Induced saturation of P6

A graph $G$ is called $H$-induced-saturated if $G$ does not contain an induced copy of $H$, but removing any edge from $G$ creates an induced copy of $H$ and adding any edge of $G^c$ to $G$ creates an induced copy of $H$. Martin and Smith studied a related problem, and proved that there does not exist a $P_4$-induced-saturated graph, where $P_4$ is the path on 4 vertices. Axenovich and Csikós gave examples of families of graphs $H$ for which $H$-induced-saturated graph $G$ exists, and asked if there exists a $P_n$-induced-saturated graph when $n\ge 5$. Our aim in this short note is to show that there exists a $P_6$-induced-saturated graph.