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 ans = 0
local tbl = {}
for cur=1, string.len(str) do
	tbl[cur] = string.sub(str,cur,cur)
end
local used = {}
local cur = 1
while cur <= #tbl -2 do
	local flag = false
	if tbl[cur] == "A" and tbl[cur+1] == "B" and tbl[cur+2] == "C" then

		ans = ans + 1
		tbl[cur] = "B"
		tbl[cur+1] = "C"
		tbl[cur+2] = "A"
		l = cur -1 
		while l > 0 and tbl[l] == "A"  do
			flag = true
			ans = ans + 1
			tbl[l] = "B"
			tbl[l+1] = "C"
			tbl[l+2] = "A"
			l = l - 1
		end
	end
    cur = cur + 1
end
print(ans)