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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main{
    public static void main(String args[]){
        Scanner in=new Scanner(System.in);
        int n=in.nextInt();

        char str[]=in.next().toCharArray();

        List<Integer> D=new ArrayList<>(),M=new ArrayList<>(),C=new ArrayList<>();

        for(int i=0;i<str.length;i++){
            switch(str[i]){
                case 'D':
                D.add(i);
                break;

                case 'M':
                M.add(i);
                break;

                case 'C':
                C.add(i);
                break;
            }
        }

        int q=in.nextInt();
        for(int i=0;i<q;i++){
            int k=in.nextInt();
            int cnt=0;

            int dp=0;
            for(int d=0;d<D.size();d++){
                dp=D.get(d);
                for(int m=0;m<M.size();m++){
                    if(M.get(m)>D.get(d)){
                        for(int c=0;c<C.size();c++){
                            if(C.get(c)>M.get(m) && C.get(c)-D.get(d)<k)cnt++;
                        }
                    }
                }
            }

            System.out.println(cnt);
        }
    }
}