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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

s = gets.chomp
cnt = 0
ac = 0
i = 0
while i < s.length-1
  bcc = 0
  if s[i] == "A"
    ac += 1
  elsif s[i] == "B" && s[i+1] == "C"
    bcc = 1
    k = 2
    while i+k <= s.length-2 && s[i+k] == "B" && s[i+k+1] == "C"
      bcc += 1
      k += 2
    end
    bcc.times do |kk|
      s[i-ac+kk*2] = "B"
      s[i-ac+1+kk*2] = "C"
    end
    s[i-ac+bcc*2..i+bcc*2-1] = "A" * ac
    cnt += ac*bcc
  else
    ac = 0
  end
  if bcc == 0
    i += 1
  else
    i = i-ac+bcc*2
    ac = 0
  end
end
puts cnt