KZ-MO 2008 Problem 1

Let $F_n$ be a set of all possible connected figures, that consist of $n$ unit cells. For each element $f_n$ of this set, let $S(f_n)$ be the area of that minimal rectangle that covers $f_n$ and each side of the rectangle is parallel to the corresponding side of the cell. Find $max(S(f_n))$ ,where $f_n\in F_n$ ?

Remark: Two cells are called connected if they have a common edge.