Small, Smaller, Smallest

You are given a **binary** string $S$ of length $N$. You can perform the following two-step operation on it: 1. Choose a non-empty contiguous substring of $S$. 2. If the substring contains an odd number of ones, delete every $0$ in it. If it instead contains an even number of ones, delete every $1$ in it. For example, suppose $S = \texttt{1010001}$, - If you choose the substring $\texttt{101}