Intersecting Lines

Time Limit: 2 Seconds
Memory Limit: 65536 KB

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.

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 x1y1x2y2x3y3x4y4. 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".

**Sample Input**

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

** Sample Output**

INTERSECTING LINES OUTPUT

POINT 2.00 2.00

NONE

LINE

POINT 2.00 5.00

POINT 1.07 2.20

END OF OUTPUT

Source:

**Mid-Atlantic USA 1996**
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