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 OCaml (4.10.0) (judge verdict: Accepted)

let () = Scanf.scanf "%d\n%s" @@ fun n s ->
  let r, g, b =
    List.fold_left (fun (r, g, b) -> function
      | 'R' -> r + 1, g, b
      | 'G' -> r, g + 1, b
      | 'B' -> r, g, b + 1) (0, 0, 0) @@
    List.init (String.length s) @@ String.get s in
  let ignore =
    List.fold_left (List.fold_left ( + )) 0 @@
    List.init (String.length s / 2) @@ fun w ->
      List.init (String.length s - 2 * (w + 1)) @@ fun i ->
        if s.[i] = s.[i + w + 1] || s.[i + w + 1] = s.[i + 2 * (w + 1)] || s.[i] = s.[i + 2 * (w + 1)]
        then 0
        else 1 in
  Printf.printf "%d\n" @@ r * g * b - ignore