I need help with my homework

Sorry for my english at first.

There is a cube with points ABCDEFGH

and AE, BF, CG and DH are its edges.

Also |BJ|=|CJ|=|BC|/2

Line m goes through H and J.

Line k goes through A and E.

Line l goes through F and G.

Line n goes through C and D.

How many lines exist, which are equaly distanted from lines k , l and n and are pararell to line m.

Please help me!

Thank you in advance