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: Wrong Answer)

<?php
$num = trim(fgets(STDIN));
$array = str_split(trim(fgets(STDIN)));
$count = 0;
$array_r = [];
$array_g = [];
$array_b = [];
foreach($array as $id => $value) {
  if($value == 'R') {
    $array_r[$id+1] = $value;
  } else if ($value == 'G') {
    $array_g[$id+1] = $value;
  } else {
    $array_b[$id+1] = $value;
  }
}

$count_r = count($array_r);
$count_g = count($array_g);
$count_b = count($array_b);

if($count_r > $count_g) {
  $tmp = $array_r;
  $array_r = $array_g;
  $array_g = $tmp;
}
if($count_r > $count_b) {
  $tmp = $array_r;
  $array_r = $array_b;
  $array_b = $tmp;
}
if($count_g > $count_b) {
  $tmp = $array_g;
  $array_g = $array_b;
  $array_b = $tmp;
}

foreach($array_r as $id_r => $value_r) {
  foreach($array_g as $id_g => $value_g) {
    foreach($array_b as $id_b => $value_b) {
      if($id_r > $id_g) {
        $tmp = $id_r;
        $id_r = $id_g;
        $id_g = $tmp;
      }
      if($id_r > $id_b) {
        $tmp = $id_r;
        $id_r = $id_b;
        $id_b = $tmp;
      }
      if($id_g > $id_b) {
        $tmp = $id_g;
        $id_g = $id_b;
        $id_b = $tmp;
      }
      if($id_r+$id_b == $id_b*2) {continue;}
      $count++;
    }
  }
}
echo $count;