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: Runtime Error)

import java.util.ArrayList;
import java.util.Scanner;

public class Main {
	public static void main(String args[]) {
		Scanner scn = new Scanner(System.in);
		ArrayList<Integer> D = new ArrayList<Integer>();
		ArrayList<Integer> M = new ArrayList<Integer>();
		ArrayList<Integer> C = new ArrayList<Integer>();


		int N = scn.nextInt();
		int[] MM = new int[N];
		int[] CC = new int[N];

		scn.nextLine();
		String S = scn.nextLine();
		for(int i = 0;i < N;i++) {
			char c = S.charAt(i);

			switch(c) {
			case 'D':
				D.add(i);
				break;
			case 'M':
				M.add(i);
				if(i != 0) {
					MM[i] = MM[i-1] + 1;
				}else {
					MM[i] = 1;
				}
				break;
			case 'C':
				C.add(i);
				if(i != 0) {
					CC[i] = CC[i-1] + 1;
				}else {
					CC[i] = 1;
				}
				break;
			default:
			}
		}

		int Q = scn.nextInt();
		int K[] = new int[Q];
		int k_max = 0;
		for(int i = 0; i < Q;i++) {
			int k = scn.nextInt();
			K[i] = k;
			k_max = Math.max(k,k_max);

			System.out.println(DMC(D,M,CC,k));
		}



		scn.close();
	}

	public static int DMC(ArrayList<Integer> D,ArrayList<Integer> M,int[] CC,int k) {
		int ans = 0;
		for(int i = 0;i < D.size();i++) {
			int a = D.get(i);
			for(int j = 0;j < M.size();j++) {
				int b = M.get(j);
				if(b < a)continue;
				if(b-a > k)break;

				ans += CC[a + k-1] - CC[b];
			}
		}
		return ans;
	}

	public static int DMC_check(ArrayList<Integer> D,ArrayList<Integer> M,ArrayList<Integer> C,int K) {
		int ans = 0;
		int Ds = D.size(), Ms = M.size(), Cs = C.size();

		for(int i = 0;i < Ds;i++) {
			int a = D.get(i);
			for(int j = 0;j < Ms;j++) {
				int b = M.get(j);
				if(b - a >= K)break;
				if(b < a)continue;

				for(int k = 0;k < Cs;k++) {
					int c = C.get(k);
					if(c - a >= K)break;
					if( c < b || c < a)continue;
					ans++;
				}
			}
		}
		return ans;
	}
}