BALKAN-SL 2010 C4

Integers are written in the cells of a table $2010 \times 2010$ . Adding $1$ to all the numbers in a row or in a column is called a move. We say that a table is equilibrium if one can obtain after finitely many moves a table in which all the numbers are equal. [list=a] []Find the largest positive integer $n$ , for which there exists an equilibrium table containing the numbers $2^0, 2^1, \ldots , 2^n$ . [] For this $n$ , find the maximal number that may be contained in such a table. [/list]