Ones and Zeroes II

Given a binary string, $f(S)$ is defined as follows: - A prefix $S[1, i]$ is called good if it contains at least as many ones as zeroes. - $f(S)$ is the number of good prefixes of the string $S$. --- You are given a binary string $S$ of length $N$. Your task is to maximize $f(S)$ by performing adjacent swaps only. What is the maximum possible $f(S)$ using any number of adjacent swaps, and wha