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 Rust (1.42.0) (judge verdict: Wrong Answer)

#[allow(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use num::*;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn main() {
  input! {
    n: usize,
    s: Chars
  };

  let mut rc = vec![0; n + 1];
  let mut gc = vec![0; n + 1];
  let mut bc = vec![0; n + 1];

  for (i, &ch) in s.iter().rev().enumerate() {
    let i = n - i;
    rc[i - 1] = rc[i];
    gc[i - 1] = gc[i];
    bc[i - 1] = bc[i];
    match ch {
      'R' => rc[i - 1] += 1,
      'G' => gc[i - 1] += 1,
      'B' => bc[i - 1] += 1,
      _ => {}
    }
  }
  let mut res = 0;
  for i in 0..n {
    for j in (i + 1)..n {
      let k = std::cmp::max(i, j) + 1;
      if k == n {
        continue;
      }
      let l = j + j - i;
      let lch = if l < n { s[l] } else { 'x' };
      let c = match (s[i], s[j]) {
        ('R', 'G') => bc[k] - if lch == 'B' { 1 } else { 0 },
        ('R', 'B') => gc[k] - if lch == 'G' { 1 } else { 0 },
        ('G', 'R') => bc[k] - if lch == 'B' { 1 } else { 0 },
        ('G', 'B') => rc[k] - if lch == 'R' { 1 } else { 0 },
        ('B', 'R') => gc[k] - if lch == 'G' { 1 } else { 0 },
        ('B', 'G') => rc[k] - if lch == 'R' { 1 } else { 0 },
        _ => 0,
      };
      res += c;
    }
  }
  println!("{}", res);
}