Max Operations on AB String

You are given a string s consisting only of the characters A and B. Your task is to determine the maximum number of operations you can perform on the string, where each operation is defined as removing a contiguous subsegment in which the number of As is equal to the number of Bs.

Formally, when iterating over the characters of the string from left to right, every time the count of As is equal to the count of Bs, one operation can be counted and these counts are reset for the next segment. This continues until the end of the string.

For example, consider the string AABBAB. We can perform 2 operations because there are two segments where the counts of A and B become equal.

Note: Use LaTeX for any mathematical formula representations if needed. In this problem, one could express the condition for an operation as when $$count_A = count_B.$$

inputFormat

The input consists of a single line containing a string s that is composed exclusively of the characters A and B.

You should read the input from stdin.

outputFormat

Output a single integer to stdout indicating the maximum number of operations that can be performed on the input string.

AABBAB

2