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 OCaml (4.02.3) (judge verdict: Accepted)

(* O(|s|) *)
let s = read_line () in
let n = String.length s in
let rec find acc bc i =
  if i < 0 then acc
  else if i >= 1 && s.[i - 1] = 'B' && s.[i] = 'C' then find acc (bc + 1) @@ i - 2
  else if s.[i] = 'A' then find (acc + bc) bc @@ i - 1
  else find acc 0 @@ i - 1 in
find 0 0 @@ n - 1 |> Printf.printf "%d\n"