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: Wrong Answer)

object Main extends App {
  val in = new java.util.Scanner(System.in)
  val N = in.nextInt
  val S = in.next
  val nR = S.count(_ == 'R')
  val nG = S.count(_ == 'G')
  val nB = N - nR - nG

  @inline 
  def c(i: Int) = S.charAt(i)

  val un = (for {
    i <- 0 to N - 3
    j <- i + 1 to N - 2 if 2 * j - i < N
  } yield if (c(i) != c(j) && c(i) != c(2 * j - i) && c(j) != c(2 * j - i)) 1 else 0).sum

  println(nR * nG * nB - un)
}