Setubal 1998
Picture
A number of rectangular posters, photographs
and other pictures of the same shape are pasted
on a wall. Their sides are all vertical or
horizontal. Each rectangle can be partially or
totally covered by the others. The length of the
boundary of the union of all rectangles is called
the perimeter.
Task
Write a program to calculate the perimeter.
An example with 7 rectangles is shown in
Figure 1.
Figure 1. A set of 7 rectangles
The corresponding boundary is the whole set of
line segments drawn in Figure 2.
Figure 2. The boundary of the set of rectangles
The vertices of all rectangles have integer
coordinates.
Input Data
The first line of the file PICTURE.IN contains
the number of rectangles pasted on the wall.
In each of the subsequent lines, one can find the
integer coordinates of the lower left vertex and
the upper right vertex of each rectangle. The
values of those coordinates are given as ordered
pairs consisting of an x-coordinate followed by
a y-coordinate.

Sample Input

7
-15 0 5 10
-5 8 20 25
15 -4 24 14
0 -6 16 4
2 15 10 22
30 10 36 20
34 0 40 16
This corresponds to the example of Figure 1.
Output Data
The file PICTURE.OUT must contain a single
line with a non-negative integer which
corresponds to the perimeter for the input
rectangles.
Sample Output:
228
This is the contents of the output file for the
example above.

0 ≤ number of rectangles < 5000
All coordinates are in the range [-10000,10000]
and any existing rectangle has a positive area.
The numeric value of the result may need a
32-bit signed representation.

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출처 IOI 1998