Školjka

%V0 In a country there are $n>3$ cities. We can add a street between $2$ cities $A$ and $B$, iff there exist $2$ cities $X$ and $Y$ different from $A$ and $B$ such that there is no street between $A$ and $X$, $X$ and $Y$, and $Y$ and $B$. Find the biggest number of streets one can construct! Official Wording The following operation is allowed on a finite graph: Choose an arbitrary cycle of length 4 (if there is any), choose an arbitrary edge in that cycle, and delete it from the graph. For a fixed integer ${n\ge 4}$, find the least number of edges of a graph that can be obtained by repeated applications of this operation from the complete graph on $n$ vertices (where each pair of vertices are joined by an edge).