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)

/* #region template */
#![allow(unused_imports)]
use std::cmp::{max, min};
use std::io::{stdin, stdout, Bytes, Read, Stdin, StdinLock, Stdout, StdoutLock, Write};
use std::iter::{repeat, repeat_with};
use std::mem::swap;
use std::str::FromStr;
#[allow(dead_code)]
struct Io<'a> {
    reader: Bytes<StdinLock<'a>>,
    writer: StdoutLock<'a>,
    in_buf: [u8; BUF_SIZE],
}
#[allow(dead_code)]
impl<'a> Io<'a> {
    fn new(stdin: &'a Stdin, stdout: &'a Stdout) -> Io<'a> {
        Io {
            reader: stdin.lock().bytes(),
            writer: stdout.lock(),
            in_buf: [0; BUF_SIZE],
        }
    }
    fn r<T: FromStr>(&mut self) -> T {
        let mut count = 0;
        loop {
            match self.reader.next() {
                Some(Ok(b' ')) | Some(Ok(b'\n')) => break,
                Some(Ok(c)) => self.in_buf[count] = c,
                _ => panic!(),
            }
            count += 1;
        }

        let s = unsafe { std::str::from_utf8_unchecked(&self.in_buf[0..count]) };
        s.parse().unwrap_or_else(|_| panic!())
    }
    fn ru(&mut self) -> usize {
        self.r()
    }
    fn iter<'b, T>(&'b mut self) -> IoIter<'a, 'b, T> {
        IoIter::new(self)
    }
    fn c<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        self.iter().take(n).collect()
    }
    fn cu(&mut self, n: usize) -> Vec<usize> {
        self.c(n)
    }
    fn w<T: std::fmt::Display>(&mut self, v: T) {
        writeln!(self.writer, "{}", v).unwrap();
    }
    fn wn<T: std::fmt::Display>(&mut self, v: T) {
        write!(self.writer, "{}", v).unwrap();
    }
}
#[allow(dead_code)]
struct IoIter<'a: 'b, 'b, T> {
    io: &'b mut Io<'a>,
    m: std::marker::PhantomData<T>,
}
#[allow(dead_code)]
impl<'a: 'b, 'b, T> IoIter<'a, 'b, T> {
    fn new(io: &'b mut Io<'a>) -> IoIter<'a, 'b, T> {
        IoIter {
            io,
            m: std::marker::PhantomData,
        }
    }
}
impl<'a, 'b, T: FromStr> Iterator for IoIter<'a, 'b, T> {
    type Item = T;
    fn next(&mut self) -> Option<Self::Item> {
        Some(self.io.r())
    }
}
fn main() {
    let stdin = stdin();
    let stdout = stdout();
    let mut io = Io::new(&stdin, &stdout);
    unsafe {
        solve(&mut io);
    }
}
/* #endregion */

const BUF_SIZE: usize = 4096;

unsafe fn solve(io: &mut Io) {
    let n = io.ru();
    let s: Vec<char> = io.r::<String>().chars().collect();

    let mut count = 0;
    for i in 0..n {
        for j in i + 1..n {
            if s[i] != s[j] {
                for k in j + 1..n {
                    if j - i != k - j && s[i] != s[k] && s[j] != s[k] {
                        count += 1;
                    }
                }
            }
        }
    }
    io.w(count);
}