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 example
	implicit none

	integer(8) ::N,i,j,k,wa=0
    character(4000) S
    
    read(*,*) N
    read(*,*) S
    
    do i=1,N,1
    
    	do j=i+1,N,1
            if(S(i:i)==S(j:j)) goto 2
        	do k=j+1,N,1
                if(j-i==k-j) goto 1

            	if(S(i:i)/=S(k:k) .and. S(k:k)/=S(j:j)) then
                	wa=wa+1
                end if
            1 end do

        2 end do
    end do
              
    write(*,*) wa

end program example