Three distinct points are plotted at random on a Cartesian plane, for which `-1000 <= x,y <= 1000`, such that a triangle is formed.

Consider the following two triangles:

~~~
A(-340,495), B(-153,-910), C(835,-947)

X(-175,41), Y(-421,-714), Z(574,-645)
~~~

It can be verified that triangle ABC contains the origin, whereas triangle XYZ does not.

Using [triangles.txt](https://projecteuler.net/project/resources/p102_triangles.txt), a 27K text file containing the co-ordinates 
of one thousand "random" triangles, find the number of triangles for which the interior contains the origin.

NOTE: The first two examples in the file represent the triangles in the example given above.