KURSCHAK 2007 Problem 1

We have placed $n>3$ cards around a circle, facing downwards. In one step we may perform the following operation with three consecutive cards. Calling the one on the center $B$ , the two on the ends $A$ and $C$ , we put card $C$ in the place of $A$ , then move $A$ and $B$ to the places originally occupied by $B$ and $C$ , respectively. Meanwhile, we flip the cards $A$ and $B$ .

Using a number of these steps, is it possible to move each card to its original place, but facing upwards?