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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading;

public class Solver
{
    public void Solve()
    {
        int n = ReadInt();
        string s = ReadToken();

        //var t = s.ToCharArray();
        //for (int i = 0; i < n; i++)
        //    if (t[i] != 'D' && t[i] != 'M' && t[i] != 'C')
        //        t[i] = ' ';
        //s = new string(t);
        //Write(s);
        
        int q = ReadInt();
        for (int i = 0; i < q; i++)
        {
            int d = ReadInt();
            int mc = 0, cc = 0;
            long tc = 0;
            for (int j = 0; j < d - 1; j++)
                if (s[j] == 'M')
                    mc++;
                else if (s[j] == 'C')
                {
                    tc += mc;
                    cc++;
                }
            long ans = 0;
            for (int j = 0; j < n; j++)
            {
                if (j + d - 1 < n)
                {
                    if (s[j + d - 1] == 'M')
                        mc++;
                    else if (s[j + d - 1] == 'C')
                    {
                        tc += mc;
                        cc++;
                    }
                }

                if (s[j] == 'D')
                    ans += tc;
                else if (s[j] == 'M')
                {
                    tc -= cc;
                    mc--;
                }
                else if (s[j] == 'C')
                    cc--;
            }

            Write(ans);
        }
    }

    #region Main

    protected static TextReader reader;
    protected static TextWriter writer;
    static void Main()
    {
#if DEBUG
        reader = new StreamReader("..\\..\\input.txt");
        //reader = new StreamReader(Console.OpenStandardInput());
        writer = Console.Out;
        //writer = new StreamWriter("..\\..\\output.txt");
#else
        reader = new StreamReader(Console.OpenStandardInput());
        writer = new StreamWriter(Console.OpenStandardOutput());
        //reader = new StreamReader("input.txt");
        //writer = new StreamWriter("output.txt");
#endif
        try
        {
            new Solver().Solve();
            //var thread = new Thread(new Solver().Solve, 1024 * 1024 * 128);
            //thread.Start();
            //thread.Join();
        }
        catch (Exception ex)
        {
#if DEBUG
            Console.WriteLine(ex);
#else
            throw;
#endif
        }
        reader.Close();
        writer.Close();
    }

    #endregion

    #region Read / Write
    private static Queue<string> currentLineTokens = new Queue<string>();
    private static string[] ReadAndSplitLine() { return reader.ReadLine().Split(new[] { ' ', '\t', }, StringSplitOptions.RemoveEmptyEntries); }
    public static string ReadToken() { while (currentLineTokens.Count == 0)currentLineTokens = new Queue<string>(ReadAndSplitLine()); return currentLineTokens.Dequeue(); }
    public static int ReadInt() { return int.Parse(ReadToken()); }
    public static long ReadLong() { return long.Parse(ReadToken()); }
    public static double ReadDouble() { return double.Parse(ReadToken(), CultureInfo.InvariantCulture); }
    public static int[] ReadIntArray() { return ReadAndSplitLine().Select(int.Parse).ToArray(); }
    public static long[] ReadLongArray() { return ReadAndSplitLine().Select(long.Parse).ToArray(); }
    public static double[] ReadDoubleArray() { return ReadAndSplitLine().Select(s => double.Parse(s, CultureInfo.InvariantCulture)).ToArray(); }
    public static int[][] ReadIntMatrix(int numberOfRows) { int[][] matrix = new int[numberOfRows][]; for (int i = 0; i < numberOfRows; i++)matrix[i] = ReadIntArray(); return matrix; }
    public static int[][] ReadAndTransposeIntMatrix(int numberOfRows)
    {
        int[][] matrix = ReadIntMatrix(numberOfRows); int[][] ret = new int[matrix[0].Length][];
        for (int i = 0; i < ret.Length; i++) { ret[i] = new int[numberOfRows]; for (int j = 0; j < numberOfRows; j++)ret[i][j] = matrix[j][i]; } return ret;
    }
    public static string[] ReadLines(int quantity) { string[] lines = new string[quantity]; for (int i = 0; i < quantity; i++)lines[i] = reader.ReadLine().Trim(); return lines; }
    public static void WriteArray<T>(IEnumerable<T> array) { writer.WriteLine(string.Join(" ", array)); }
    public static void Write(params object[] array) { WriteArray(array); }
    public static void WriteLines<T>(IEnumerable<T> array) { foreach (var a in array)writer.WriteLine(a); }
    private class SDictionary<TKey, TValue> : Dictionary<TKey, TValue>
    {
        public new TValue this[TKey key]
        {
            get { return ContainsKey(key) ? base[key] : default(TValue); }
            set { base[key] = value; }
        }
    }
    private static T[] Init<T>(int size) where T : new() { var ret = new T[size]; for (int i = 0; i < size; i++)ret[i] = new T(); return ret; }
    #endregion
}