CF1552A.Subsequence Permutation

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

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

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.

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

In the first test case, we can choose the $k=2$ characters \texttt{"_ol"} and rearrange them as \texttt{"_lo"} (so the resulting string is $\texttt{"llo"}$ ). 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 \texttt{"_o__force_"} and rearrange them as \texttt{"_c__efoor_"} (so the resulting string is $\texttt{"ccdeefoors"}$ ). 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 $\texttt{"dcba"}$ and reverse the whole string (so the resulting string is $\texttt{"abcd"}$ ).