#include <bits/stdc++.h>
using namespace std;
const bool testcases = true;
int64_t seed;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
inline int64_t rnd(int64_t l = 0, int64_t r = INT_MAX) {
  return uniform_int_distribution<int64_t>(l, r)(rng);
}
inline bool in_range(int64_t a, int64_t l, int64_t r) {
  return (a >= l && a <= r);
}
template <typename H, typename... T>
void inp(H &head) {
  cin >> head;
}
template <typename H, typename... T>
void inp(H &head, T &...tail) {
  cin >> head;
  inp(tail...);
}
template <typename T>
bool isPrime(T n) {
  for (T i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return n >= 2;
}
template <typename T>
inline istream &operator>>(istream &in, vector<T> &a) {
  for (T &x : a) in >> x;
  return in;
}
template <typename T, typename U>
inline istream &operator>>(istream &in, pair<T, U> &a) {
  in >> a.first >> a.second;
  return in;
}
void solve();
void fast_io();
int32_t main(int32_t argc, char **argv) {
  fast_io();
  int64_t TC = 1;
  if (testcases) cin >> TC;
  for (int64_t tc = 1; tc <= TC; tc++) solve(), 108;
  return 0;
}
string s;
const int64_t INF = INT_MAX;
int64_t solve(int64_t req, int64_t l, int64_t r) {
  char ch = req + 'a';
  if (req >= 26) return INF;
  if (l == r) return (s[l] == ch ? 0 : 1);
  int64_t mid = (l + r) / 2;
  int64_t L = solve(req + 1, l, mid);
  int64_t R = solve(req + 1, mid + 1, r);
  for (int64_t i = mid + 1; i <= r; i++) L += (s[i] == ch ? 0 : 1);
  for (int64_t i = l; i <= mid; i++) R += (s[i] == ch ? 0 : 1);
  return min(L, R);
}
void solve() {
  int64_t n;
  cin >> n >> s;
  int64_t ans = solve(0, 0, n - 1);
  cout << ans << '\n';
}
void fast_io() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
}

### Prompt

Your task is to create 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>
using namespace std;
const bool testcases = true;
int64_t seed;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
inline int64_t rnd(int64_t l = 0, int64_t r = INT_MAX) {
  return uniform_int_distribution<int64_t>(l, r)(rng);
}
inline bool in_range(int64_t a, int64_t l, int64_t r) {
  return (a >= l && a <= r);
}
template <typename H, typename... T>
void inp(H &head) {
  cin >> head;
}
template <typename H, typename... T>
void inp(H &head, T &...tail) {
  cin >> head;
  inp(tail...);
}
template <typename T>
bool isPrime(T n) {
  for (T i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return n >= 2;
}
template <typename T>
inline istream &operator>>(istream &in, vector<T> &a) {
  for (T &x : a) in >> x;
  return in;
}
template <typename T, typename U>
inline istream &operator>>(istream &in, pair<T, U> &a) {
  in >> a.first >> a.second;
  return in;
}
void solve();
void fast_io();
int32_t main(int32_t argc, char **argv) {
  fast_io();
  int64_t TC = 1;
  if (testcases) cin >> TC;
  for (int64_t tc = 1; tc <= TC; tc++) solve(), 108;
  return 0;
}
string s;
const int64_t INF = INT_MAX;
int64_t solve(int64_t req, int64_t l, int64_t r) {
  char ch = req + 'a';
  if (req >= 26) return INF;
  if (l == r) return (s[l] == ch ? 0 : 1);
  int64_t mid = (l + r) / 2;
  int64_t L = solve(req + 1, l, mid);
  int64_t R = solve(req + 1, mid + 1, r);
  for (int64_t i = mid + 1; i <= r; i++) L += (s[i] == ch ? 0 : 1);
  for (int64_t i = l; i <= mid; i++) R += (s[i] == ch ? 0 : 1);
  return min(L, R);
}
void solve() {
  int64_t n;
  cin >> n >> s;
  int64_t ans = solve(0, 0, n - 1);
  cout << ans << '\n';
}
void fast_io() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
}

```