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 test

integer :: n,i,j,k,ans=0,rgb(3,4000)=0,hoge=0
character(len=4000) :: 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 i=1,n-2
    if(s(i:i) =='R') then
      do j=i+1,n-1
        hoge = j+j-i
        if(s(j:j)=='G') then
          ans = ans + rgb(3,n) - rgb(3,j)
          if(j+j-i <= n) then
            if(s(hoge:hoge) == 'B') then
              ans = ans - 1
            endif
          endif
        else if(s(j:j)=='B') then
          ans = ans + rgb(2,n) - rgb(2,j)
          if(j+j-i <= n) then
            if(s(hoge:hoge) == 'G') then
              ans = ans - 1
            endif
          endif
        endif
      enddo
    endif
    

    if(s(i:i) =='G') then
      do j=i+1,n-1
        hoge = j+j-i
        if(s(j:j)=='R') then
          ans = ans + rgb(3,n) - rgb(3,j)
          if(j+j-i <= n) then
            if(s(hoge:hoge) == 'B') then
              ans = ans - 1
            endif
          endif
        else if(s(j:j)=='B') then
          ans = ans + rgb(1,n) - rgb(1,j)
          if(j+j-i <= n) then
            if(s(hoge:hoge) == 'R') then
              ans = ans - 1
            endif
          endif
        endif
      enddo
    endif

    if(s(i:i) =='B') then
      do j=i+1,n-1
        hoge = j+j-i
        if(s(j:j)=='R') then
          ans = ans + rgb(2,n) - rgb(2,j)
          if(j+j-i <= n) then
            if(s(hoge:hoge) == 'G') then
              ans = ans - 1
            endif
          endif
        else if(s(j:j)=='G') then
          ans = ans + rgb(1,n) - rgb(1,j)
          if(j+j-i <= n) then
            if(s(hoge:hoge) == 'R') then
              ans = ans - 1
            endif
          endif
        endif
      enddo
    endif
  
  
  enddo
endif

write(*,*) ans

end