You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
You are given a string $$$s[1 \dots n]$$$ consisting of lowercase Latin letters. It is guaranteed that $$$n = 2^k$$$ for some integer $$$k \ge 0$$$.

The string $$$s[1 \dots n]$$$ is called $$$c$$$-good if at least one of the following three conditions is satisfied:

- The length of $$$s$$$ is $$$1$$$, and it consists of the character $$$c$$$ (i.e. $$$s_1=c$$$);
- The length of $$$s$$$ is greater than $$$1$$$, the first half of the string consists of only the character $$$c$$$ (i.e. $$$s_1=s_2=\dots=s_{\frac{n}{2}}=c$$$) and the second half of the string (i.e. the string $$$s_{\frac{n}{2} + 1}s_{\frac{n}{2} + 2} \dots s_n$$$) is a $$$(c+1)$$$-good string;
- The length of $$$s$$$ is greater than $$$1$$$, the second half of the string consists of only the character $$$c$$$ (i.e. $$$s_{\frac{n}{2} + 1}=s_{\frac{n}{2} + 2}=\dots=s_n=c$$$) and the first half of the string (i.e. the string $$$s_1s_2 \dots s_{\frac{n}{2}}$$$) is a $$$(c+1)$$$-good string.

For example: "aabc" is 'a'-good, "ffgheeee" is 'e'-good.

In one move, you can choose one index $$$i$$$ from $$$1$$$ to $$$n$$$ and replace $$$s_i$$$ with any lowercase Latin letter (any character from 'a' to 'z').

Your task is to find the minimum number of moves required to obtain an 'a'-good string from $$$s$$$ (i.e. $$$c$$$-good string for $$$c=$$$ 'a'). It is guaranteed that the answer always exists.

You have to answer $$$t$$$ independent test cases.

Another example of an 'a'-good string is as follows. Consider the string $$$s = $$$"cdbbaaaa". It is an 'a'-good string, because:

- the second half of the string ("aaaa") consists of only the character 'a';
- the first half of the string ("cdbb") is 'b'-good string, because:   the second half of the string ("bb") consists of only the character 'b';  the first half of the string ("cd") is 'c'-good string, because:   the first half of the string ("c") consists of only the character 'c';  the second half of the string ("d") is 'd'-good string.

## Input Format
The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 2 \cdot 10^4$$$) — the number of test cases. Then $$$t$$$ test cases follow.

The first line of the test case contains one integer $$$n$$$ ($$$1 \le n \le 131~072$$$) — the length of $$$s$$$. It is guaranteed that $$$n = 2^k$$$ for some integer $$$k \ge 0$$$. The second line of the test case contains the string $$$s$$$ consisting of $$$n$$$ lowercase Latin letters.

It is guaranteed that the sum of $$$n$$$ does not exceed $$$2 \cdot 10^5$$$ ($$$\sum n \le 2 \cdot 10^5$$$).

## Output Format
For each test case, print the answer — the minimum number of moves required to obtain an 'a'-good string from $$$s$$$ (i.e. $$$c$$$-good string with $$$c =$$$ 'a'). It is guaranteed that the answer exists.

## Examples
```input
6
8
bbdcaaaa
8
asdfghjk
8
ceaaaabb
8
bbaaddcc
1
z
2
ac
```
```output
0
7
4
5
1
1
```

Now solve the problem and return the code.