Suppose $K_1$ is a knot diagram colored by a dihedral quandle $R_n$ of order $n$, By applying crossing change (exchanging over and under arcs) to one crossing in $K_1$, we obtain a new diagram let us say $K_2$. Then is it possible that $K_2$ is also colorable by the dihedral qaundle $R_n$ or it will be colored by a dihedral quandle of different cardinality
Thank you in advance.