Segments

Consider a set $S$ of $n$ vertical segments in the plane (each segment includes its two endpoints). No two segments of $S$ have a point in common.

Two segments see each other if there is a horizontal segment that joins them and has no point in common with any other segment of $S$.

The figure below shows an example set of segments. The pairs of segments that see each other are 1-2, 1-3, 2-3, 1-5, and 4-5. Segments 1 and 4 do not see each other.

Among all sets of exactly $n$ pairwise disjoint vertical segments, we look for the largest possible number of pairs of segments that see each other. Given $n$, compute this maximum number of visible pairs.

The only line of input contains one integer $n$ ($1 \le n \le 20\,000$).

Print one integer: the maximum possible number of pairs of segments that can see each other, taken over all sets of $n$ pairwise disjoint vertical segments.