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 Fortran (GNU Fortran 9.2.1) (judge verdict: Time Limit Exceeded)

program main
  implicit none

  integer :: n, i, j, k, ans
  character(4000) :: s

  read *, n
  read *, s

  ans = 0
  do i = 1, n-2
     do j = i, n-1
        do k = j, n
           if (s(i:i) /= s(j:j) .and. s(k:k) /= s(j:j) .and. s(i:i) /= s(k:k) &
                & .and. j-i /= k-j) then
              ans = ans + 1
           end if
        end do
     end do
  end do

  print *, ans
  
  stop
end program main