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: Accepted)

program main
  implicit none
  integer :: N
  character(len=4000) :: S
  integer(8) :: out
  integer :: i,j,k
  integer(8) :: iR(3)
  integer,parameter :: I_R = 1, I_G = 2, I_B = 3
  read(*,*) N
  read(*,*) S
  iR(:) = 0
  do i = 1,N
     if (S(i:i) == "R") then
        iR(I_R) = iR(I_R) + 1
     end if 
     if (S(i:i) == "G") then
        iR(I_G) = iR(I_G) + 1
     end if
     if (S(i:i) == "B")  then
        iR(I_B) = iR(I_B) + 1
     end if
  end do
  out = iR(1)*iR(2)*iR(3)
  do i = 1,N-2
     do j = i+1,N-1
        k = 2*j-i
        if ( k>N) cycle
        if (k <= N ) then
           if ( (S(i:i) /= S(j:j)) .and. ( S(i:i) /= S(k:k) )&
                .and. (S(j:j) /= S(k:k)) ) then
              out = out - 1
           end if
        end if
     end do
  end do
  write(*,'(i0)') out
  stop
end program main