D. a-Good Stringtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.   InputThe 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).OutputFor 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.ExampleInput
6
8
bbdcaaaa
8
asdfghjk
8
ceaaaabb
8
bbaaddcc
1
z
2
ac
Output
0
7
4
5
1
1

6
8
bbdcaaaa
8
asdfghjk
8
ceaaaabb
8
bbaaddcc
1
z
2
ac

0 7 4 5 1 1 
['bitmasks', 'brute force', 'divide and conquer', 'dp', 'implementation', '*1500']