Binary String Happiness

For a binary string $S$, define its **beauty** to be the maximum number of [substrings](https://en.wikipedia.org/wiki/Substring) $S$ can be partitioned into, such that each substring has strictly more ones than zeroes. For example, the beauty of $11011$ is $3$, as it can be partitioned as $[110][1][1]$. If such a partition doesn't exist, the beauty is defined to be $0$. Also, define the **happin