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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
fscanf(STDIN, "%s", $S);
$S = str_replace("BC", "D", $S);
$ans = 0;

while(true) {
    $cnt = substr_count($S, "ADDDDDDDDDD");
    $ans += $cnt * 10;
    $S = str_replace("ADDDDDDDDDD", "DDDDDDDDDDA", $S);

    $cnt = substr_count($S, "AAAAAAAAAAD");
    $ans += $cnt * 10;
    $S = str_replace("AAAAAAAAAAD", "DAAAAAAAAAA", $S);

    $cnt = substr_count($S, "AD");
    if ($cnt === 0) break;
    $ans += $cnt;
    $S = str_replace("AD", "DA", $S);
}
echo $ans;