CF1822E.Making Anti-Palindromes

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.

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 $1$ .