Question 122
Each cell of a $2016 \times 2016$ table is painted either in white or in black. We say that a positive integer $k$ is lucky if $k \le 2016$, and each of cellular $k \times k$ squares within the table contains exactly $k$ black cells. (For example, if all the cells are black, then only the number 1 is lucky.) Determine the greatest possible amount of lucky numbers. (E. Bakaev)