Elena Andreeva (original idea), Roman Elizarov (text)

Time limit:

2 sec

Input file:

find.in

Memory limit:

64 Mb

Output file:

find.out

Statement

Closed polyline (with possible self-intersections) partitions a plane into
a number of regions. One of the regions is unbounded — it is an
exterior of the polyline. All the bounded regions together with the
polyline itself form an interior of the polyline (shaded in the picture
below). The border of the interior (bold line in the picture)
is a polyline as well. This polyline has the same interior as the original one.
Your task is to find the border of the interior of the given polyline.

To guarantee the uniqueness (up to the starting point) of the polyline representing the border we
require that the following conditions are satisfied for it:

- it has no self-intersections, although may have self-touchings;

- no adjacent vertices of the border coincide;

- no adjacent edges of the border are collinear;

- when traversing the border, its interior is always to the left of its edges.

Input file format

The first line of the input file contains an integer number n — the number of vertices in the original polyline.
Following n lines contain two integer numbers x_{i} and y_{i} on
a line — coordinates of the vertices.
All vertices are different and no vertex lies on an edge between
two other vertices. Adjacent edges of the polyline are not collinear.

Output file format

Write to the output file an integer number m — the number of
vertices of the border. Then write m lines with coordinates
of the vertices. Coordinates must be precise up to 4 digits
after the decimal point.