Any two tracks crossing?

A map has straight pieces of track, each given by its two ends. Two pieces meet if they share any point: they cross, touch, share an end or overlap. Return the positions (i, j) of any two different pieces that meet, or None if no two meet. When several pairs meet, any one of them is accepted; the tests check that the two pieces you name really share a point.

any_crossing([((0, 0), (4, 4)), ((0, 4), (4, 0))])   # (0, 1)
any_crossing([((0, 0), (1, 0)), ((2, 0), (3, 0))])   # None
any_crossing([((0, 0), (2, 2)), ((2, 2), (4, 0))])   # (0, 1)

Each piece has two different ends, given in either order. Pieces may be upright. Coordinates are whole numbers up to about 3 million.

Limits

• Up to 20,002 pieces. The big tests have 4 seconds each.
• Checking every pair is 200 million pair checks, far too slow.