Solve the programming task below in a Python markdown code block.
A string $s$ of length $n$, consisting of lowercase letters of the English alphabet, is given.

You must choose some number $k$ between $0$ and $n$. Then, you select $k$ characters of $s$ and permute them however you want. In this process, the positions of the other $n-k$ characters remain unchanged. You have to perform this operation exactly once.

For example, if $s={"andrea"}$, you can choose the $k=4$ characters ${"a_d_ea"}$ and permute them into ${"d_e_aa"}$ so that after the operation the string becomes ${"dneraa"}$.

Determine the minimum $k$ so that it is possible to sort $s$ alphabetically (that is, after the operation its characters appear in alphabetical order).


-----Input-----

The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases. Then $t$ test cases follow.

The first line of each test case contains one integer $n$ ($1 \le n \le 40$) — the length of the string.

The second line of each test case contains the string $s$. It is guaranteed that $s$ contains only lowercase letters of the English alphabet.


-----Output-----

For each test case, output the minimum $k$ that allows you to obtain a string sorted alphabetically, through the operation described above.


-----Examples-----

Input
4
3
lol
10
codeforces
5
aaaaa
4
dcba
Output
2
6
0
4


-----Note-----

In the first test case, we can choose the $k=2$ characters ${"_ol"}$ and rearrange them as ${"_lo"}$ (so the resulting string is ${"llo"}$). It is not possible to sort the string choosing strictly less than $2$ characters.

In the second test case, one possible way to sort $s$ is to consider the $k=6$ characters ${"_o__force_"}$ and rearrange them as ${"_c__efoor_"}$ (so the resulting string is ${"ccdeefoors"}$). One can show that it is not possible to sort the string choosing strictly less than $6$ characters.

In the third test case, string $s$ is already sorted (so we can choose $k=0$ characters).

In the fourth test case, we can choose all $k=4$ characters ${"dcba"}$ and reverse the whole string (so the resulting string is ${"abcd"}$).