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 ABC162_D
  character(4000)::S
  read(5,*)N
  read(5,*)S
  L=0
  do I=1,N-3
     do J=I+1,N-1
        do K=J+1,N
           if(S(I:I)/=S(J:J)) then
              if(S(J:J)/=S(K:K) .and. S(I:I)/=S(K:K)) then
                 if(J-I/=K-J) L=L+1
              end if
           end if
        end do
     end do
  end do
  write(6,*)L
end program ABC162_D