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.

Examples

Input

18
DWANGOMEDIACLUSTER
1
18


Output

1


Input

18
DDDDDDMMMMMCCCCCCC
1
18


Output

210


Input

54
DIALUPWIDEAREANETWORKGAMINGOPERATIONCORPORATIONLIMITED
3
20 30 40


Output

0
1
2


Input

30
DMCDMCDMCDMCDMCDMCDMCDMCDMCDMC
4
5 10 15 20


Output

10
52
110
140
import java.util.Arrays;
import java.util.Scanner;

public class Main{
	public static void main(String args[]) {
	
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		String s=sc.next();
		int q=sc.nextInt();
		int k[]=new int[q];

		
		for(int i=0;i<q;++i) {
			k[i]=sc.nextInt();
			int countd=0, countm=0;
			long ans=0,next=0;
			for (int m=0;m<n;++m) {
				
				if(m-k[i]>=0) {
				if(s.charAt(m-k[i])=='D') {--countd; next=next-countm;}
				else if(s.charAt(m-k[i])=='M')--countm; 
				}
				
				if(s.charAt(m)=='D')++countd;
				else if(s.charAt(m)=='M') {++countm; next=next+countd;} 
				else if(s.charAt(m)=='C')ans=ans+next;
			}
			System.out.println(ans);
		}
		
	}
}
