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)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
fn main() {
    input!(
       n: usize,
       s: chars,
    );
    let mut e = 0;
    let mut ans = 0;
    let mut ns = Vec::new();
    for ss in s {
        let p = match ss {
            'R' => 1,
            'G' => 2,
            'B' => 3,
            _ => 0,
        };
        ns.push(p)
    }

    for i in 0..n - 2 {
        let mut j = 1;
        while j * 2 + i < n {
            if ns[i] + ns[i + j] + ns[i + 2 * j] == 6 && ns[i] != ns[i + j] { e += 1 }
            j += 1;
        }
    }
    for i in 2..=n {
        let j = n - i;
        let mut rb = (n, 0);
        let mut gb = (n, 0);
        let mut bb = (n, 0);
        match ns[j] {
            1 => {
                let t = search(j, rb, &ns);
                ans += t;
                rb = (j, t);
            },
            2 => {
                let t = search(j, gb, &ns);
                ans += t;
                gb = (j, t);
            },
            3 => {
                let t = search(j, bb, &ns);
                ans += t;
                bb = (j, t);
            },
            _ => continue
        }
    }
    ans -= e;
    println!("{}", ans);
}

fn search(j: usize, b: (usize, usize), ns: &Vec<usize>) -> usize {
    let mut n = 0;
    for x in j + 1..b.0 {
        for y in x + 1..b.0 {
            if ns[x] + ns[y] + ns[j] == 6 && ns[x] != ns[y] { n += 1 }
        }
    }
    n + b.1
}