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 proconio::{fastout, input};

#[fastout]
fn main() {
    input!(n: usize);
    input!(s: String);

    let mut r = Vec::new();
    let mut g = Vec::new();
    let mut b = Vec::new();

    for i in 0..n {
        if s.chars().nth(i).unwrap() == 'R' {
            r.push(i);
        }

        if s.chars().nth(i).unwrap() == 'G' {
            g.push(i);
        }

        if s.chars().nth(i).unwrap() == 'B' {
            b.push(i);
        }
    }

    let mut count = 0;
    for &r_ in &r {
        for &g_ in &g {
            for &b_ in &b {
                let mut v = vec![r_, g_, b_];
                v.sort();
                if v[1] - v[0] != v[2] - v[1] {
                    count += 1;
                }
            }
        }
    }

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