Making Anti-Palindromes
Description
You are given a string $s$, consisting of lowercase English letters. In one operation, you are allowed to swap any two characters of the string $s$.
A string $s$ of length $n$ is called an anti-palindrome, if $s[i] \ne s[n - i + 1]$ for every $i$ ($1 \le i \le n$). For example, the strings "codeforces", "string" are anti-palindromes, but the strings "abacaba", "abc", "test" are not.
Determine the minimum number of operations required to make the string $s$ an anti-palindrome, or output $-1$, if this is not possible.
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of the test cases follows.
Each test case consists of two lines. The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $s$.
The second line contains the string $s$, consisting of $n$ lowercase English letters.
The sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
For each test case, output a single integer — the minimum number of operations required to make the string $s$ an anti-palindrome, or $-1$ if this is not possible.
Input
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of the test cases follows.
Each test case consists of two lines. The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $s$.
The second line contains the string $s$, consisting of $n$ lowercase English letters.
The sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case, output a single integer — the minimum number of operations required to make the string $s$ an anti-palindrome, or $-1$ if this is not possible.
10
10
codeforces
3
abc
10
taarrrataa
10
dcbdbdcccc
4
wwww
12
cabbaccabaac
10
aadaaaaddc
14
aacdaaaacadcdc
6
abccba
12
dcbcaebacccd
0
-1
1
1
-1
3
-1
2
2
2
Note
In the first test case, the string "codeforces" is already an anti-palindrome, so the answer is $0$.
In the second test case, it can be shown that the string "abc" cannot be transformed into an anti-palindrome by performing the allowed operations, so the answer is $-1$.
In the third test case, it is enough to swap the second and the fifth characters of the string "taarrrataa", and the new string "trararataa" will be an anti-palindrome, so the answer is $1$.