PROBLEM STATEMENT

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Given a list of two-dimensional rectangles, compute the area of their union.  For example, the 
union of the three rectangles shown in the figure below:





cover an area of 35 units.



The list of rectangles will be given as a vector <string>, where each element describes one 
rectangle.  Each string will be formatted as 4 space-separated integers with no leading zeros, 
giving the coordinates of the left, bottom, right, and top of the rectangle (in that order).  The 
three rectangles shown above would be given as:



    { "1 3 5 6",
      "3 1 7 5",
      "4 4 9 7" }


DEFINITION
Class:BoxUnion
Method:area
Parameters:vector <string>
Returns:int
Method signature:int area(vector <string> rectangles)


CONSTRAINTS
-rectangles will contain between 1 and 3 elements, inclusive.
-Each element of rectangles will be formatted as described in the problem statement.
-For each rectangle, the left coordinate will be less than the right coordinate and the bottom 
coordinate will be less than the top coordinate.
-All coordinates will be between 0 and 20000, inclusive.


EXAMPLES

0)
{ "200 300 203 304" }

Returns: 12

A single rectangle with area 12.

1)
{ "0 0 10 10",
  "20 20 30 30" }

Returns: 200

Two disjoint rectangles, each of area 100.

2)
{ "0 500 20000 501",
  "500 0 501 20000" }

Returns: 39999

These two rectangles intersect at a single point.

3)
{ "4 6 18 24",
  "7 2 12 19",
  "0 0 100 100" }

Returns: 10000

The third rectangle completely overlaps the first two.

4)
{ "1 3 5 6",
  "3 1 7 5",
  "4 4 9 7" }

Returns: 35

This is the example from the problem statement.

5)
{ "0 0 20000 20000",
  "0 0 20000 20000",
  "0 0 20000 20000" }

Returns: 400000000

 This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any 
 unauthorized use or reproduction of this information without the prior written consent of 
 TopCoder, Inc. is strictly prohibited. (c)2010, TopCoder, Inc. All rights reserved.
 
  This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2010, TopCoder, Inc. All rights reserved.