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;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		string str = Console.ReadLine();
		int Q = int.Parse(Console.ReadLine());
		string[] str2 = Console.ReadLine().Split();
		var list = new List<int[]>();
		for(var i=0;i<N;i++){
			string s = str.Substring(i,1);
			switch(s){
				case "D":
					list.Add(new int[2]{i,0});
					break;
				case "M":
					list.Add(new int[2]{i,1});
					break;
				case "C":
					list.Add(new int[2]{i,2});
					break;
			}
		}
		int listct = list.Count;
		for(var i=0;i<Q;i++){
			int A = int.Parse(str2[i]);
			int Dt = 0;
			int Mt = 0;
			long DM = 0;
			long ans = 0;
			int ai = 0;
			int ai2 = 0;
			while(ai < listct){
				while(list[ai2][0]+A <= list[ai][0]){
					switch(list[ai2][1]){
						case 0:
							Dt -= 1;
							DM -= Mt;
							break;
						case 1:
							Mt -= 1;
							break;
					}
					ai2 += 1;
				}
				switch(list[ai][1]){
					case 0:
						Dt += 1;
						break;
					case 1:
						Mt += 1;
						DM += Dt;
						break;
					default:
						ans += DM;
						break;
				}
				ai += 1;
			}
			Console.WriteLine(ans);
		}
	}
}