ILL 1976 Problem 2

Let $P$ be a set of $n$ points and $S$ a set of $l$ segments. It is known that: $(i)$ No four points of $P$ are coplanar. $(ii)$ Any segment from $S$ has its endpoints at $P$ . $(iii)$ There is a point, say $g$ , in $P$ that is the endpoint of a maximal number of segments from $S$ and that is not a vertex of a tetrahedron having all its edges in $S$ . Prove that $l \leq \frac{n^2}{3}$