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
#include "bits/stdc++.h"
using namespace std;
long long a[2][1000001];
char b[1000001];
int main()
{
	int n, q;
	scanf("%d\n", &n);
	for(int i = 1; i <= n; ++i)
	{
		scanf("%c", &b[i]);
		switch(b[i])
		{
			case 'D':
				a[0][i] = 1;
				break;
			case 'M':
				a[1][i] = 1;
				break;
		}
		for(int j = 0; j < 2; ++j) 
		{
			a[j][i] += a[j][i - 1]; 
		}
	}
	scanf("%d", &q);
	for(int i = 0, j; i < q; ++i)
	{
		scanf("%d", &j);
		long long total = 0, dm = 0;
		for(int k = 1; k <= n; k++)
		{
			if(k - j >= 1) 
			{
				if(b[k - j] == 'D')
				{
					dm -= a[1][k - 1] - a[1][k - j - 1];
				}
			}
			switch(b[k])
			{
				case 'M':
					dm += a[0][k] - a[0][max(0, k - j)]; 
					break;
				case 'C':
					total += dm;
					break;
			}
		}
		printf("%lld\n", total);
	}
}