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 <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <queue>
#include <vector>
#include <utility>
#define maxn 1000005
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
int n,Q;
char s[maxn];
ll calc(int k){
	ll cntc = 0,cntm = 0,ans = 0,tmp = 0;
	int j = n;
	for(int i=n;i>=1;i--){
		if(i + k - 1 < j){
			if(s[j] == 'M'){
				cntm--;
			}else if(s[j] == 'C'){
				cntc--;
				tmp -= cntm;
			}
			j--;
		}
		if(s[i] == 'M'){
			cntm++;
			tmp += cntc;
		}else if(s[i] == 'C'){
			cntc++;
		}else if(s[i] == 'D'){
			ans += tmp;
		}
	}
	return ans;
}
int main(){
	scanf("%d",&n);
	scanf("%s",s + 1);
	scanf("%d",&Q);
	while(Q--){
		int k;
		scanf("%d",&k);
		printf("%lld\n",calc(k));
	}
	return 0;
}
