Školjka

Let $n \geq 2$ be an integer. Consider an $n \times n$ chessboard divided into $n^2$ unit squares. We call a configutaion of $n$ rooks on this board \emph{happy} if every row and every column contains exactly one rook. Find the gretest positive integer $k$ such that for every happy configuration of rooks, we can find a $k \times k$ square without a rook on any of its $k^2$ unit squares. \begin{flushright}\emph{(Croatia)}\end{flushright}