Maximise The Minimum

You are given a **binary** string $S$ of length $N$. Let $F(X)$ denote the length of **longest non-decreasing** [subsequence](https://en.wikipedia.org/wiki/Subsequence) of the binary string $[X_1, X_2, \ldots, X_{|X|}]$. Your task is to partition $S$ into two disjoint non-empty subsequences, $S_1$ and $S_2$, such that $\min(F(S_1),F(S_2))$ is as large as possible. Find the maximum value of $\