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 :: n, i, j, k, cnt, r, g, b, dis
  character(4000) :: s

  read *, n
  read *, s

  r = 0
  g = 0
  b = 0
  do i = 1, n
     select case(s(i:i))
     case('R')
        r = r + 1
     case('G')
        g = g + 1
     case('B')
        b = b + 1
     end select
  end do
  
  cnt = 0
  do dis = 1, n/2
     do i = 1, n-2*dis
        if (s(i:i) /= s(i+dis:i+dis) &
             .and. s(i:i) /= s(i+2*dis:i+2*dis) &
               .and. s(i+dis:i+dis) /= s(i+2*dis:i+2*dis)) then
           cnt = cnt + 1
        end if
     end do
  end do

  print *, r*g*b - cnt
  
  stop
end program main