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You are given a string $S$ with length $N$ and you should change it to a palindrome using a sequence of zero or more operations. In one operation, you should choose two adjacent elements of $S$ (two characters) and swap them; however, neither of these elements may be used in any other operation.

Find the minimum number of operations you have to perform in order to change the string $S$ into a palindrome, or determine that it is impossible.

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a single integer $N$.
The second line contains a single string $S$ with length $N$.

------ Output ------
For each test case:
If it is impossible to make the string $S$ a palindrome, print a single line containing the string "NO" (without quotes).
Otherwise, print two lines. The first of these lines should contain the string "YES" (without quotes). The second line should contain a single integer ― the minimum required number of operations.

------ Constraints ------
$1 ≤ T ≤ 10,000$
$1 ≤ N ≤ 10^{5}$
$S$ contains only lowercase English letters
the sum of $N$ over all test cases does not exceed $10^{6}$

------ Subtasks ------
Subtask #1 (50 points):
$N ≤ 10^{3}$
$S$ contains only characters 'a' and 'b'
the sum of $N$ over all test cases does not exceed $10^{4}$

Subtask #2 (50 points): original constraints

----- Sample Input 1 ------
3

4

abab

5

acbba

5

aaaab
----- Sample Output 1 ------
YES

1

YES

1

NO

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