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 abc162dr
      implicit none
      integer::n
      character(len=4000)::s
      integer::i,j,k
      integer(8)::ans
      integer(8)::x(3)=0

         read *,n
         read *,s

         do i=1,n
            if (s(i:i)=='R') x(1)=x(1)+1
            if (s(i:i)=='G') x(2)=x(2)+1
            if (s(i:i)=='B') x(3)=x(3)+1
         end do

         ans=x(1)*x(2)*x(3)

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

         print *,ans

   end program abc162dr