The Necklace

Chef wants to buy a necklace for Chefina. The necklace will consist of $N$ beads joined together in a circular manner, i.e., the $1^{st}$ bead will lie between $N^{th}$ and $2^{nd}$ beads. The $2^{nd}$ bead will lie between $3^{rd}$ and $1^{st}$ beads and so on. Each bead has a certain colour (some beads can have the same colour). Chef considers the necklace good if no two neighbouring beads have