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)

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
//#define int long long
template<class T> inline bool chmax(T& a,T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a,T b) { if (a > b) { a = b; return 1; } return 0; }

int N;
string S;
long long M, C, P;

void add (int i) {
    if (S[i] == 'M') M++;
    else if (S[i] == 'C') { C++; P += M; }
}

void erase (int i) {
    if (S[i] == 'M') { M--; P -= C; }
    else if (S[i] == 'C') C--;
}

long long solve(int K) {
    long long ans = 0;
    M = 0, C = 0, P = 0;
    int left = 0;
    for (int right = 0; right < N;) {
        while (left < N && abs(right-left) < K) add(left++);
        if (S[right] == 'D') ans += P;
        erase(right++);
    }
    return ans;
}

int main() {
    int Q;
    cin >> N >> S >> Q;
    for (int i = 0; i < Q; i++) {
        int k; cin >> k;
        cout << solve(k) << endl;
    }
    return 0;
}