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 PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php

$n = trim(fgets(STDIN));
$s = trim(fgets(STDIN));

$s = str_split($s);

$r = [];
$g = [];
$b = [];

for ($i=1;$i<=$n;++$i) {
    $offset = $i-1;
    if ($s[$offset] === 'R') {
        $r[] = $i;
    } else if ($s[$offset] === 'G') {
        $g[] = $i;
    } else if ($s[$offset] === 'B') {
        $b[] = $i;
    }
}

$count = 0;
foreach ($r as $rv) {
    foreach ($g as $gv) {
        foreach ($b as $bv) {
            $array = [$rv, $gv , $bv];
            sort($array);
            if (($array[2] - $array[1]) !== ($array[1] - $array[0])) {
                ++$count;

            }
        }
    }
}
echo $count . PHP_EOL;