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 rgb_triplets
  implicit none
  integer :: n, i, j, a(4000) = 0, p, q
  integer(8) :: c(3) = 0_8, x = 0_8
  character(4000) :: s
  read(*,*) n
  read(*,*) s
  do i = 1, n
    if (s(i:i) == "R") then
      a(i) = 1
    else if (s(i:i) == "G") then
      a(i) = 2
    else
      a(i) = 3
    end if
  end do
  do i = 1, n
    p = mod(a(i),3)+1
    q = mod(p,3)+1
    x = x+c(p)*c(q)
    c(a(i)) = c(a(i))+1_8
  end do
  do j = 1, n
    do i = 1, n
      p = i+j
      q = p+j
      if (q > n) exit
      if (a(i) == a(p) .or. a(p) == a(q) .or. a(q) == a(i)) cycle
      x = x-1_8
    end do
  end do
  write(*,'(i0)') x
end program rgb_triplets