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: Accepted)

<?php
fscanf(STDIN, "%d", $n);
$s = str_split(trim(fgets(STDIN)));

$rgb = array(
  'R' => 0,
  'G' => 0,
  'B' => 0,
);
foreach ($s as $k => $v) {
  $rgb[$v]++;
}
$sum = $rgb['R'] * $rgb['G'] * $rgb['B'];

$count = 0;
for ($i=0; $i < $n; $i++) {
  for ($j=$i+1; $j < $n; $j++) {
    $k = 2 * $j - $i;
    if ($k >= $n) {
      continue;
    }
    if ($s[$i] != $s[$j] && $s[$i] != $s[$k] && $s[$j] != $s[$k]) {
      if ($j-$i == $k-$j) {
        $count++;
      }
    }
  }
}

echo $sum - $count;