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 test
implicit none
integer(8) :: n,i,j,k,ans=0,rgb(3,5000)=0,hoge=0,big=0,small=0
character(len=10000) :: s



read(*,*) n
read(*,*) s

do i=1,n
  if(s(i:i)=='R')then
    rgb(1,i:n) = rgb(1,i:n) + 1
  else if(s(i:i)=='G')then
    rgb(2,i:n) = rgb(2,i:n) + 1
  else if(s(i:i)=='B')then
    rgb(3,i:n) = rgb(3,i:n) + 1
  endif
enddo


if(n<=2)then
  ans = 0
else
  
  do j=2,n-1
    if(s(j:j) == 'R') then
      ans = ans + rgb(2,j-1)*(rgb(3,n)-rgb(3,j))
      ans = ans + rgb(3,j-1)*(rgb(2,n)-rgb(2,j))
      
      big = j+1
      small = j-1
      
      do while(big <= n .and. small >= 1)
        if((s(small:small)=='G' .and. s(big:big)=='B') .or. (s(small:small)=='B' .and. s(big:big)=='G')) then
         ans = ans - 1
        endif
        big = big + 1
        small = small - 1
      enddo
      
    endif

    if(s(j:j) == 'G') then
      ans = ans + rgb(1,j-1)*(rgb(3,n)-rgb(3,j))
      ans = ans + rgb(3,j-1)*(rgb(1,n)-rgb(1,j))

      big = j+1
      small = j-1
      
      do while(big <= n .and. small >= 1)
        if((s(small:small)=='R' .and. s(big:big)=='B') .or. (s(small:small)=='B' .and. s(big:big)=='R')) then
         ans = ans - 1
        endif
        big = big + 1
        small = small - 1
      enddo

    endif

    if(s(j:j) == 'B') then
      ans = ans + rgb(1,j-1)*(rgb(2,n)-rgb(2,j))
      ans = ans + rgb(2,j-1)*(rgb(1,n)-rgb(1,j))

      big = j+1
      small = j-1
      
      do while(big <= n .and. small >= 1)
        if((s(small:small)=='R' .and. s(big:big)=='G') .or. (s(small:small)=='G' .and. s(big:big)=='R')) then
         ans = ans - 1
        endif
        big = big + 1
        small = small - 1
      enddo

    endif
    
  enddo
  
endif

write(*,*) ans

end