Problem:
Score : 600 points

Problem Statement

You are given a string s consisting of A, B and C.

Snuke wants to perform the following operation on s as many times as possible:

Choose a contiguous substring of s that reads ABC and replace it with BCA.

Find the maximum possible number of operations.

Constraints

1 \leq |s| \leq 200000

Each character of s is A, B and C.

Input

Input is given from Standard Input in the following format:

s

Output

Find the maximum possible number of operations.

Sample Input 1

ABCABC

Sample Output 1

3

You can perform the operations three times as follows: ABCABC → BCAABC → BCABCA → BCBCAA. This is the maximum result.

Sample Input 2

C

Sample Output 2

0

Sample Input 3

ABCACCBABCBCAABCB

Sample Output 3

6

Solution in Fortran (gfortran v4.8.4) (judge verdict: Time Limit Exceeded)

program abc
  implicit none
  character(200000) :: s
  integer :: x(200000), a(3), b(3), n, m, i
  x = 0
  read(*,*) s
  s = trim(adjustl(s))
  n = len_trim(s)
  if (n.lt.3) then
    write(*,'(i0)') 0
    stop
  end if
  do i = 1, n
    x(i) = ichar(s(i:i))-66
  end do
  a = (/-1,0,1/)
  b = (/0,1,-1/)
  m = 0
  i = 1
  do while (i.le.n-2)
    if (sum(abs(x(i:i+2)-a)).eq.0) then
      x(i:i+2) = b
      m = m+1
      i = max(1,i-1)
      if (x(i).ne.-1) i = i+2
    else
      i = i+1
    end if
  end do
  write(*,'(i0)') m
  stop
end program abc