Question 131
There is a chair on every cell of a $2n \times 2n$ board. Now $2n^2$ couples are to be seated, each person in one seat. The distance between a couple is defined as the difference of the column numbers plus the difference of the row numbers of their seats (for example, if a couple sit at (3,3) and (2,5), their distance is $|3-2| + |3-5| = 3$). The total distance of all couples is defined as the sum of the distances of these $2n^2$ couples. Find the maximum possible total distance.