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 abc162d
   implicit none
   integer :: N, i, j, k
   character(4000) :: str
   character, allocatable :: S(:)
   integer :: count


   read(*,*) N
   read(*,*) str

   allocate(S(N))

   do i = 1, N
      S(i) = str(i:i)
   enddo

   count = 0
   do k = 3, N
      do j = 2, k-1
         if (S(j) == S(k)) cycle
         do i = 1, j-1
            if (j-i == k-j) cycle
            if (S(i).ne.S(j) .and. S(i).ne.S(k) ) then
               count= count + 1
            endif
         enddo
      enddo
   enddo

   print *, count


end program abc162d