\problemname{Keeping On Track}
Acmar and Ibmar are at war! You are in charge of a rail network that transports
important supplies throughout the great state of Acmar during this delicate
time. The rail system is made up of a set of rail lines which meet at various
junction points. While there is no limit to the number of rail lines that can
meet at a junction, the network is set up so that there is only one path between
any two junctions. You've tried to argue for some redundancy in the system,
i.e., extra rail lines so that there are two or more paths connecting some
junctions, but it's wartime and budgets are tight.

However, this may soon change as you've just been given some terrible news from
double agents working in Ibmar:  within the next month enemy spies plan to blow
up one of the junctions!  Unfortunately, the exact junction is not known, but
knowing your enemy well you are certain that they will undoubtedly strike the
{\em critical junction}, specifically the junction whose removal disconnects the
most pairs of other remaining junctions in the system.  You don't have much time
to act, so the most you can do is add one new line connecting two currently
unconnected junctions, thereby reducing the number of disconnected pairs after
the critical junction has been destroyed. Your job is to determine how to make
the number of disconnected pairs as small as possible by adding in the best
possible rail line.

\section*{Input}
Input starts with a line containing an integer $n$ ($2 \leq n \leq 10\,000$)
indicating the number of rail lines in the system. Following that are $n$ lines
of the form $i_1$ $i_2$ indicating that a rail line connects junctions $i_1$ and
$i_2$.  Junctions are numbered consecutively starting at $0$.  All rail lines are
two-way and no rail line appears more than once in the input.  There is exactly
one path between any two junction points given in the input.

\section*{Output}
Display two values $n_1$ and $n_2$, where $n_1$ is the number of pairs of
junctions which will be disconnected when the enemy destroys the critical
junction, and $n_2$ is the number of pairs of junctions still disconnected after
you add in the best possible rail line. There will never be more than one
critical junction.
