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: Wrong Answer)

use proconio::{input, fastout};
use proconio::marker::Chars;

#[fastout]
fn main() {
    input! {
        n: usize,
        s: Chars,
    }

    let mut r_count = 0;
    let mut g_count = 0;
    let mut b_count = 0;
    for c in s.iter() {
        match c {
            &'R' => r_count += 1,
            &'G' => g_count += 1,
            &'B' => b_count += 1,
            _ => {}
        }
    }

    let mut ans = r_count*g_count*b_count;

    for i in 0..n {
        for j in i+1..n {
            let k = 2 * j - i;
            if k >= n {
                break;
            }

            if check(s[i], s[j], s[k]) {
                ans -= 1;
            }
        }
    }

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

fn check(a: char, b: char, c: char) -> bool {
    a != b && b != c && c != a
}