The Perfect Symmetry

During a summit, the representatives of NATO countries must be protected by many bodyguards. Each V.I.P. is accompanied by their own bodyguards and is also assigned other specialists, snipers, and so on. To keep the guards effective and the protected person as safe as possible, the bodyguards are spread out in many directions around that person.

The optimal arrangement is one in which the V.I.P. stands exactly at the center of symmetry of all the guards. Unfortunately, whenever the V.I.P. moves it is very hard to rearrange the bodyguards in real time.

So the procedure is reversed: the bodyguards take their positions first, and then it is up to the V.I.P. to find the correct spot at the center of symmetry. If the person stands anywhere else, their safety cannot be guaranteed.

Your task is to automate this. Given a set of $N$ points (the bodyguard positions), find its center of symmetry $S$, the spot where the V.I.P. is relatively safe. A more formal description follows.

Take a point $A$ and a candidate center $S$. A point $A'$ is the image of $A$ with respect to the center $S$ if and only if $S$ is the midpoint of the segment joining $A$ and $A'$.

The image of a set of points $X$ with respect to $S$ is the set of the images of all its individual points. The set $X$ has a center of symmetry if there exists a point $S$ such that the image of $X$ with respect to $S$ equals $X$ itself.

The input contains several assignments. Each assignment begins with a line containing one integer $N$ ($1 \le N \le 20000$). It is followed by $N$ lines, each containing two integers $X_i$ and $Y_i$ separated by a space, where $-10^5 \le X_i, Y_i \le 10^5$. These are the Cartesian coordinates of the $i$-th point of the set.

Since no two bodyguards share a place, no point appears twice within one assignment. A bodyguard, however, may stand at the very same place as the V.I.P.

After the last assignment comes a line containing $0$ instead of a point count; this line is not processed.

For each assignment, print exactly one line.

If the set has a center of symmetry, print

V.I.P. should stay at (X,Y).

where X and Y are the Cartesian coordinates of the center, each rounded to exactly one digit after the decimal point.

If the set has no center of symmetry, print

This is a dangerous situation!