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 Data.List
main :: IO ()
main = do
  _ <- getLine
  s <- getLine
  let ss = zip [1,2 ..] s
  let rs = map fst $ filter (\(_, a) -> a == 'R') ss
  let gs = map fst $ filter (\(_, a) -> a == 'G') ss
  let bs = map fst $ filter (\(_, a) -> a == 'B') ss
  let ss = length [(r, g, b) | r <- rs, g <- gs, b <- bs, (abs(g - r) == abs (b - g)) ||(abs(b - r) == abs (g - b) || (abs (r- b) == abs (g - r)))]
  print $ (length rs) * (length gs) * (length bs) - ss