Define $corner $ as a 'broken' line(in Cartesian coordinate plane) consisting of one vertical and one horizontal line, with $ends$ at first point and last point of 'broken' line (for example $ABC$ is corner if $B$ is in plane such that $AB\perp BC$ and $AB||x$ or $AB||y$ ( note that in following statement one chooses one of such $B$)). In Cartesian coordinate plane there are $n$ blue and $n$ red points with all different $x$ and $y$ coordinates. Prove that one can draw $n$ $corners $ without common points such that every $corner $ has one blue and one red $end$.