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 main
    implicit none
    integer n, i, j, k
    integer :: count = 0
    character(:), allocatable :: s

    read *, n
    allocate( character(n) :: s)

    read *, s

    do i=1, n-3
        do j=i+1, n-1
            do k=j+1, n
                if ( s(i:i) /= s(j:j) .and. s(i:i) /= s(k:k) .and. s(j:j) /= s(k:k) .and. j-i /= k-j) then
                    count = count + 1
                endif
            enddo
        enddo
    enddo
    print *, count
    end program main