Problem 2: Intersecting Lines

We all know that a pair of distinct points on a plane defines a line
and that a pair of lines on a plane will intersect in one of three
ways: 1) no intersection because they are parallel, 2) intersect in a
line because they are on top of one another (i.e. they are the same
line), 3) intersect in a point.  In this problem you will use your
algebraic knowledge to create a program that determines how and
where two lines intersect.

Problem Statement: Your program will repeatedly read in four
points that define two lines in the x-y plane and determine how and
where the lines intersect.  All numbers required by this problem
will be reasonable, say between -1000 and 1000. 

Input:   The first line contains an integer N between 1 and 10
describing how many pairs of lines  are represented.  The next N
lines will each contain eight integers.  These integers represent the
coordinates of four points on the plane in the order x1 y1 x2 y2 x3
y3 x4 y4.  Thus each of these input lines represents two lines on
the plane: the line through (x1,y1) and (x2,y2) and the line through
(x3,y3) and (x4,y4).  The point (x1,y1) is always distinct from
(x2,y2).  Likewise with (x3,y3) and (x4,y4).

Output: There should be N+2 lines of output.  The first line of
output should read INTERSECTING LINES OUTPUT.  There will
then be one line of output for each pair of planar lines represented
by a line of input, describing how the lines intersect: none, line, or
point.  If the intersection is a point then your program should
output the x and y coordinates of the point, correct to two decimal
places.  The final line of output should read "END OF OUTPUT".

Example:   The following input data:

5
0 0 4 4 0 4 4 0
5 0 7 6 1 0 2 3
5 0 7 6 3 -6 4 -3
2 0 2 27 1 5 18 5
0 3 4 0 1 2 2 5

should produce the following output:

INTERSECTING LINES OUTPUT
POINT 2.00 2.00
NONE
LINE
POINT 2.00 5.00
POINT 1.07 2.20
END OF OUTPUT