There are many secret openings in the floor which are covered by a big
heavy stone. When the stone is lifted up, a special mechanism detects this
and activates poisoned arrows that are shot near the opening. The only
possibility is to lift the stone very slowly and carefully. The ACM team
must connect a rope to the stone and then lift it using a pulley.
Moreover, the stone must be lifted all at once; no side can rise before
another. So it is very important to find the centre of gravity and connect
the rope exactly to that point. The stone has a polygonal shape and its
height is the same throughout the whole polygonal area. Your task is to
find the centre of gravity for the given polygon.
Input SpecificationThe input consists of T test cases.
The number of them (T) is given on the first line of the input
file. Each test case begins with a line containing a single integer
N (3 <= N <= 1000000) indicating the number of
points that form the polygon. This is followed by N lines, each
containing two integers Xi and
Yi (|Xi|, |Yi| <=
20000). These numbers are the coordinates of the i-th
point. When we connect the points in the given order, we get a polygon.
You may assume that the edges never touch each other (except the
neighboring ones) and that they never cross. The area of the polygon is
never zero, i.e. it cannot collapse into a single line.
Output SpecificationPrint exactly one line for each test case.
The line should contain exactly two numbers separated by one space. These
numbers are the coordinates of the centre of gravity. Round the
coordinates to the nearest number with exactly two digits after the
decimal point (0.005 rounds up to 0.01). Note that the centre of gravity
may be outside the polygon, if its shape is not convex. If there is such a
case in the input data, print the centre anyway.
Output for the Sample Input