mapping and symmetric replacement logic.
4. **Repetitive Patterns**: Strings with repetitive patterns can test the consistency of the mapping and replacement logic.

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

```plaintext
3
1
a
5
aaaaa
26
abcdefghijklmnopqrstuvwxyz
```

### Explanation:
1. **Test Case 1**: A single character string "a". This tests the edge case where the string has only one unique character.
2. **Test Case 2**: A string "aaaaa" with all characters being the same. This tests the edge case where the string has only one unique character repeated multiple times.
3. **Test Case 3**: A string "abcdefghijklmnopqrstuvwxyz" with all distinct characters. This tests the edge case where the string contains all 26 lowercase letters, which should be symmetrically mapped.

These test cases are designed to be small and complete, yet challenging enough to expose potential bugs in the given buggy code.

3
1
a
5
aaaaa
26
abcdefghijklmnopqrstuvwxyz


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
/**
 * test
 */
import java.util.*;

public class test {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- >0) {
            int n = sc.nextInt();
            TreeSet<Character> set = new TreeSet<>();
            Map<Character,Character> mpp = new HashMap<>();
            String s = sc.next();
            for (char c :s.toCharArray() ) {
                set.add(c);
            }
            List<Character> list = new ArrayList<>(set);
            int l = 0;int r = set.size()-1;
           while (l<=r) {
                mpp.put(list.get(l), list.get(r));
                mpp.put(list.get(r), list.get(l));
                l++;r--;
            }
            String f = "";
            for (char c : s.toCharArray()) {
                f=f+(mpp.get(c));
            }
            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:
To generate a challenging test input that exposes the bug in the given buggy code, we need to focus on edge cases and scenarios that can highlight the issues. Here are the steps to consider:

1. **Single Character String**: Test the case where the input string has only one character. This can help verify if the code handles such a simple case correctly.
2. **String with All Unique Characters**: Test a string where all characters are unique. This can help verify if the mapping is done correctly for all characters.
3. **String with Repeated Characters**: Test a string where some characters are repeated. This can help verify if the code correctly maps repeated characters.
4. **String with Alphabetical Order**: Test a string that is already in alphabetical order. This can help verify if the code correctly handles such a string.
5. **String with Reversed Alphabetical Order**: Test a string that is in reverse alphabetical order. This can help verify if the code correctly handles such a string.
6. **String with Mixed Characters**: Test a string with a mix of characters that are not in alphabetical order. This can help verify if the code correctly handles a more complex scenario.

Given the constraints, we will generate a small-scale test input that covers these scenarios.

Here is the test input:

```plaintext
6
1
a
5
abcde
5
edcba
5
aabbcc
7
abacaba
10
zyxwvuts
```

Explanation:
1. **Single Character String**: "a" (Length 1)
2. **String with All Unique Characters in Alphabetical Order**: "abcde" (Length 5)
3. **String with All Unique Characters in Reverse Alphabetical Order**: "edcba" (Length 5)
4. **String with Repeated Characters**: "aabbcc" (Length 5)
5. **String with Mixed Characters**: "abacaba" (Length 7)
6. **String with Reversed Alphabetical Order (Longer)**: "zyxwvuts" (Length 10)

This test input covers a variety of edge cases and should help expose any bugs in the code.

6
1
a
5
abcde
5
edcba
5
aabbcc
7
abacaba
10
zyxwvuts


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        for (int i = 0; i < N; i++) {
            int len=sc.nextInt();
            String str=sc.next();
            int cot[]=new int[26];
            for (int j = 0; j < str.length(); j++) {
                cot[str.charAt(j)-'a']++;
            }
            String ss="";
            for (int t = 0; t < 26; t++) {
                if(cot[t]!=0) ss=ss+(char)((int)'a'+t);
            }
            int cot2[]=new int[26];
            int l=0,r=ss.length()-1;
            while (l<=r){
                cot2[ss.charAt(l)-'a']=ss.charAt(r)-'a';
                cot2[ss.charAt(r)-'a']=ss.charAt(l)-'a';
                l++;
                r--;
            }
            String ans="";
            for (int j = 0; j < str.length(); j++) {
                ans=ans+(char)(cot2[str.charAt(j)-'a']+'a');
            }
            System.out.println(ans);
        }
    }
}

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to consider edge cases and scenarios that can maximize the failure probability. Here are some key points to consider:

1. **Empty or Single Character Strings**: These can be edge cases where the encoding and decoding process might not handle them correctly.
2. **Strings with Repeated Characters**: The code might not handle repeated characters correctly, especially if the distinct characters in the string are not handled properly.
3. **Strings with All Unique Characters**: This can test the symmetric encoding and decoding logic.
4. **Strings with Alphabetic Order**: This can test how the code handles the alphabetical order of characters.

