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 Scala (2.13.1) (judge verdict: Time Limit Exceeded)

object Main extends App {
  val n = io.StdIn.readInt()
  val s = io.StdIn.readLine()

  var count = 0
  for (i <- 0 until n-2)
    for (j <- i until n-1; if (s(i) != s(j)))
      for (k <- j until n; if (s(i) != s(k) && s(j) != s(k) && j-i != k-j)) {
          count += 1
      }

  println(count)
}