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: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.NoSuchElementException;

public class Main {
	public static void main(String[] args) {
		new Main().run();
	}

	void run() {
		Scanner sc = new Scanner();
		PrintWriter pw = new PrintWriter(System.out);
		int N = sc.nextInt();
		char[] cs = sc.next().toCharArray();
		int Q = sc.nextInt();
		int[] K = new int[Q];
		for (int i = 0; i < Q; ++i) {
			K[i] = sc.nextInt();
		}
		for (int i = 0; i < Q; ++i) {
			pw.println(solve(cs, K[i]));
		}
		pw.close();
	}

	long solve(char[] cs, int K) {
		int n = cs.length;
		int d = 0, m = 0, c = 0, dm = 0, mc = 0, dmc = 0;
		for (int i = 0; i < K; ++i) {
			if (cs[i] == 'D') {
				++d;
			} else if (cs[i] == 'M') {
				++m;
				dm += d;
			} else if (cs[i] == 'C') {
				++c;
				mc += m;
				dmc += dm;
			} else {
				continue;
			}
		}
		long ret = 0;
		for (int i = 0; i < n; ++i) {
			if (cs[i] == 'D') {
				ret += mc;
				dmc -= mc;
				dm -= m;
				--d;
			} else if (cs[i] == 'M') {
				mc -= c;
				--m;
			} else if (cs[i] == 'C') {
				--c;
			}
			int tail = i + K;
			if (i + K >= n)
				continue;
			if (cs[tail] == 'D') {
				++d;
			} else if (cs[tail] == 'M') {
				++m;
				dm += d;
			} else if (cs[tail] == 'C') {
				++c;
				mc += m;
				dmc += dm;
			}
		}
		return ret;
	}

	static class Scanner {
		private final InputStream in = System.in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;

		private boolean hasNextByte() {
			if (ptr < buflen) {
				return true;
			} else {
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (buflen <= 0) {
					return false;
				}
			}
			return true;
		}

		private int readByte() {
			if (hasNextByte())
				return buffer[ptr++];
			else
				return -1;
		}

		private boolean isPrintableChar(int c) {
			return 33 <= c && c <= 126;
		}

		private void skipUnprintable() {
			while (hasNextByte() && !isPrintableChar(buffer[ptr]))
				ptr++;
		}

		public boolean hasNext() {
			skipUnprintable();
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (isPrintableChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			long n = 0;
			boolean minus = false;
			int b = readByte();
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			if (b < '0' || '9' < b) {
				throw new NumberFormatException();
			}
			while (true) {
				if ('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				} else if (b == -1 || !isPrintableChar(b)) {
					return minus ? -n : n;
				} else {
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}

		public int nextInt() {
			return (int) nextLong();
		}
	}

	public static void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
}