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;
const int N=1e6+5;
typedef int _int;
#define int long long
int n,q,k,ans,cntd,cntm,cnts;char a[N];
_int main(){
    cin>>n>>a+1>>q;
    while(q--){
        ans=0;cin>>k;cntd=cntm=cnts=0;
        for(int i=1;i<=n;++i){
            if(a[i]=='D'){
                ++cntd;
            }if(a[i]=='M'){
                ++cntm;
                cnts+=cntd;
            }if(a[i]=='C')ans+=cnts;
            int j=i-k+1;
            if(j>0){
                if(a[j]=='D'){
                    --cntd;
                    cnts-=cntm;
                }if(a[j]=='M'){
                    --cntm;
                }
            }
        }cout<<ans<<"\n";
    }return 0;
}