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

```plaintext
5
1
a
2
aa
3
abc
4
abcd
5
abcde
```

This test input includes:
- A single character string.
- A string with repeated characters.
- A string with all unique characters.
- A string with a few unique characters.
- A string with a larger set of unique characters.

This 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: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
#include<bits/stdc++.h>
using namespace std;
#define ll long long
int main() {

	// freopen("inputff.in","r",stdin);
	// freopen("outputff.in","w",stdout);

  int t;
  cin>>t;

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

    string b;
    cin>>b;
    set<char>st;
    for(int i=0;i<n;i++){
      st.insert(b[i]);
    }

    vector<char>r;
   for(auto it:st){
    r.push_back(it);
   }

   sort(r.begin(),r.end());
    vector<char>dummy;
    for(int i=0;i<n;i++){
      dummy.push_back(b[i]);
    }
    map<char,char>mp;
      for(int i=0;i<n;i++){
        mp[r[i]]=r[n-1-i];
      }

      for(int i=0;i<n;i++){
        for(int j=0;j<r.size();j++){
          if(dummy[i]==r[j]){
            cout<<r[r.size()-j-1];
          }
        }
      }

   cout<<endl;
  }

}

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

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

Think step by step.

Response:
To expose the bug in the provided code, we need to focus on edge cases and scenarios that can maximize the failure probability. The code has a few potential issues:

1. **Handling of Duplicates**: The code uses a set to collect unique characters, which is correct. However, it then maps characters in the set to their symmetric positions without considering the original frequency of characters in the input string.
2. **Symmetric Mapping**: The code maps characters in the set to their symmetric positions, but it does not handle cases where the set of unique characters is not symmetrically balanced.
3. **Character Replacement**: The code uses nested loops to find and replace characters, which can be inefficient and prone to errors.

Given these potential issues, let's create a test input that can expose the bug:

### Test Input
We will use a string where the set of unique characters is not symmetrically balanced, and the frequency of characters in the input string is important.

```plaintext
1
5
abcba
```

### Explanation
- **Test Case 1**: The input string is "abcba".
- **Unique Characters**: The set of unique characters is {'a', 'b', 'c'}.
- **Symmetric Mapping**:
  - 'a' should map to 'c'.
  - 'b' should map to 'b'.
  - 'c' should map to 'a'.
- **Expected Output**: The original string should be "abcba" after decoding.

This test input should expose the bug because:
- The set of unique characters is not symmetrically balanced.
- The frequency of characters in the input string is important, and the code might not handle it correctly.

By using this test input, we can observe if the code correctly decodes the string "abcba" to "abcba". If the code fails, it will help us identify the specific issue in the symmetric mapping or character replacement logic.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <stdbool.h>
#include <ctype.h>
#include <math.h>

