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 ABC162D
    implicit none
    integer(8)::N,r,g,b,i,j,ans
    character(4000)::S
    read*,N,S
    r=0
    g=0
    b=0

    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

    ans=r*g*b

    do i=1,N
        do j=1,N
            if(i+2*j<=N)then
                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))then
                    ans=ans-1
                end if
            end if
        end do
    end do

    print'(i0)',ans
end program ABC162D