a-Good String

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.