Flip or Compress

You are given a binary string $S$. You can perform the following operations on $S$: - Flip: Pick an index $i$ $(1 \le i \le |S|)$ and flip the $i$-th character (i.e change $1$ to $0$ or $0$ to $1$). For e.g. $01\underline{1}001 \rightarrow 01\underline{0}001$ - Compress: Pick any non-empty substring consisting of the same character and replace it with a single occurrence of that character. For e.