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.

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.

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 $$$1$$$.

Making Anti-Palindromes

Examples