Alternative Sufferings

You are given a binary string $S$. In one second, the following scenario happens **simultaneously** and **independently** for **all** the bits which are set to $1$ in the string: - Change the bit from $1$ to $0$. - If the left neighbour exists and is $0$, change it to $1$. - If the right neighbour exists and is $0$, change it to $1$. For example, if $S = 010$ initially, then after $1$ second, $