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
// D
fscanf(STDIN, '%d', $n);
fscanf(STDIN, '%s', $s);
// RGBの個数の累積和
$c['R'][0] = $c['G'][0] = $c['B'][0] = 0;
for ($i = 0; $i < $n; $i++) {
    foreach (array_keys($c) as $k) {
        $c[$k][$i + 1] = $c[$k][$i];
        if ($k === $s[$i]) $c[$k][$i + 1]++;
    }
}
$ans = 0;
for ($i = 1; $i < $n - 1; $i++) {
    $s1 = array_pop(array_diff(array_keys($c), [$s[$i]]));
    $s2 = array_pop(array_diff(array_keys($c), [$s[$i], $s1]));
    $ans += $c[$s1][$i] * ($c[$s2][$n] - $c[$s2][$i + 1]);
    $ans += $c[$s2][$i] * ($c[$s1][$n] - $c[$s1][$i + 1]);
    for ($j = 1; $j <= $n; $j++) {
        if ($i - $j < 0 || $i + $j >= $n) break;
        if ($s[$i - $j] !== $s[$i] && $s[$i] !== $s[$i + $j] && $s[$i - $j] !== $s[$i + $j]) $ans--;
    }
}
echo $ans;