ISL 1979 Problem 14

Let $S$ be a set of $n^2 + 1$ closed intervals ( $n$ a positive integer). Prove that at least one of the following assertions holds:(i) There exists a subset $S'$ of $n+1$ intervals from $S$ such that the intersection of the intervals in $S'$ is nonempty.(ii) There exists a subset $S''$ of $n + 1$ intervals from $S$ such that any two of the intervals in $S''$ are disjoint.