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 split_string ?(pattern="") = Str.split @@ Str.regexp pattern
let n = Scanf.sscanf (read_line ()) "%d" @@ fun n -> n
let s = read_line () |> split_string

let cnt = List.fold_left (fun acc n ->
  match acc with
    | [] -> [(n, 1)]
    | (v, cnt) as t :: xs -> if v = n then (v, cnt + 1) :: xs else (n, 1) :: t :: xs
) [] @@ List.sort compare s

let () = 
  if List.length cnt < 3 then
    print_endline "0"
  else begin
    let s = Array.of_list s in
    let ans = ref @@ List.fold_left ( * ) 1 @@ List.map snd cnt in
    for i = 0 to n - 2 do
      for j = i + 1 to n - 1 do
        let k = j + (j - i) in
        if k < n && s.(i) <> s.(j) && s.(j) <> s.(k) && s.(i) <> s.(k) then ans := !ans - 1
      done
    done;
    Printf.printf "%d\n" !ans
  end