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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program atcoder
    implicit none
    integer(8) :: N,Q,k,i,j,ans,D,M,DM,qq
    integer(8),allocatable,dimension(:) :: a
    character(1000007) S
    read(*,*)N,S,Q
    allocate( a(Q) )
    read(*,*)(a(i),i=1,Q)
    do qq = 1,Q
        k = a(qq)
        ans = 0
        D = 0
        M = 0
        DM = 0
        do i = 1,k
            if(S(i:i)=='D')then
                D = D+1
            else if(S(i:i)=='M')then
                M = M+1
                DM = DM + D
            else if(S(i:i)=='C')then
                ans = ans + DM
            endif
        enddo
        do i = k+1,N
            if(S(i-K:i-K)=='D')then
                D = D-1
                DM = DM-M
            else if(S(i-K:i-K)=='M')then
                M = M-1
            end if
            if(S(i:i)=='D')then
                D = D + 1
            else if(S(i:i)=='M')then
                M = M+1
                DM = DM+D
            else if(S(i:i)=='C')then
                ans = ans + DM
            endif
        enddo
        write(*,'(I0)')ans
    end do
end program atcoder