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 f i =
  let rec loop_a a j =
    if j >= n then a
    else if s.[j] <> 'A' then a
    else loop_a (a + 1) (j + 1) in
  let rec loop_bc bc j =
    if j >= n - 1 then bc
    else if s.[j] <> 'B' || s.[j + 1] <> 'C' then bc
    else loop_bc (bc + 1) (j + 2) in
  let a = loop_a 0 i in
  if a = 0 then 0, 0, i + 1
  else
    let bc = loop_bc 0 (i + a) in
    if bc = 0 then 0, 0, i + a + 1
    else a, bc, i + a + 2 * bc in
let rec find acc a0 i =
  if i >= n then acc
  else
    let a, bc, j = f i in
    if a = 0 then find acc 0 j
    else
      let a1 = a0 + a in
      find (acc + a1 * bc) a1 j in
find 0 0 0 |> Printf.printf "%d\n"