#include <bits/stdc++.h>
#pragma warning(disable : 4996)
using namespace std;
map<tuple<int, int, char>, int> cache;
string str;
int count(int begin, int end, char symbol) {
  int res = 0;
  for (int i = begin; i < end; i++) {
    if (str[i] != symbol) res++;
  }
  return res;
}
long long calc(int begin, int end, char symb) {
  int res = INT_MAX;
  if (end - begin == 2) {
    if (str[begin] == symb && str[begin + 1] == symb + 1 ||
        str[begin + 1] == symb && str[begin] == symb + 1)
      return 0;
    else if (str[begin] != symb && str[begin + 1] != symb &&
             str[begin] != symb + 1 && str[begin + 1] != symb + 1)
      return 2;
    else
      return 1;
  }
  if (end - begin == 1) {
    if (str[begin] == symb)
      return 0;
    else
      return 1;
  }
  tuple<int, int, char> key = {begin, end, symb};
  if (cache.count(key) == 1) {
    return cache[key];
  }
  int mid = begin + (end - begin) / 2;
  int change_left = count(begin, mid, symb);
  int change_right = count(mid, end, symb);
  int first = change_left + calc(mid, end, symb + 1);
  int second = change_right + calc(begin, mid, symb + 1);
  res = min(first, second);
  return cache[key] = res;
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    cache.clear();
    int n;
    cin >> n;
    cin >> str;
    long long res = calc(0, str.size(), 'a');
    cout << res << endl;
  }
}

### Prompt

Please formulate a CPP solution to the following problem:

You are given a string s[1 ... n] consisting of lowercase Latin letters. It is guaranteed that n = 2^k 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. 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=...=s_{n/2}=c) and the second half of the string (i.e. the string s_{n/2 + 1}s_{n/2 + 2} ... 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_{n/2 + 1}=s_{n/2 + 2}=...=s_n=c) and the first half of the string (i.e. the string s_1s_2 ... s_{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

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 = 2^k 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).

Output

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.

Example

Input


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


Output


0
7
4
5
1
1

### Response

```cpp
#include <bits/stdc++.h>
#pragma warning(disable : 4996)
using namespace std;
map<tuple<int, int, char>, int> cache;
string str;
int count(int begin, int end, char symbol) {
  int res = 0;
  for (int i = begin; i < end; i++) {
    if (str[i] != symbol) res++;
  }
  return res;
}
long long calc(int begin, int end, char symb) {
  int res = INT_MAX;
  if (end - begin == 2) {
    if (str[begin] == symb && str[begin + 1] == symb + 1 ||
        str[begin + 1] == symb && str[begin] == symb + 1)
      return 0;
    else if (str[begin] != symb && str[begin + 1] != symb &&
             str[begin] != symb + 1 && str[begin + 1] != symb + 1)
      return 2;
    else
      return 1;
  }
  if (end - begin == 1) {
    if (str[begin] == symb)
      return 0;
    else
      return 1;
  }
  tuple<int, int, char> key = {begin, end, symb};
  if (cache.count(key) == 1) {
    return cache[key];
  }
  int mid = begin + (end - begin) / 2;
  int change_left = count(begin, mid, symb);
  int change_right = count(mid, end, symb);
  int first = change_left + calc(mid, end, symb + 1);
  int second = change_right + calc(begin, mid, symb + 1);
  res = min(first, second);
  return cache[key] = res;
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    cache.clear();
    int n;
    cin >> n;
    cin >> str;
    long long res = calc(0, str.size(), 'a');
    cout << res << endl;
  }
}

```