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::*;

fn run() {
    input! {
        n: usize,
        s: String,
    }
    let mut map = std::collections::BTreeMap::new();
    map.insert('R', 0);
    map.insert('G', 1);
    map.insert('B', 2);
    let s: Vec<usize> = s.chars().map(|c| *map.get(&c).unwrap()).collect();
    let mut cnt = [0; 3];
    for &k in s.iter() {
        cnt[k] += 1;
    }
    let mut ans = cnt.iter().fold(1, |s, a| s * *a);
    for l in 0..n {
        let mut d = 1;
        while l + 2 * d < n {
            let (a, b, c) = (s[l], s[l + d], s[l + 2 * d]);
            if a != b && b != c && c != a {
                ans -= 1;
            }
            d += 1;
        }
    }
    println!("{}", ans);
}

fn main() {
    run();
}