KöMaL 2022 B5284

Let $n>2$. Alan has selected an edge of the complete graph of $2n$ vertices. Paula wants to find out which. If she pays 1 forint (Hungarian currency, HUF) she may name any pairing of all vertices and ask whether the selected edge is contained in it. What is the minimum number of forints that Paula needs to have in her pockets in order to be certain that she can find out the selected edge by asking the appropriate questions?