Codeforces Round #656 (Div. 3) D. a-Good String

Codeforces Round #656 (Div. 3) D. a-Good String

题目链接

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.

Input

The first line of the input contains one integer t (1≤t≤2e4) — 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 2e5 (∑n≤2e5).

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

久违地补补 cf
这题典型的 DFS，每次对半 DFS，当 $l=r$ 时，更新一下答案即可，AC代码如下：

#include
using namespace std;
typedef long long ll;
const int N=2e5+5;
char s[N];
int ans;
void dfs(int l,int r,int cnt,char c){
    if(l==r){
        if(s[l]!=c) cnt++;
        ans=min(ans,cnt);
        return ;
    }
    int cnt1=0,cnt2=0,mid=l+r>>1;
    for(int i=l;i<=mid;i++) if(s[i]!=c) cnt1++;
    for(int i=mid+1;i<=r;i++) if(s[i]!=c) cnt2++;
    dfs(l,mid,cnt+cnt2,c+1);
    dfs(mid+1,r,cnt+cnt1,c+1);
}

int main(){
    int t,n;
    scanf("%d",&t);
    while(t--){
        scanf("%d%s",&n,s+1);
        ans=n;
        dfs(1,n,0,'a');
        printf("%d\n",ans);
    }
    return 0;
}