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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns          #-}
{-# LANGUAGE CPP                   #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE OverloadedStrings     #-}
{-# LANGUAGE RecordWildCards       #-}
{-# LANGUAGE TupleSections         #-}
{-# LANGUAGE TypeFamilies          #-}

import           Control.Applicative
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bool
import qualified Data.ByteString.Char8       as B
import qualified Data.ByteString.Unsafe      as B
import           Data.Char
import           Data.Function
import qualified Data.IntMap.Strict          as IM
import qualified Data.IntSet                 as IS
import           Data.List
import qualified Data.Map.Strict             as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive.MutVar
import qualified Data.Set                    as S
import           Data.Tuple
import qualified Data.Vector                 as V
import qualified Data.Vector.Generic         as G
import qualified Data.Vector.Generic.Mutable as GM
import qualified Data.Vector.Unboxed         as U
import qualified Data.Vector.Unboxed.Mutable as UM
import           Debug.Trace
import           Foreign                     hiding (void)
import           Unsafe.Coerce

main :: IO ()
main = do
    !n <- readLn :: IO Int
    cs <- getLine
    q <- readLn :: IO Int
    ks <- map read.words <$> getLine
    mapM_ (print.solve n cs) ks

solve :: Int -> String -> Int -> Int
solve n cs k = countDMC0 k cs

countDMC0 :: Int -> String -> Int
countDMC0 k = go 0 0 0 0 0 []
  where
    go !i !freqD !freqM !freqDM !freqDMC buf rest | i == k = countDMC freqD freqM freqDM freqDMC buf rest
    go !i !freqD !freqM !freqDM !freqDMC buf ('D':rest) = go (i+1) (freqD+1) freqM freqDM freqDMC ('D':buf) rest
    go !i !freqD !freqM !freqDM !freqDMC buf ('M':rest) = go (i+1) freqD (freqM+1) (freqDM+freqD) freqDMC ('M':buf) rest
    go !i !freqD !freqM !freqDM !freqDMC buf ('C':rest) = go (i+1) freqD freqM freqDM (freqDMC+freqDM) ('C':buf) rest
    go !i !freqD !freqM !freqDM !freqDMC buf (c:rest) = go (i+1) freqD freqM freqDM freqDMC (c:buf) rest

countDMC :: Int -> Int -> Int -> Int -> String -> String -> Int
countDMC freqD0 freqM0 freqDM0 freqDMC0 = go freqDMC0 freqD0 freqM0 freqDM0 []
  where
    go !res !freqD !freqM !freqDM _ _ [] = res
    go !res !freqD !freqM !freqDM [] rs rest = go res freqD freqM freqDM (reverse rs) [] rest
    go !res !freqD !freqM !freqDM (f:fs) rs (r:rest) = go res' freqD' freqM' freqDM' fs (r:rs) rest
      where
        !freqD' = freqD - fromEnum (f == 'D') + fromEnum (r == 'D')
        !freqM' = freqM - fromEnum (f == 'M') + fromEnum (r == 'M')
        !freqDM' = freqDM - fromEnum (f == 'D') * freqM + freqD * fromEnum (r == 'M')
        !res' = res + freqDM' * fromEnum (r == 'C')