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 ABC162_D
  character(4000)::S
  integer::R=0,G=0,B=0,A
  read(*,*)N
  read(*,*)S
  do i=1,N
     if(S(i:i)=='R') R=R+1
     if(S(i:i)=='G') G=G+1
     if(S(i:i)=='B') B=B+1
  end do
  A=R*G*B
  do i=1,N
     do j=1,N
        if(i+2*j>N) cycle
        if(S(i:i)/=S(i+j:i+j) .and. S(i+j:i+j)/=S(i+2*j:i+2*j) .and. S(i+2*j:i+2*j)/=S(i:i)) A=A-1
     end do
  end do
  write(*,*)A
end program ABC162_D