A new computer game has just arrived and as an active and always-in-the-scene player, you should finish it before the next university term starts. At each stage of this game, you have to shoot an enemy robot on its weakness point. The weakness point of a robot is always the ``center of mass" of its 2D shape in the screen. Fortunately, all robot shapes are simple polygons with uniform density and you can write programs to calculate exactly the center of mass for each polygon.

Let's have a more formal definition for center of mass (COM). The center of mass for a square, (also circle, and other symmetric shapes) is its center point. And, if a simple shape C
is partitioned into two simple shapes A

and B
with areas S_A
and S_B
, then COM(C)

(as a vector) can be calculated by

<!-- MATH
\begin{displaymath}
COM (C) = \frac{S_{A} \times COM(A) + S_{B} \times COM(B)}{S_{A} + S_{B}}.
\end{displaymath}
-->

COM(C) = .

As a more formal definition, for a simple shape A with area S_A :

COM(A) =