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)

// -*- coding:utf-8-unix -*-

use proconio::input;

fn main() {
    input! {
        n: usize,
        s: String,
    }

    let vc: Vec<char> = s.chars().collect();
    let mut vidx = vec![vec![]; 3];
    for i in 0..n {
        match vc[i] {
            'R' => vidx[0].push(i as u32),
            'G' => vidx[1].push(i as u32),
            'B' => vidx[2].push(i as u32),
            _ => unreachable!(),
        }
    }

    let mut ans = vidx[0].len() * vidx[1].len() * vidx[2].len();
    for i in 0..n {
        for j in i + 1..n {
            if vc[i] == vc[j] {
                continue;
            }

            let k = 2 * j - i;
            if k >= n || vc[k] == vc[i] || vc[k] == vc[j] {
                continue;
            }

            ans -= 1;
        }
    }

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