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: Wrong Answer)

program main
      implicit none
      integer(4) :: n, i, j, k
      integer(4) :: sumR, sumB, sumG
      integer(8) :: sum
      character(4000) :: s

      read *, n
      read *, s

      sumR = 0
      sumB = 0
      sumG = 0

      do i = 1, n
        if ( s(i:i) == 'R' ) sumR = sumR + 1
        if ( s(i:i) == 'B' ) sumB = sumB + 1
        if ( s(i:i) == 'G' ) sumG = sumG + 1
      end do
      sum = sumR*sumB*sumG

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

      print *, sum

end program main