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)

main = do
  n <- readLn
  s <- getLine
  let r = length .filter (== 'R') $ s
      g = length .filter (== 'G') $ s
      b = length .filter (== 'B') $ s
      triplet = [(i,j,k) | i <- [0..n-1], j <- [i+1..n-1], let k = 2*j - i, k < n]
      diff = length . filter (\(i,j,k) -> (s!!i /= s!!j) && (s!!j /= s!!k) && (s!!i /= s!!k)) $ triplet
      rgb = r * g * b - diff
  print $ rgb