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: Accepted)

#[allow(unused_imports)]
use std::cmp;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use proconio::derive_readable;
use proconio::fastout;
#[allow(unused_imports)]
use num::Integer;
#[allow(unused_imports)]
use itertools::Itertools;

#[fastout]
fn main() {
  input! {
    n: usize,
    s: Chars,
  }
  let s: Vec<usize> = s.into_iter().map(|c| match c {
    'R' => 0,
    'G' => 1,
    _ => 2,
  }).collect();
  let mut count = vec![vec![0; 3]; n+1];
  for (i, &c) in s.iter().enumerate() {
    for x in 0 .. 3 {
      count[i+1][x] = count[i][x];
    }
    count[i+1][c] += 1;
  }
  let mut ans = 0i64;
  for j in 0 .. n {
    for k in j+1 .. n {
      if s[j] == s[k] {
        continue;
      }
      let x = 3 - s[j] - s[k];
      ans += count[j][x];
      if let Some(i) = (2 * j).checked_sub(k) {
        if s[i] == x {
          ans -= 1;
        }
      }
    }
  }

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