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: Time Limit Exceeded)

open Batteries
(* 文字列をcharのlistにする *)
let explode s = List.init (String.length s) (String.get s)
let n = read_int ()
let s = read_line () |> explode |> Array.of_list
let rec loop1 i =  
  let rec loop2 i2 =
    let rec loop3 i3 ans =
      if i3 >= n then ans else 
      (* ここに処理を書く *)
        (
        if (s.(i2) != s.(i3)) && (s.(i) != s.(i3)) then (
          if (i3 - i2) != (i2 - i) then loop3 (i3+1) (ans+1) else loop3 (i3+1) ans
        ) else (
        loop3 (i3+1) ans))
    in if i2 >= n-1 then 0 else (
      if s.(i) = s.(i2) then loop2 (i2+1) else
      loop3 (i2+1) 0 + loop2 (i2+1)
    )
  in if i >= n-2 then 0 else (
    loop2 (i+1) + loop1 (i+1))


let _ = Printf.printf "%d\n" @@ loop1 0