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<algorithm>
#include<vector>
#include<queue>
#define lol(i,n) for(int i=0;i<n;i++)
#define mod 1000000007
typedef long long ll;

using namespace std;
#define N 1000010
string s;
ll n,q,cs[N];
vector<ll> c;
void Solve(ll k){
    ll ans=0,l=0,r=0,cur=0,cnt=0;
    lol(i,n){
	for(;l<c.size()&&c[l]<i;l++){
	    cnt--;
	}
	for(;r<c.size()&&c[r]<i+k;r++){
	    cur+=max((ll)0,cs[c[r]+1]-cs[i]);
	    cnt++;
	}
	if(s[i]=='M')cur-=cnt;
	if(s[i]=='D')ans+=cur;
    }
    cout<<ans<<endl;
}
int main(){
    cin>>n>>s>>q;
    cs[0]=0;
    lol(i,n)cs[i+1]=cs[i]+(s[i]=='M');
    lol(i,n)if(s[i]=='C')c.push_back(i);
    
    lol(i,q){
	ll k;cin>>k;
	Solve(k);
    }
    return 0;
}
