Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

18
DWANGOMEDIACLUSTER
1
18

Sample Output 1

1

(a,b,c) = (0, 6, 11) satisfies the conditions.

Strangely, Dwango Media Cluster does not have so much DMC-ness by his definition.

Sample Input 2

18
DDDDDDMMMMMCCCCCCC
1
18

Sample Output 2

210

The number of triples can be calculated as 6\times 5\times 7.

Sample Input 3

54
DIALUPWIDEAREANETWORKGAMINGOPERATIONCORPORATIONLIMITED
3
20 30 40

Sample Output 3

0
1
2

(a, b, c) = (0, 23, 36), (8, 23, 36) satisfy the conditions except the last one, namely, c-a < k_i.

By the way, DWANGO is an acronym for "Dial-up Wide Area Network Gaming Operation".

Sample Output 4

30
DMCDMCDMCDMCDMCDMCDMCDMCDMCDMC
4
5 10 15 20

Sample Output 4

10
52
110
140

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
typedef long long ll;
const ll INF = 1e9;
const ll MOD = 1e9+7;
const ll LINF = 1e18;
using namespace std;

#define dump(x)  cout << #x << " = " << (x) << endl;
#define YES(n) cout << ((n) ? "YES" : "NO"  ) << endl
#define Yes(n) cout << ((n) ? "Yes" : "No"  ) << endl
#define POSSIBLE(n) cout << ((n) ? "POSSIBLE" : "IMPOSSIBLE"  ) << endl
#define Possible(n) cout << ((n) ? "Possible" : "Impossible"  ) << endl
#define possible(n) cout << ((n) ? "possible" : "impossible"  ) << endl

#define SANKOU(n,a,b) cout << ((n) ? (#a) : (#b) ) << endl

#define FOR(i,a,b) for(ll i=(a);i<(b);++i)
#define REP(i,n) for(ll i=0;i<(n);++i)
#define REPR(i,n) for(ll i=n;i>=0;i--)

#define FOREACH(x,a) for(auto&& (x) : (a) )

#define WFA(d,v) REP(k,v)REP(i,v)REP(j,v)d[i][j]=min(d[i][j],d[i][k]+d[k][j])

#define SCOUT(x) cout<<(x)<<" "
#define ENDL cout<<endl

#define VECCIN(x) for(auto&youso_: (x) )cin>>youso_
#define VECIN2(x,y) REP(i,x.size())cin>>x[i]>>y[i]
#define VECCOUT(x) if(1){for(auto tt=x.begin();tt!=x.end();tt++){if(tt!=x.begin())cout<<" ";cout<<(*tt);}cout<<endl;}

#define ALL(obj) (obj).begin(),(obj).end()

#define EXIST(n,x) (find(ALL(n),x)!=n.end())
#define UNIQUE(obj) sort(ALL( obj )); obj.erase(unique(ALL(obj)),obj.end())
#define EN(x) if(1){cout<<#x<<endl;return 0;}
#define COUT(x) cout<<(x)<<endl
void CINT(){}
template <class Head,class... Tail>
void CINT(Head&& head,Tail&&... tail){
    cin>>head;
    CINT(move(tail)...);
}
#define CIN(...) ll __VA_ARGS__;CINT(__VA_ARGS__)
#define LCIN(...) ll __VA_ARGS__;CINT(__VA_ARGS__)
#define SCIN(...) string __VA_ARGS__;CINT(__VA_ARGS__)

template <class T = ll>
T IN(){T x;cin>>x;return (x);}

template <class Head>
void VT(Head head){}
template <class Head,class Seco,class... Tail>
void VT(Head&& head,Seco&& seco,Tail&&... tail){
    seco.resize(head);
    VT(head,move(tail)...);
}
void VT2(){}
template <class Head,class... Tail>
void VT2(Head&& head,Tail&&... tail){
  VECCIN(head);
  VT2(move(tail)...);
}

template <class Head>
void VT3(Head&& head){}
template <class Head,class Seco,class... Tail>
void VT3(Head&& head,Seco&& seco,Tail&&... tail){
  seco[head]=IN();
  VT3(head,move(tail)...);
}

#define VC1(n,...) V __VA_ARGS__;VT(n,__VA_ARGS__);VT2(__VA_ARGS__); //aaabbbccc
#define VC2(n,...) V __VA_ARGS__;VT(n,__VA_ARGS__);REP(i,n)VT3(i,__VA_ARGS__); //abcabcabc

// #include <boost/multiprecision/cpp_ll.hpp>
// using namespace boost::multiprecision; // cpp_ll

#define P pair<ll,ll>
#define V vector<ll>
#define M map<ll,ll>
#define S set<ll>

#define pb(a) push_back(a)
#define mp make_pair


signed main(){
    CIN(n);SCIN(s);CIN(q);

    V crui(n+1, 0);
    REP(i,n)crui[i+1]=crui[i]+(s[i]=='C');

    REP(hog,q){
        // ll cou = 0;
        CIN(k);

        V hoge(n,0);
        /*

        REP(i,n){
            FOR(j,i+2,n){
                if(j - i < k && s[i] == 'D' && s[j] == 'C'){
                    FOR(l,i+1,j){
                        if(s[l] == 'M'){
                            // COUT(s.substr(i,j-i+1));
                            ++cou;
                        }
                    }
                }
            }
        }
        dump(cou);
        */

        V imo(n,0);
        REP(i,n){
            if(s[i] == 'D'){
                hoge[i] = crui[min(i+k,n)] - crui[i];
                ++imo[i];
                if(i + k < n)
                    --imo[i+k];
            }
        }
        REP(i,n-1)imo[i+1]+=imo[i];

        V bimo(n,0);
        REP(i,n){
            if(s[i] == 'C'){
                bimo[i] += imo[i];
            }
            if(s[i] == 'D'){
                bimo[i] -= hoge[i];
                // --bimo[i];
            }
        }
        REPR(i,n-2)bimo[i]+=bimo[i+1];
        ll ans = 0;
        REP(i,n){
            if(s[i] == 'M' && bimo[i] >= 0){
                ans += bimo[i];
            }
        }
        COUT(ans);
    }
}