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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

DBG = !true
n = gets.to_i
s = gets.chomp!
q = gets.to_i
ks = gets.split.map{|x| x.to_i}

def selgoodc(d,k,cs)
  a = []
  for c in cs
    a << c if d < c && c < d+k
  end
  return a
end

def selgoodm(d,c,ms)
  return selgoodc(d,c-d,ms)
end

ds = []
ms = []
cs = []
for i in 0...s.size
  ds << i if s[i] == 'D'
  ms << i if s[i] == 'M'
  cs << i if s[i] == 'C'
end

if DBG
  print "----\n"
  print ds
  print "----\n"
  print ms
  print "----\n"
  print cs
  print "----\n"
end

for k in ks
  sum = 0
  for d in ds
    goodcs = selgoodc(d,k,cs)
    if DBG
      printf("k:%d d:%d goodcs:", k, d)
      print goodcs
      print "\n"
    end

    for c in goodcs
      goodms = selgoodm(d,c,ms)
      if DBG
        printf("c:%d goodms:", c)
        print goodms
        printf("  -- add %d\n", goodms.size)
      end
      sum += goodms.size
    end
  end
  puts sum
end