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 piyo
      IMPLICIT NONE
      character(4000) :: s
      integer(16) :: numR(4000)=0,numG(4000)=0,numB(4000)=0
      integer(16) :: rgb(3)=0,i,j,n,ans=0,notK
      
      read*,n
      read*,s(1:n)
      
      if( s(1:1)=='R' )then
          numR(1) = 1
      else if( s(1:1)=='G' )then
          numG(1) = 1
      else
          numB(1) = 1
      endif
      
      do i = 2,n
        if( s(i:i)=='R' )then
          rgb(1) = 1
        else if( s(i:i)=='G' )then
          rgb(2) = 1
        else
          rgb(3) = 1
        end if
        
        numR(i) = numR(i-1) + rgb(1)
        numG(i) = numG(i-1) + rgb(2)
        numB(i) = numB(i-1) + rgb(3)
        rgb = 0
      end do
      
      ans = 0
      do i = 1,n-2
        do j = i+1,n-1
        
          notK = j + (j-i)
          if( notK>4000 ) notK = 4000
          rgb(:) = 0
          
          if( (s(i:i)=='R'.and.s(j:j)=='G') .or. &
            & (s(j:j)=='R'.and.s(i:i)=='G') )then
            rgb(3) = 1
          else if( (s(i:i)=='G'.and.s(j:j)=='B') .or. &
                 & (s(j:j)=='G'.and.s(i:i)=='B') )then
            rgb(1) = 1
          else
            rgb(2) = 1
          end if
          
          if( rgb(1)==1 )then
            ans = ans + (numR(n)-numR(j))
            if( s(notK:notK)=='R' ) ans = ans - 1
          else if( rgb(2)==1 )then
            ans = ans + (numG(n)-numG(j))
            if( s(notK:notK)=='G' ) ans = ans - 1
          else
            ans = ans + (numB(n)-numB(j))
            if( s(notK:notK)=='B' ) ans = ans - 1
          end if
        end do
      end do
      
      
      print*,ans
      
      !debugg
  !    print*,numR(1:n)
  !    print*,numG(1:n)
  !    print*,numB(1:n)
      
      
      END PROGRAM