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 Lua (Lua 5.3.5) (judge verdict: Time Limit Exceeded)

local str = io.read()
local index = 1
local tStr = {}
for i = 1, #str do
    tStr[i] = string.sub(str, i, i)
end
local sum = 0
local function A(index)
    for i = index, #str -  2 do
        if string.byte(tStr[i]) == string.byte(tStr[i + 1]) - 1 and string.byte(tStr[i]) == string.byte(tStr[i + 2]) - 2 then
            tStr[i] = "B"
            tStr[i + 1] = "C"
            tStr[i + 2] = "A"
            sum = sum + 1
            if index > 1 then
                A(index - 1)
            end
        end
    end
    if index <= #str -  2 then
        A(index + 1)
    end
end
A(1)
print(sum)