char str[200001] = {};
int main(int argc, char* argv[]) {
    int t = 0;
    scanf("%d", &t);
    while(t--) {
        int n = 0, i = 0;
        scanf("%d%s", &n, &str[0]);
        int arr[26] = {0}, acc = 0;
        for(i = 0; i < (int)strlen(str); i++) {
            if(arr[(int)str[i]-97] == 0) {
                acc++;
                arr[(int)str[i]-97] = 1;
            }
            if(acc == 26)
                break;
        }
        char temp[26] = {};
        int x = 0;
        for(i = 0; i < 26; i++) {
            if(arr[i] != 0)
                temp[x++] = (char)(i+97);
        }
        char replace[26] = {};
        for(i = 0; i < x; i++)
            replace[i] = temp[x-1-i];
        char aux[26] = {};
        for(i = 0; i < x; i++) {
            aux[(int)temp[i]-97] = replace[i];
        }
        for(i = 0; i < (int)strlen(str); i++)
            str[i] = aux[(int)str[i]-97];
        printf("%s\n", str);
    }
    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
a
26
abcdefghijklmnopqrstuvwxyz
10
abccbaabcc
```

3
1
a
26
abcdefghijklmnopqrstuvwxyz
10
abccbaabcc


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
for _ in range(int(input())):
    n = int(input())
    s = input()
    arr = set()
    for i in range(n):
        arr.add(s[i])
    arr = list(arr)
    arr.sort()
    m = {}
    for i in range(len(arr)):
        m[arr[i]] = arr[len(arr)-1-i]
    ans = ''
    for i in range(n):
        ans += m[s[i]]
    print(ans)

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to focus on edge cases and scenarios that might cause issues in the code's logic. Here are some key points to consider:

1. **Empty or Single Character String**: Test cases with very short strings, especially those that are empty or have only one character, can expose issues in how the code handles these edge cases.
2. **Strings with All Identical Characters**: This can test how the code handles the creation of the auxiliary string `r` and the mapping.
3. **Strings with All Distinct Characters**: This can test the symmetry and the mapping logic.
4. **Strings with Repeated Characters**: This can test the handling of multiple occurrences of the same character.

Let's construct a small-scale test input that includes these scenarios:

```plaintext
4
1
a
3
aaa
5
abcde
10
ababababab
```

### Explanation:
1. **Test Case 1**: A single character string "a".
   - Expected output: "a"
2. **Test Case 2**: A string with all identical characters "aaa".
   - Expected output: "aaa"
3. **Test Case 3**: A string with all distinct characters "abcde".
   - Expected output: "edcba"
4. **Test Case 4**: A string with repeated characters "ababababab".
   - Expected output: "bababababa"

These test cases cover a range of edge cases and should help in exposing any bugs in the provided buggy code.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
def solve():
    n = int(input())
    b = input()
    cnt = [0] * 26
    for c in b:
        cnt[ord(c) - ord('a')] = 1
    tmp = ''
    for i in range(26):
        if cnt[i] > 0:
            tmp += chr(ord('a') + i)
    a = ''
    for c in b:
        a += tmp[-1 - tmp.find(c)]
    print(a)

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

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

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

Think step by step.

Response:
To generate a challenging test input that exposes the bug in the provided buggy code, we need to consider edge cases and scenarios that might cause the code to fail. The buggy code has a few potential issues:

1. **Handling of Duplicate Characters**: The code constructs the auxiliary string `tmp` by adding each unique character from `b` in alphabetical order. However, it does not handle the case where the input string `b` has duplicate characters correctly.

2. **Symmetry in Encoding**: The code assumes that the characters in `b` are symmetrically replaced, but it does not handle the case where the input string `b` is not a valid encoding of some string `s`.

3. **Edge Cases**: The code might fail for very short strings or strings with a very limited set of characters.

Given these points, let's construct a test input that could expose these issues:

1. **Short String with Repeated Characters**: A string like "aaa" should be encoded to "ccc" if the original string was "ccc". This will test how the code handles repeated characters.
2. **String with All Unique Characters**: A string like "abcdef" should be encoded to "fedcba" if the original string was "abcdef". This will test how the code handles a string with all unique characters.
3. **String with a Limited Set of Characters**: A string like "abab" should be encoded to "baba" if the original string was "baba". This will test how the code handles a string with a limited set of characters.

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

