Problem:
Score : 600 points

Problem Statement

In Dwango Co., Ltd., there is a content distribution system named 'Dwango Media Cluster', and it is called 'DMC' for short.

The name 'DMC' sounds cool for Niwango-kun, so he starts to define DMC-ness of a string.

Given a string S of length N and an integer k (k \geq 3),
he defines the k-DMC number of S as the number of triples (a, b, c) of integers that satisfy the following conditions:

0 \leq a < b < c \leq N - 1

S[a] = D

S[b] = M

S[c] = C

c-a < k

Here S[a] is the a-th character of the string S. Indexing is zero-based, that is, 0 \leq a \leq N - 1 holds.

For a string S and Q integers k_0, k_1, ..., k_{Q-1}, calculate the k_i-DMC number of S for each i (0 \leq i \leq Q-1).

Constraints

3 \leq N \leq 10^6

S consists of uppercase English letters

1 \leq Q \leq 75

3 \leq k_i \leq N

All numbers given in input are integers

Input

Input is given from Standard Input in the following format:

N
S
Q
k_{0} k_{1} ... k_{Q-1}

Output

Print Q lines.
The i-th line should contain the k_i-DMC number of the string S.

Sample Input 1

18
DWANGOMEDIACLUSTER
1
18

Sample Output 1

1

(a,b,c) = (0, 6, 11) satisfies the conditions.

Strangely, Dwango Media Cluster does not have so much DMC-ness by his definition.

Sample Input 2

18
DDDDDDMMMMMCCCCCCC
1
18

Sample Output 2

210

The number of triples can be calculated as 6\times 5\times 7.

Sample Input 3

54
DIALUPWIDEAREANETWORKGAMINGOPERATIONCORPORATIONLIMITED
3
20 30 40

Sample Output 3

0
1
2

(a, b, c) = (0, 23, 36), (8, 23, 36) satisfy the conditions except the last one, namely, c-a < k_i.

By the way, DWANGO is an acronym for "Dial-up Wide Area Network Gaming Operation".

Sample Output 4

30
DMCDMCDMCDMCDMCDMCDMCDMCDMCDMC
4
5 10 15 20

Sample Output 4

10
52
110
140

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>

typedef long long int int64;

int64 calc(const char *s,const int n,const int k){
  int64 res=0;
  int64 cntD=0;
  int64 cntM=0;
  int64 cntDM=0;
  int64 cntLDM=0;
  int i;
  for(i=0;i<n;i++){
    if(i>=k){
      if(s[i-k]=='D'){
	cntLDM+=cntM;
	cntD--;
      } else if(s[i-k]=='M'){
	cntM--;
      }
    }
    if(s[i]=='D'){
      cntD++;
    } else if(s[i]=='M'){
      cntM++;
      cntDM+=cntD;
    } else if(s[i]=='C'){
      res+=cntDM-cntLDM;
    }
  }
  return res;
}

void run(void){
  int n;
  scanf("%d",&n);
  char *s=(char *)calloc(n+1,sizeof(char));
  scanf("%s",s);
  int q;
  scanf("%d",&q);
  while(q--){
    int k;
    scanf("%d",&k);
    int64 ans=calc(s,n,k);
    printf("%lld\n",ans);
  }
}

int main(void){
  run();
  return 0;
}