#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
using pcc = pair<char, char>;
using pdd = pair<double, double>;
template <typename T>
inline T Set(T &n, T p) {
  T on = 1;
  return n = n | (on << p);
}
template <typename T>
inline T Reset(T &n, T p) {
  T on = 1;
  return n = n & (~(on << p));
}
template <typename T>
inline bool Check(T n, T p) {
  T on = 1;
  return (bool)(n & (on << p));
}
template <typename T>
inline T Toggle(T &n, T p) {
  T on = 1;
  return n = n ^ (on << p);
}
template <typename T>
T POW(T a, T b) {
  T x = 1;
  while (b) {
    if (b & 1) x *= a;
    a *= a;
    b >>= 1;
  }
  return x;
}
template <typename T>
T mPOW(T a, T b, T M) {
  T x = 1;
  while (b) {
    if (b & 1) x = (x * a) % M;
    a = (a * a) % M;
    b >>= 1;
  }
  return x;
}
template <typename T>
T Sqrt(T a) {
  T x = (T)sqrt(a);
  if ((x + 1) * (x + 1) == a) x++;
  return x;
}
int chk(string &s, int l, int r, char c) {
  int cnt = 0;
  for (; l <= r; l++) {
    if (s[l] != c) cnt++;
  }
  return cnt;
}
int call(string &s, int l, int r, char ch) {
  if (l == r) {
    if (ch == s[l])
      return 0;
    else
      return 1;
  }
  int a, b, c, d;
  a = l;
  b = l + ((r - l) / 2);
  c = b + 1;
  d = r;
  int ret1, ret2;
  ret1 = call(s, a, b, ch + 1) + chk(s, c, d, ch);
  ret2 = call(s, c, d, ch + 1) + chk(s, a, b, ch);
  return min(ret1, ret2);
}
int main(int argc, char *argv[]) {
  int testcase, cs = 1;
  cin >> testcase;
  while (testcase--) {
    int n;
    string s;
    cin >> n >> s;
    int ans = call(s, 0, n - 1, 'a');
    printf("%d", (ans));
    printf("\n");
  }
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
using pcc = pair<char, char>;
using pdd = pair<double, double>;
template <typename T>
inline T Set(T &n, T p) {
  T on = 1;
  return n = n | (on << p);
}
template <typename T>
inline T Reset(T &n, T p) {
  T on = 1;
  return n = n & (~(on << p));
}
template <typename T>
inline bool Check(T n, T p) {
  T on = 1;
  return (bool)(n & (on << p));
}
template <typename T>
inline T Toggle(T &n, T p) {
  T on = 1;
  return n = n ^ (on << p);
}
template <typename T>
T POW(T a, T b) {
  T x = 1;
  while (b) {
    if (b & 1) x *= a;
    a *= a;
    b >>= 1;
  }
  return x;
}
template <typename T>
T mPOW(T a, T b, T M) {
  T x = 1;
  while (b) {
    if (b & 1) x = (x * a) % M;
    a = (a * a) % M;
    b >>= 1;
  }
  return x;
}
template <typename T>
T Sqrt(T a) {
  T x = (T)sqrt(a);
  if ((x + 1) * (x + 1) == a) x++;
  return x;
}
int chk(string &s, int l, int r, char c) {
  int cnt = 0;
  for (; l <= r; l++) {
    if (s[l] != c) cnt++;
  }
  return cnt;
}
int call(string &s, int l, int r, char ch) {
  if (l == r) {
    if (ch == s[l])
      return 0;
    else
      return 1;
  }
  int a, b, c, d;
  a = l;
  b = l + ((r - l) / 2);
  c = b + 1;
  d = r;
  int ret1, ret2;
  ret1 = call(s, a, b, ch + 1) + chk(s, c, d, ch);
  ret2 = call(s, c, d, ch + 1) + chk(s, a, b, ch);
  return min(ret1, ret2);
}
int main(int argc, char *argv[]) {
  int testcase, cs = 1;
  cin >> testcase;
  while (testcase--) {
    int n;
    string s;
    cin >> n >> s;
    int ans = call(s, 0, n - 1, 'a');
    printf("%d", (ans));
    printf("\n");
  }
  return 0;
}

```