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 Perl (5.26.1) (judge verdict: Accepted)

use strict;
use warnings;
use utf8;

my $n = int(<STDIN>);
my $s = <STDIN>;
my @ss = ($s =~ m/[RGB]/g);

my $r = () = $s =~ m/R/g;
my $g = () = $s =~ m/G/g;
my $b = () = $s =~ m/B/g;

my $ans = $r * $g * $b;

for my $i (0..($n - 2)) {
    for my $j (($i + 1)..($n - 1)) {
        my $k = $j*2 - $i;
        if($k >= $n) {
            next;
        }
        if($ss[$i] ne $ss[$j] && $ss[$i] ne $ss[$k] && $ss[$j] ne $ss[$k]) {
            $ans--;
        }
    }
}

print $ans;