CONO-SUR 2015 Problem 2

$3n$ lines are drawn on the plane ( $n > 1$ ), such that no two of them are parallel and no three of them are concurrent. Prove that, if $2n$ of the lines are coloured red and the other $n$ lines blue, there are at least two regions of the plane such that all of their borders are red.

Note: for each region, all of its borders are contained in the original set of lines, and no line passes through the region.