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;

typedef long long ll;
const int N=1e6+100;
ll n,Q,k;
char s[N];
ll x[N];

int main(){
	scanf("%lld\n%s\n%lld\n",&n,s,&Q);
	for(ll i=1;i<=Q;i++) scanf("%lld\n",x+i);
	for(ll b=1;b<=Q;b++){
		ll l=x[b]-1;
		queue<ll>q;
		ll cnt=0,ans=0,res=0;
		for(ll i=0;i<n;i++){
			if(s[i]=='D') q.push(cnt);
			if(s[i]=='M') res+=(ll)q.size(),cnt++;
			if(s[i]=='C') ans+=res;
			if(i>=l){
				k=i-l;
				if(s[k]=='D'){
					res-=(cnt-q.front());
					q.pop();
				}
			}
		}
		printf("%lld\n",ans);
	}
	return 0;
}