CONO-SUR 2009 Problem 2

A hook consists of three segments of longitude $1$ forming two right angles as demonstrated in the figure.

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We have a square of side length $n$ divided into $n^2$ squares of side length $1$ by lines parallel to its sides. Hooks are placed on this square in such a way that each segment of the hook covers one side of a little square. Two segements of a hook cannot overlap. Determine all possible values of n for which it is possible to cover the sides of the $n^2$ small squares.