# Problem F

# Overlapping Areas

Consider a set of rectangles in **2D** space as illustrated in the
figure below. Overlapping or not, they define a set of regions with
different shapes (in the example given, there are twelve regions,
identified from **A** to **L**). Lets **OD** (Overlapping
Depth) be the number of rectangles that overlap in each region (in the
figure, **OD** is the number associated to each region). In this
example, the maximum value of **OD** is 3 and it appears twice, in
regions **E** and **G**.

## Problem

Write a program that given a set of rectangles, computes
the total area of the regions with the maximum value
**OD**_{MX} (this corresponds to the sum of the areas of
region **E** and region **G** shown in the figure). In order
to avoid numerical problems, it is ensured that there are no
coincidences between edges of different rectangles.

## Input

The first input line contains the number **NR** (integer format)
of rectangles (0 <= **NR** <= 100). Each of the following
**NR** lines contain the coordinates of two opposed vertices of a
rectangle, in the sequence **x1 y1 x2 y2**, separated by single
spaces. In this case, no order is assumed for point 1 and point 2 and
numbers may be written in integer or in decimal format. The separator
between values is the space character.

## Output

One decimal number, rounded to two decimal digits, representing the
computed area.

## Sample Input

The graphical representation of the sample input is as follows:

3
-5.00 -2.00 -1.0 2.0
2.5 -1 -4.5 1.0
4 3 0 -4

## Sample Output

12.00

University of Porto / 2003 ACM Programming Contest / Round 2 / 2003/09/24