Swapping Operations

You say a binary string is good if all the $1$s form a consecutive substring. For example, $011100$, $111$ and $000$ are good strings but $101$ is not. For a binary string $S$ of length $N$, you define $f(S)$ as the minimum operations to convert $S$ into a good string. In each operation, we can do the following: - Choose $(i, j)$ such that $1 \le i < j \le N$, swap $S_i$ and $S_j$. Unfortun