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.

给你一个由小写英文字母组成的字符串 $s$。在一次操作中，你可以交换字符串 $s$ 中任意两个字符。

长度为 $n$ 的字符串 $s$ 被称为反回文串（anti-palindrome），当且仅当对每个 $i$（$1 \le i \le n$），均有 $s[i] \ne s[n - i + 1]$。例如，字符串 "codeforces"、"string" 是反回文串，但字符串 "abacaba"、"abc"、"test" 不是。

请确定使字符串 $s$ 变为反回文串所需的最少操作次数；若无法实现，则输出 $-1$。

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 $2 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。随后是各测试用例的描述。

每个测试用例由两行组成。第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）—— 字符串 $s$ 的长度。

第二行包含字符串 $s$，由 $n$ 个小写英文字母组成。

所有测试用例的 $n$ 值之和不超过 $2 \cdot 10^5$。

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.

对于每个测试用例，输出一个整数——使字符串 $s$ 变为反回文串所需的最少操作次数；如果无法实现，则输出 $-1$。

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 $1$.

在第一个测试用例中，字符串 "codeforces" 本身已是一个反回文串，因此答案为 $0$。

在第二个测试用例中，可以证明字符串 "abc" 无法通过执行允许的操作转变为反回文串，因此答案为 $-1$。

在第三个测试用例中，只需交换字符串 "taarrrataa" 的第二个字符与第五个字符，即可得到新字符串 "trararataa"，该字符串为反回文串，因此答案为 $1$。