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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (sb-int:defconstant-eqx OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0))
    #'equal)
  #+swank (ql:quickload '(:cl-debug-print :fiveam) :silent t)
  #-swank (set-dispatch-macro-character
           #\# #\> (lambda (s c p) (declare (ignore c p)) (read s nil nil t))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
(declaim (inline read-line-into))
(defun read-line-into (buffer-string &key (in *standard-input*) (term-char #\Space))
  "Receives ASCII inputs and returns multiple values: the string and the end
position.

This function calls READ-BYTE to read characters though it calls READ-CHAR
instead on SLIME because SLIME's IO is not bivalent."
  (declare (inline read-byte)
           #-swank (sb-kernel:ansi-stream in))
  (loop for c of-type base-char =
           #-swank (code-char (read-byte in nil #.(char-code #\Newline)))
           #+swank (read-char in nil #\Newline)
        for idx from 0
        until (char= c #\Newline)
        do (setf (char buffer-string idx) c)
        finally (when (< idx (length buffer-string))
                  (setf (char buffer-string idx) term-char))
                (return (values buffer-string idx))))

(defmacro dbg (&rest forms)
  #+swank
  (if (= (length forms) 1)
      `(format *error-output* "~A => ~A~%" ',(car forms) ,(car forms))
      `(format *error-output* "~A => ~A~%" ',forms `(,,@forms)))
  #-swank (declare (ignore forms)))

(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~A" b)) () '(unsigned-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~A" b)) () '(signed-byte ,b))) bits)))
(define-int-types 2 4 7 8 15 16 31 32 62 63 64)

(declaim (inline println))
(defun println (obj &optional (stream *standard-output*))
  (let ((*read-default-float-format* 'double-float))
    (prog1 (princ obj stream) (terpri stream))))

(defconstant +mod+ 1000000007)

;;;
;;; Body
;;;

(defun main ()
  (declare #.OPT)
  (let* ((n (read))
         (s (let ((s (make-string n :element-type 'base-char)))
              (read-line-into s)))
         (q (read))
         (ks (make-array q :element-type 'uint32))
         (cumul-d (make-array (+ n 1) :element-type 'uint31))
         (cumul-m (make-array (+ n 1) :element-type 'uint31))
         (cumul-c (make-array (+ n 1) :element-type 'uint31))
         (cumul-dm (make-array (+ n 1) :element-type 'uint62))
         (total-dmc 0))
    (declare (uint31 n q)
             (uint62 total-dmc)
             (simple-base-string s))
    (dotimes (i q)
      (setf (aref ks i) (read)))
    (dotimes (i n)
      (setf (aref cumul-d (+ i 1))
            (+ (aref cumul-d i)
               (if (char= #\D (aref s i)) 1 0)))
      (setf (aref cumul-m (+ i 1))
            (+ (aref cumul-m i)
               (if (char= #\M (aref s i)) 1 0)))
      (setf (aref cumul-c (+ i 1))
            (+ (aref cumul-c i)
               (if (char= #\C (aref s i)) 1 0)))
      (setf (aref cumul-dm (+ i 1))
            (if (char= #\M (aref s i))
                (+ (aref cumul-dm i) (aref cumul-d i))
                (aref cumul-dm i))))
    (dotimes (i n)
      (when (char= #\M (aref s i))
        (incf total-dmc (* (aref cumul-d i)
                           (- (aref cumul-c n) (aref cumul-c i))))))
    (labels ((calc (k)
               (let ((res 0))
                 (declare (uint62 res))
                 (dotimes (z n)
                   (when (char= #\C (aref s z))
                     (incf res (aref cumul-dm (max 0 (+ 1 (- z k)))))
                     (incf res (* (aref cumul-d (max 0 (+ 1 (- z k))))
                                  (- (aref cumul-m z)
                                     (aref cumul-m (max 0 (+ 1 (- z k)))))))))
                 res)))
      (sb-int:dovector (k ks)
        (println (- total-dmc (calc k)))))))

#-swank (main)