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)

#![allow(unused_mut)]
#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(unused_imports)]
#![allow(dead_code)]
macro_rules! input {
  (source = $s:expr, $($r:tt)*) => {
    let mut iter = $s.split_whitespace();
    let mut next = || { iter.next().unwrap() };
    input_inner!{next, $($r)*}
  };
  ($($r:tt)*) => {
    let stdin = std::io::stdin();
    let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
    let mut next = move || -> String{
      bytes
        .by_ref()
        .map(|r|r.unwrap() as char)
        .skip_while(|c|c.is_whitespace())
        .take_while(|c|!c.is_whitespace())
        .collect()
    };
    input_inner!{next, $($r)*}
  };
}
macro_rules! input_inner {
  ($next:expr) => {};
  ($next:expr, ) => {};

  ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
    let $var = read_value!($next, $t);
    input_inner!{$next $($r)*}
  };
}
macro_rules! read_value {
  ($next:expr, ( $($t:tt),* )) => {
    ( $(read_value!($next, $t)),* )
  };

  ($next:expr, [ $t:tt ; $len:expr ]) => {
    (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
  };

  ($next:expr, chars) => {
    read_value!($next, String).chars().collect::<Vec<char>>()
  };

  ($next:expr, usize1) => {
    read_value!($next, usize) - 1
  };

  ($next:expr, $t:ty) => {
    $next().parse::<$t>().expect("Parse error")
  };
}

fn gcd(a: u64, b: u64) -> u64 {
  if b == 0 {
    a
  } else {
    gcd(b, a % b)
  }
}

fn main() {
  input!{
    N: usize,
    S: chars,
  }

  let mut ans = 0;
  for i in 0..N {
    for j in i..N {
      if S[i] == S[j] {continue}
      for k in j..N {
        if S[j] == S[k] || S[k] == S[i] {continue}
        if j-i == k-j {continue}
        ans += 1;
      }
    }
  }
  println!("{}", ans);

}