Problem:
Score : 400 points

Problem Statement

We have a string S of length N consisting of R, G, and B.

Find the number of triples (i,~j,~k)~(1 \leq i < j < k \leq N) that satisfy both of the following conditions:

S_i \neq S_j, S_i \neq S_k, and S_j \neq S_k.

j - i \neq k - j.

Constraints

1 \leq N \leq 4000

S is a string of length N consisting of R, G, and B.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the number of triplets in question.

Sample Input 1

4
RRGB

Sample Output 1

1

Only the triplet (1,~3,~4) satisfies both conditions. The triplet (2,~3,~4) satisfies the first condition but not the second, so it does not count.

Sample Input 2

39
RBRBGRBGGBBRRGBBRRRBGGBRBGBRBGBRBBBGBBB

Sample Output 2

1800

Solution in Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

import           Control.Monad
import qualified Data.Array.IO               as IO
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Foldable
import           Data.List
import           Data.Maybe
import qualified Data.Sequence               as Seq
import qualified Data.Vector.Unboxed         as V
import qualified Data.Vector.Unboxed.Mutable as VM
import           Debug.Trace

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine
getIntVec n = V.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

readInteger = fst . fromJust . BS.readInteger
readIntegerList = map readInteger . BS.words
getInteger = readInteger <$> BS.getLine
getIntegerList = readIntegerList <$> BS.getLine

main = do
  n <- getInt
  s <- getLine

  let checkIdx []     rs gs bs _ = (V.fromList rs, V.fromList gs, V.fromList bs)
      checkIdx (c:cs) rs gs bs i | c == 'R' = checkIdx cs (i:rs) gs bs (i+1)
                                 | c == 'G' = checkIdx cs rs (i:gs) bs (i+1)
                                 | c == 'B' = checkIdx cs rs gs (i:bs) (i+1)

      (rs, gs, bs) = checkIdx s [] [] [] 1 :: (V.Vector Int, V.Vector Int, V.Vector Int)

  ans <- VM.new 1
  VM.set ans (0::Int)

  let goodijk x y z = let [i, j, k] = sort [x, y, z]
                      in k - j /= j - i

  V.forM_ rs $ \i -> do
    V.forM_ gs $ \j -> do
      let c = V.length $ V.filter (\k -> goodijk i j k) bs
      t <- VM.read ans 0
      VM.write ans 0 (t+c)

  res <- VM.read ans (0::Int)
  print res