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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)


object Main extends App {

  import scala.io.StdIn._


  val n = readLine.trim.toInt
  val chars = readLine.trim.toCharArray
  val q = readLine.trim.toInt
  val index = readLine.trim.split(' ').map(_.toInt)
  val counter = Counter(chars)
  val indices = index.zipWithIndex
  val memo = Array.tabulate(index.length){ _ ⇒ 0L}
  val result = Array.tabulate(index.length){ _ ⇒ 0L}
  println(
    search(0, chars, counter, indices, memo, result).mkString("\n")
  )
  case class Counter(chars: Array[Char]){
    private val mDCount = chars.map{c ⇒ if (c == 'D') 1 else 0 : Int}.also{a ⇒ for (i ← 1 until chars.size) a(i) += a(i - 1)}
    private val mMCount = chars.map{ c ⇒ if (c == 'M') 1 else 0 : Int}.also{ a ⇒ for (i ← 1 until chars.size) a(i) += a(i - 1)}
    def dSum(from: Int, to: Int): Int = {
      val left = (from - 1) match {
        case i if mDCount.indices.contains(i) ⇒ mDCount(i)
        case _ ⇒ 0
      }
      val right = to match {
        case i if mDCount.indices.contains(i) ⇒ mDCount(i)
        case i if i < 0 ⇒ 0
        case _ ⇒ mDCount.last
      }
      right - left
    }
    def mSum(from: Int, to: Int): Int = {
      val left = (from - 1) match {
        case i if mMCount.indices.contains(i) ⇒ mMCount(i)
        case _ ⇒ 0
      }
      val right = to match {
        case i if mMCount.indices.contains(i) ⇒ mMCount(i)
        case i if i < 0 ⇒ 0
        case _ ⇒ mMCount.last
      }
      right - left
    }
  }
  def search(currentPosition: Int, chars: Array[Char], counter: Counter, indices: Array[(Int, Int)], memo: Array[Long], result: Array[Long]): Array[Long] = {

    if (currentPosition == chars.length){
      result
    }else {
      for ((k, i) ← indices.filter{case (k, i) ⇒ chars.indices.contains(currentPosition - k) && chars(currentPosition - k) == 'D'}) {
        memo(i) -= counter.mSum(currentPosition - k + 1, currentPosition - 1)
      }
      chars(currentPosition) match {
        case 'M' ⇒
          for ((k, i) ← indices) {
            memo(i) += counter.dSum(currentPosition - k + 1, currentPosition - 1)
          }
        case 'C' ⇒
          for ((_, i) ← indices){
            result(i) += memo(i)
          }
        case _ ⇒
      }
      search(currentPosition + 1, chars, counter, indices, memo, result)
    }
  }
  implicit class Extenion[T](val value :T){
    def also(func: T ⇒ Unit): T = {
      func(value)
      value
    }
    def let[R](func: T ⇒ R): R = func(value)
  }
}