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 proconio::*;
use num::Integer;

#[fastout]
fn main() {
   input! {
       n: usize,
       s: String
   }
   let mut r = 0i64;
   let mut g = 0i64;
   let mut b = 0i64;
   let ss:Vec<char> = s.as_str().chars().collect();
   for c in &ss {
       match c {
           'R' => r += 1,
           'G' => g += 1,
           'B' => b += 1,
           _ => ()
       }
   }
   let mut ans = r*g*b;
   for i in 0..n {
       let mut j = i+2;
       while j < n {
           match (ss[i]!=ss[(i+j)/2], ss[j]!=ss[(i+j)/2], ss[i]!=ss[j]) {
               (true, true, true) => ans -= 1,
               _ => (),
           };
           j += 2;
       }
   }
   println!("{}", ans);
}