```plaintext
3
3
aaa
6
abcdef
4
abab
```

This test input will help identify issues in the buggy code by covering different edge cases and ensuring the code handles them correctly.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeSet;

public class cf_1974B {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for (int i = 0; i < t; i++) {
            // System.out.println("Enter n:");
            int n = sc.nextInt();
            // System.out.println("String s: ");
            String s = sc.next();

            s = s.toLowerCase();

            String ans = encode(s, n);
            System.out.println(ans);
        }

    }

    private static String encode(String s, int n) {
        String ans = "";
        String r = "";
        // List<Character> list = new ArrayList<>();
        TreeSet<Character> set = new TreeSet<>();
        char[] ch = new char[s.length()];
        for (int i = 0; i < s.length(); i++) {
            // list.add(s.charAt(i));
            set.add(s.charAt(i));
        }
        for (char x : set) {
            r += x;
        }
        // System.out.println("r is: "+r);
        int a = 0, b = r.length() - 1;
        Map<Character, Character> map = new HashMap<>();
        while (a <= b) {
            char c = r.charAt(a);
            char d = r.charAt(b);
            map.put(c, map.getOrDefault(c, d));
            map.put(d, map.getOrDefault(d, c));
            a++;
            b--;
        }
        ch = s.toCharArray();
        for (int i = 0; i < ch.length; i++) {
            if (map.containsKey(ch[i])) {
                ch[i] = map.get(ch[i]);

            }
            ans += ch[i];
        }

        // for(char c: ch){
        // System.out.print(c+"");
        // }

        return ans;
    }
}

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

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

Think step by step.

Response:
To expose the bug in the given code, we need to focus on edge cases and scenarios that might cause the code to fail. Let's consider the following aspects:

1. **Single Character Strings**: If the input string has only one unique character, the symmetric encoding should not change the string.
2. **Strings with Repeated Characters**: If the input string has repeated characters, the encoding should handle them correctly.
3. **Strings with All Unique Characters**: If the input string has all unique characters, the encoding should work as expected.
4. **Strings with a Small Set of Unique Characters**: If the input string has a small set of unique characters, the encoding should handle the symmetric mapping correctly.

Let's create a small-scale test input that covers these scenarios:

```plaintext
4
1
a
3
aaa
6
abcdef
6
aabbcc
```

### Explanation:
1. **Single Character String**: `"a"`. The encoded string should remain `"a"`.
2. **String with Repeated Characters**: `"aaa"`. The encoded string should remain `"aaa"`.
3. **String with All Unique Characters**: `"abcdef"`. The encoded string should be `"fedcba"`.
4. **String with a Small Set of Unique Characters**: `"aabbcc"`. The encoded string should be `"ccbbaa"`.

This test input should help expose any issues in the code, especially in handling edge cases and ensuring the symmetric mapping is correct.


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: Symmetric Encoding
time_limit_ms: 2000
memory_limit_mb: 256
Description: Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:

  * first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order;    * then the encoding happens as follows: each character in the string $s$ is replaced by its symmetric character from the string $r$ (the first character of the string $r$ will be replaced by the last, the second by the second from the end, and so on).

For example, encoding the string $s$="codeforces" happens as follows:

  * the string $r$ is obtained as "cdefors";    * the first character $s_1$='c' is replaced by 's';    * the second character $s_2$='o' is replaced by 'e';    * the third character $s_3$='d' is replaced by 'r';    * ...    * the last character $s_{10}$='s' is replaced by 'c'.

![](CDN_BASE_URL/e120531cc984becdbbab53f80507a062) The string $r$ and replacements for $s$="codeforces".

Thus, the result of encoding the string $s$="codeforces" is the string "serofedsoc".

Write a program that performs decoding — that is, restores the original string $s$ from the encoding result.

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $b$.

The second line of each test case contains a string $b$ of length $n$, consisting of lowercase Latin letters — the result of encoding the original string $s$.

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

Output: For each test case, output the string $s$ from which the encoding result $b$ was obtained.

Examples:
input:
5
10
serofedsoc
3
ttf
9
tlrhgmaoi
1
w
15
hnndledmnhlttin
output:
codeforces
fft
algorithm
w
meetinthemiddle

Note:

Buggy Code:
import java.util.*;
public class Main
{
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while(t-->0)
        {
            int n = sc.nextInt();
            String s = sc.next();
            String b = "";
            TreeSet<Character> h = new TreeSet<>();
            for(int i=0;i<n;i++)
            h.add(s.charAt(i));
            Character[] r = h.toArray(new Character[0]);
            HashMap<Character,Character> m = new HashMap<>();
            int size = r.length;
            for(int i=0;i<size;i++)
            m.put(r[i],r[size-1-i]);
            for(int i=0;i<n;i++)
            {
                b+=m.get(s.charAt(i));
            }
            System.out.println(b);

        }
    }
}

**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
10
serofedsoc
3
aaa
9
tlrhgmaoi
1
z
15
hnndledmnhlttin
```

