Discrete Mathematics Level pending

On a plane, 27181 parallel lines are drawn. Then another 31415 parallel lines are drawn, not one of which is parallel to the previously drawn set of 27181 lines.

Then, to make it even worse, some more number of lines are drawn(all parallel to each other) through the points of intersection of the previously drawn 58596 lines.

If the number of parallelopipeds formed is N,

What is \(N\) \(mod\) \(1000\) ?


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