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: Runtime Error)

using System;

namespace C
{
	internal class Program
	{
		public static void Main(string[] args)
		{
			var n = int.Parse(Console.ReadLine());
			var s = Console.ReadLine();
			var q = int.Parse(Console.ReadLine());
			var kInputs = Console.ReadLine().Split();
			var ks = new int[q];
			for (var i = 0; i < q; i++) { ks[i] = int.Parse(kInputs[i]); }

			var numD = 0;
			var numC = 0;
			var indexD = new int[1000000];
			var indexC = new int[1000000];
			for (var i = 0; i < n; i++)
			{
				switch (s[i])
				{
				case 'D':
					indexD[numD++] = i;
					break;
				case 'C':
					indexC[numC++] = i;
					break;
				}
			}

			var dc = new MatrixDC[numD, numC];
			for (var i = 0; i < numD; i++)
			{
				for (var j = 0; j < numC; j++)
				{
					dc[i, j] = new MatrixDC();
					var tmp = dc[i, j].Distance = indexC[j] - indexD[i];
					if (tmp < 0) { dc[i, j].NumM = 0; }
				}
			}

			for (var i = 0; i < n; i++)
			{
				if (s[i] != 'M') { continue; }

				for (var j = 0; j < numD; j++)
				{
					if (i < indexD[j]) { continue; }

					for (var k = 0; k < numC; k++)
					{
						if (i > indexC[k]) { continue; }

						dc[j, k].NumM++;
					}
				}
			}

			foreach (var k in ks)
			{
				var result = 0;
				foreach (var cell in dc)
				{
					if (cell.Distance >= k) { continue; }

					result += cell.NumM;
				}

				Console.WriteLine(result);
			}
		}
	}

	class MatrixDC
	{
		public int Distance { get; set; }
		public int NumM { get; set; }
	}
}