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)

open Batteries
(* charのカウント *)
let count_char target str =
  let rec count lst =
    match lst with
    | [] -> 0
    | first :: rest -> if first = target then 1 + count rest else count rest
  in let explode s = List.init (String.length s) (String.get s)
  in count @@ explode str
(* 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 ()
let s2 = s |> explode |> Array.of_list

let r = count_char 'R' s
let g = count_char 'G' s
let b = count_char 'B' s
let rgb = r * g * b
let rec loop i ans2 =
  let rec loop2 j ans =
    if i >= n - 1 then ans else
    let k = 2 * j - i in
    if k >= n then ans else
    if (s2.(i) <> s2.(j)) && (s2.(j) <> s2.(k)) && (s2.(i) <> s2.(k)) then loop2 (j+1) (ans+1)
    else loop2 (j+1) ans
  in if i >= n-2 then ans2 else
  loop (i+1) (ans2 + loop2 (i+1) 0)

let _ = Printf.printf "%d\n" (rgb-(loop 0 0))