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]≠s[n−i+1]�[�]≠�[�−�+1] for every i� (1≤i≤n1≤�≤�). 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 −1−1, if this is not possible.
The first line contains a single integer t� (1≤t≤1041≤�≤104) — 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≤n≤2⋅1051≤�≤2⋅105) — 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⋅1052⋅105.
For each test case, output a single integer — the minimum number of operations required to make the string s� an anti-palindrome, or −1−1 if this is not possible.
In the first test case, the string “codeforces” is already an anti-palindrome, so the answer is 00.
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 −1−1.
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 11.