You are given a string s[1…n] consisting of lowercase Latin letters. It is guaranteed that n=2k for some integer k≥0.
The string s[1…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. s1=c);
The length of s is greater than 1, the first half of the string consists of only the character c (i.e. s1=s2=⋯=sn2=c) and the second half of the string (i.e. the string sn2+1sn2+2…sn) 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. sn2+1=sn2+2=⋯=sn=c) and the first half of the string (i.e. the string s1s2…sn2) 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 si 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.
The first line of the input contains one integer t (1≤t≤2⋅10^4) — the number of test cases. Then t test cases follow.
The first line of the test case contains one integer n (1≤n≤131 072) — the length of s. It is guaranteed that n=2k for some integer k≥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⋅10^5 (∑n≤2⋅10^5).
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.
6 8 bbdcaaaa 8 asdfghjk 8 ceaaaabb 8 bbaaddcc 1 z 2 ac
0 7 4 5 1 1