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)

macro_rules! scan_sub {
    ( $itr:ident, $t:ty ) => {
        let mut buf = String::new();
        let $itr = {
            while buf.trim().len() == 0 {
                buf = String::new();
                std::io::stdin().read_line(&mut buf).unwrap();
            }
            buf.split_whitespace().map(|n| n.parse::<$t>().unwrap())
        };
    };
}

macro_rules! scan {
    ( $x:ident; Vec<$t:ty> ) => {
        scan_sub!(itr, $t);
        let $x = itr.collect::<Vec<_>>();
    };
    ( $( $x:ident ),*; $t:ty ) => {
        scan_sub!(itr, $t);
        let mut itr = itr;
        $(
            let $x = itr.next().unwrap();
        )*
    };
}

fn main() {
    scan!(n; usize);
    scan!(s; String);

    let mut r = 0;
    let mut g = 0;
    let mut b = 0;

    let mut s2 = Vec::with_capacity(n);

    for c in s.chars() {
        match c {
            'R' => r += 1,
            'G' => g += 1,
            'B' => b += 1,
            _ => (),
        }
        s2.push(c);
    }

    let mut res = r * g * b;
    let s = s2;

    for k in 1..n {
        for i in 0..k {
            if (k + i) % 2 == 1 { continue; }
            let j = (i + k) / 2;

            if s[i] == s[j] || s[i] == s[k] || s[j] == s[k] {
                continue;
            }

            if res > 0 { res -= 1; }
        }
    }

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