A growing number of people accept nowadays the theory of strings and
superstrings and of the mirror world. One of the most interesting objects of
study within this theory is circular strings. They can be used for traveling
between worlds: flying through the ring of such a string, an observer finds
himself in the mirror world, which can have entirely different stars, galaxies,
and, possibly, life. The traveler can return to his world by flying backward
through the same or any other circular string. Unfortunately, superstrings are
unstable. Gradually losing their energy, they contract and eventually explode
when their diameter decreases to the diameter of an elementary particle. Which
means that a travel to the mirror world is potentially dangerous.
Circular strings also have a practical application. They can be used to draw
any regular polygon without ruler or compasses. For this, a string should be
made to oscillate exactly in a plane at one of its resonance frequencies. In
this situation, several points of the string stay fixed. According to the
theory, these points are vertices of the required polygon. Physicists have just
made such an experiment and now ask you to analyze the results.
You are given n pairs of real numbers. The physicists claim that these are
the coordinates of vertices of a nondegenerate n-gon written in the traversal
The first line contains the integer n (3 ≤ n ≤ 100). The i-th
of the following n lines contains real numbers xi and yi separated with
a space (0 ≤ xi, yi ≤ 1); these numbers are the coordinates of the
i-th point. The coordinates of different points may coincide, but it is
guaranteed that there exists at least one pair of points at a distance of at
least 0.3. The coordinates are given with accuracy of at least 10−10.
If the experiment didn't produce vertices of a regular n-gon in
the traversal order, output “NO”. Otherwise,
output “YES”. It is guaranteed that in the case of the negative
answer the coordinates of the points can't be changed by less than 10−5 so
that they become the coordinates of vertices of a regular n-gon written in
the traversal order.
Problem Author: Dmitry Ivankov
Problem Source: The 14th Urals Collegiate Programing Championship, April 10, 2010