Invert And Equalize

You are given a **binary** string $S$ of length $N$. You can perform the following operation on it: - Choose a **continuous** substring such that all of its characters are equal, and then invert the whole substring (i.e., if they were $0$, change them to $1$ and vice versa). For example, suppose $S = 101111000$. We may choose the substring $10{\color{blue}1111}000$ and change it to $10{\color{bl