Question 22
The numbers $1, 2, 3, \ldots, 2008^2$ are distributed on a $2008 \times 2008$ board so that each cell contains a different number. For each row and each column of the board, the difference between the largest and the smallest of its elements is computed. Let $S$ be the sum of the $4016$ numbers obtained. Determine the largest possible value of $S$.