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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

// 

public class Program_DPC5_C // ←Class名変更！！
{
    public static void Main()
    {
        var n = Ri();
        var s = Rca();
        var q = Ri();
        var k = Ria();
        var r = new int[k.Length];

        for (int a = 0; a < s.Length; a++)
        {
            if (s[a]=='D')
            {
                for (int b = a+1; b < s.Length; b++)
                {
                    if (s[b]=='M')
                    {
                        for (int c = b + 1; c < s.Length; c++)
                        {
                            if (s[c] == 'C')
                            {
                                var ka = c - a;
                                for (int i = 0; i < k.Length; i++)
                                {
                                    if (ka<k[i])
                                    {
                                        r[i] += 1;
                                    }

                                }


                            }
                        }

                    }
                }
            }
        }

        foreach (var item in r)
        {
            WriteLine(item);
        }
 
    } // Main

    public static string Rs() { return ReadLine(); }
    public static int Ri() { return int.Parse(ReadLine()); }
    public static long Rl() { return long.Parse(ReadLine()); }
    public static int[] Ria() { return Array.ConvertAll(ReadLine().Split(' '), int.Parse); }
    public static long[] Rla() { return Array.ConvertAll(ReadLine().Split(' '), long.Parse); }
    public static char[] Rca() { return ReadLine().ToCharArray(); }
}     // Class