A unit square is removed from the corner of an $n\times n$ grid where $n \geq 2$. Prove that the remainder can be covered by copies of the "L-shapes" consisting of $3$ or $5$ unit square, as depicted in the figure below. Every square must be covered once and the L-shapes must not go over the bounds of the grid. [asy][asy] import geometry; draw((-1.5,0)--(-3.5,0)--(-3.5,2)--(-2.5,2)--(-2.5,1)--(-1.5,1)--cycle); draw((-3.5,1)--(-2.5,1)--(-2.5,0)); draw((0.5,0)--(0.5,3)--(1.5,3)--(1.5,1)--(3.5,1)--(3.5,0)--cycle); draw((1.5,0)--(1.5,1)); draw((2.5,0)--(2.5,1)); draw((0.5,1)--(1.5,1)); draw((0.5,2)--(1.5,2)); [/asy][/asy]Estonian Olympiad, 2009