CAYLEY 2000 Problem 20

Twenty pairs of integers are formed using each of the integers 1,2,3,\dots,40 once. The positive difference between the integers in each pair is 1 or 3. (For example, 5 can be paired with 2,4,6 or 8.) If the resulting differences are added together, the greatest possible sum is

Answer Choices
A. 50
B. 54
C. 56
D. 58
E. 60