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: Accepted)

use proconio::fastout;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::{Chars, Bytes};
#[allow(unused_imports)]
use num::integer::gcd;

#[allow(dead_code)]
type Pi = (i32, i32);
#[allow(dead_code)]
fn pri<T: std::fmt::Display>(x: T) {println!("{}", x);}

#[fastout]
fn main() {
    input!{
        n: u64, s: Chars,
    }
    let mut r = 0; let mut g = 0; let mut b = 0;
    for c in &s {
        if *c == 'R' {r += 1;} else if *c == 'G' {g += 1;} else {b += 1;}
    }
    let mut ans:u64 = r*g*b;
    for i in 1..n as usize {
        for j in 0..i {
            let k = 2*i-j;
            if k < n as usize && s[k] != s[i] && s[k] != s[j] && s[j] != s[i] {ans -= 1;}
        }
    }
    pri(ans);
}