Consider a regular -gon
,
in the plane, where
is a positive integer. We say that a point
on one of the sides of
can be seen from a point
that is external to
, if the line segment
contains no other points that lie on the sides of
except
. We color the sides of
in 3 different colors (ignore the vertices of
, we consider them colorless), such that every side is colored in exactly one color, and each color is used at least once. Moreover, from every point in the plane external to
, points of most 2 different colors on
can be seen. Find the number of distinct such colorings of
(two colorings are considered distinct if at least one of sides is colored differently).