2005 Cayley Problem 16

The *non-negative difference* between two numbers a and b is a - b or b - a, whichever is greater than or equal to 0. For example, the non-negative difference between 24 and 64 is 40. In the sequence 88, 24, 64, 40, 24, \ldots, each number after the second is obtained by finding the non-negative difference between the previous 2 numbers. The sum of the first 100 numbers in this sequence is

\textbf{(A)}\ 496\quad \textbf{(B)}\ 760\quad \textbf{(C)}\ 752\quad \textbf{(D)}\ 776\quad \textbf{(E)}\ 405

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.