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;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)

int main()
{
ll n ;
cin >> n ;
string s ;
cin >> s ;
ll q ;
cin >> q ;
vector<ll> k(q);
rep(i, q){
  cin >> k[i];
}
rep(i,q){
ll nummc=0,numm=0,numc=0,ans=0;
rep(j,k[i]){
  if(s[j]=='M')numm++;
  if(s[j]=='C'){numc++;nummc+=numm;}
}
rep(j,n-k[i]){
  if(s[j]=='D')ans+=nummc;
  if(s[j]=='M'){nummc-=numc;numm--;}
  if(s[j]=='C')numc--;
  if(s[j+k[i]]=='M')numm++;
  if(s[j+k[i]]=='C'){numc++;nummc+=numm;}
}
rep(j,k[i]){
  if(s[n-k[i]+j]=='D')ans+=nummc;
  if(s[n-k[i]+j]=='M'){nummc-=numc;numm--;}
  if(s[n-k[i]+j]=='C')numc--;
}
cout << ans << endl;
}
return 0;
}