5
10
serofedsoc
3
aaa
9
tlrhgmaoi
1
z
15
hnndledmnhlttin


**Task:**
Generate a challenging test input that exposes the bug in the buggy code of the algorithm problem:
Algorithm Problem:
Title: The Strict Teacher (Easy Version)
time_limit_ms: 1500
memory_limit_mb: 256
Description: This is the easy version of the problem. The only differences between the two versions are the constraints on $m$ and $q$. In this version, $m=2$ and $q=1$. You can make hacks only if both versions of the problem are solved.

Narek and Tsovak were busy preparing this round, so they have not managed to do their homework and decided to steal David's homework. Their strict teacher noticed that David has no homework and now wants to punish him. She hires other teachers to help her catch David. And now $m$ teachers together are chasing him. Luckily, the classroom is big, so David has many places to hide.

The classroom can be represented as a one-dimensional line with cells from $1$ to $n$, inclusive.

At the start, all $m$ teachers and David are in distinct cells. Then they make moves. During each move

  * David goes to an adjacent cell or stays at the current one.    * Then, each of the $m$ teachers simultaneously goes to an adjacent cell or stays at the current one.

This continues until David is caught. David is caught if any of the teachers (possibly more than one) is located in the same cell as David. Everyone sees others' moves, so they all act optimally.

Your task is to find how many moves it will take for the teachers to catch David if they all act optimally.

Acting optimally means the student makes his moves in a way that maximizes the number of moves the teachers need to catch him; and the teachers coordinate with each other to make their moves in a way that minimizes the number of moves they need to catch the student.

Also, as Narek and Tsovak think this task is easy, they decided to give you $q$ queries on David's position. Note: this is the easy version, and you are given only one query.

Input: In the first line of the input, you are given a single integer $t$ ($1 \le t \le 10^5$) — the number of test cases. The description of each test case follows.

In the first line of each test case, you are given three integers $n$, $m$, and $q$ ($3 \le n \le 10^9$, $m=2$, $q=1$) — the number of cells on the line, the number of teachers, and the number of queries.

In the second line of each test case, you are given $m$ distinct integers $b_1, b_2, \ldots, b_m$ ($1 \le b_i \le n$) — the cell numbers of the teachers.

In the third line of each test case, you are given $q$ integers $a_1, a_2, \ldots, a_q$ ($1 \le a_i \le n$) — David's cell number for every query.

It is guaranteed that for any $i$, $j$ such that $1 \le i \le m$ and $1 \le j \le q$, $b_i \neq a_j$.

Output: For each test case, output $q$ lines, the $i$-th of them containing the answer of the $i$-th query.

Examples:
input:
3
10 2 1
1 4
2
8 2 1
3 6
1
8 2 1
3 6
8
output:
1
2
2

Note: In the first example, the student can just stay at cell $2$. The teacher, initially located in cell $1$, can reach cell $2$ in one move. Therefore, the answer is $1$.

In the second example, the student should just stay at cell $1$. The teacher, initially located in cell $3$, can reach cell $1$ in two moves. Therefore, the answer is $2$.

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

int main(){
 int T;
 cin >> T;
 while(T--){
  ll n,m,q;
  ll m1,m2;
  ll posdavid;
  cin >> n >> m >> q;
  cin >> m1 >> m2;
  cin >> posdavid;
  ll teach1=min(m1,m2);
  ll teach2=max(m1,m2);
  ll ans=0;
  if(posdavid>=teach1 && posdavid<=teach2){
    ll boxes=teach2-teach1-1;
    if(boxes>=3 && posdavid!=teach1 && posdavid!=teach2){
      ans=boxes-1;
      cout<<ans<<endl;
    }
    else{
      ans=1;
      cout<<ans<<endl;
    }
  }
  else if(posdavid<teach1){
    ll boxes1=teach1-1;
    cout<<boxes1<<endl;
  }
  else if(posdavid>teach2){
    ll boxes2=n-teach2;
    cout<<boxes2<<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
10 2 1
1 10
5
```