PAMO 2018 Problem 6

A circle is divided into $n$ sectors ( $n \geq 3$ ). Each sector can be filled in with either $1$ or $0$ . Choose any sector $\mathcal{C}$ occupied by $0$ , change it into a $1$ and simultaneously change the symbols $x, y$ in the two sectors adjacent to $\mathcal{C}$ to their complements $1-x$ , $1-y$ . We repeat this process as long as there exists a zero in some sector. In the initial configuration there is a $0$ in one sector and $1$ s elsewhere. For which values of $n$ can we end this process?