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: Time Limit Exceeded)

use strict;
use warnings;
use utf8;

my $n = int(<STDIN>);
my @ss = split '', <STDIN>;

my @r_cnt = ();
my @g_cnt = ();
my @b_cnt = ();

for my $i (0..$#ss) {
    if ($ss[$i] eq 'R') {
        push @r_cnt, $i;
    }
    elsif ($ss[$i] eq 'G') {
        push @g_cnt, $i;
    }
    elsif ($ss[$i] eq 'B') {
        push @b_cnt, $i;
    }
}

my $ans = scalar(@r_cnt) * scalar(@g_cnt) * scalar(@b_cnt);

for my $i (@r_cnt) {
    for my $j (@g_cnt) {
        for my $k (@b_cnt) {
            my ($x, $y, $z) = (($i - $j)**2, ($i - $k)**2, ($j - $k)**2);
            if( $x == $y || $x == $z || $y == $z ) {
                $ans--;
            }
        }
    }
}

print $ans;