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 Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defparameter s (read-line))
 
(defun cut (text)
  (if (equal "BC" (subseq text 0 2))
      (cut (subseq text 2))
      (if (or (equal "C" (subseq text 0 1))
              (equal "B" (subseq text 0 1)))
          (cut (subseq text 1))
          text)))
 
(let ((counter 0))
     (defun answer (text)
       (let ((pos (search "ABC" text)))
            (if pos
                (progn
                  (incf counter)
                  (answer (subseq text (+ pos 2))))
                counter))))
 
(print (answer (cur s)))