The village's carpentry is located by a hill side. The carpenter's two
little boys play with a piece of wood which looks like a deformed wheel
with two identical convex polygon-shaped faces. One boy sets the wooden
wheel on a slope at the hill top and let it roll down. The other boy is
to quickly place himself at where he guesses the rolling wood would
stop. Your program is to help him make the right guess.
More formally, we consider the wooden wheel as a simple convex polygon
and we approximate the hill by a sequence of connected line segments
with decreasing slopes. The slope of the last segment in the sequence is
assumed to be zero, and the slope of the first segment is assumed to be
a positive number. Initially, the wheel is placed on the hill such that
there is at least one point of contact between the wheel and segments.
For example in the following figure, the wheel in its initial position
is drawn in solid lines, while the final position is drawn in dashed
lines.
At any instant, the wheel rotates around one of its vertices, say P, if
the y-coordinate of its center of gravity is decreased (note that this
condition is necessary at any instant during the motion). It can be
easily shown that at any instant, there is at most one such vertex.
Rotation around P is stopped when the wheel touches a segment. The
motion continues until no vertex can be found such that the wheel can
rotate around it. At any instant, assume that changing the position of
the center of gravity in any direction for at most 10-5 units, does not
affect the stability of the wheel. Also assume that the friction between
the wheel and the surface of the hill is so high that the wheel never
slides on the surface.输入描述
The first line of the input contains a single intege输出描述
For each test case, there should be a single line in the output ,
containing two numbers which are x and y coordinates of the wheel's
center of gravity. Round the numbers in the output to 3 digits after
decimal point.输入例子
1
4
40 30
30 37
24 30
30 26
27 29
30 1
100 0
40 30
输出例子
28.854 20.031