Problem
You are given a set of two-dimensional rectangular boxes on a two-dimensional Cartesian plane
with the following assumptions and constraints:
● All boxes are axis-aligned, i.e. each box can be defined in terms of the Cartesian
coordinates of its minimum corner {a, b} and its maximum corner {c, d} such that a < c and
b < d.
● Boxes may be contained within other boxes or may be disjoint from one another, i.e.
boxes do not overlap or touch one another..
● The boxes therefore partition the plane into a number of regions. The unbounded region,
which lies outside of all the boxes, is classified as “sea”.
● All other regions are classified either as “sea” or as “land”, subject to the constraint that
adjacent regions must not share the same classification.
The task is to read the definition of the rectangles from standard input formatted as defined
below, and output the number of regions classified as “land” to standard output.

If you make any other assumptions as part of your solution then please make comments in the
code. If there are further considerations that might affect the memory use or performance of your
solution then do make a note of them.

Input Format
Some sample data is provided below for you to use when testing your solution. The first line
contains an integer N denoting the number of boxes. The next N lines contain the four floating
point values a, b, c, d that define Cartesian coordinates of the minimum corner and
maximum corner of each box separated by a single space.

<N>
a1 b1 c1 d1

aN bN cN dN
Sample Input
14
1.0 1.0 10.0 6.0
1.5 1.5 6.0 5.0
2.0 2.0 3.0 3.0
2.0 3.5 3.0 4.5
3.5 2.0 5.5 4.5
4.0 3.5 5.0 4.0
4.0 2.5 5.0 3.0
7.0 3.0 9.5 5.5
7.5 4.0 8.0 5.0
8.5 3.5 9.0 4.5
3.0 7.0 8.0 10.0
5.0 7.5 7.5 9.5
5.5 8.0 6.0 9.0
6.5 8.0 7.0 9.0
Sample Output:
9