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 Scala (2.11.7) (judge verdict: Runtime Error)

import scala.math.BigInt
import scala.io.StdIn

object Main {

  type BI = BigInt
  val s: List[Char] = StdIn.readLine().toList
  println(s"${solve(s, 0, 0)}")

  def solve(s: List[Char], aAlive: BI, ans: BI): BI = {
    s match {
      case Nil => ans
      case 'A' :: t => solve(t, aAlive + 1, ans)
      case 'B' :: 'C' :: t => solve(t, aAlive, ans + aAlive)
      case _ :: t => solve(t, 0, ans)
    }
  }

}