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: Time Limit Exceeded)

use std::vec::Vec;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

fn read_touple<T: std::str::FromStr + Copy>() -> (T, T) {
  let v: Vec<T> = read_vec();
  assert_eq!(v.len(), 2);
  (v[0], v[1])
}

fn main() {
    let n: usize = read();
    let s: Vec<char> = read::<String>().chars().collect();

    let mut R = vec![];
    let mut G = vec![];
    let mut B = vec![];

    for i in 0..n {
      if s[i] == 'R' {
        R.push(i);
      } else if s[i] == 'G' {
        G.push(i);
      } else {
        B.push(i);
      }
    }

    let mut ans: usize = 0;

    // (R, G, B)
    for &r in &R {
      for &g in &G {
        for &b in &B {
          let mut v = vec![r, g, b];
          v.sort();
          let (i, j, k) = (v[0], v[1], v[2]);
          if 2 * j != k + i {
            ans += 1;
          }
        }
      }
    }

    println!("{}", ans);
}