2018 little ducklings numbered 1 through 2018 are standing in a line, with each holding a slip of paper with a nonnegative number on it. It is given that ducklings 1 and 2018 have the number zero. At some point, ducklings 2 through 2017 change their number to equal the average of the numbers of the ducklings to their left and right. Suppose the new numbers on the ducklings sum to 1000. What is the maximum possible sum of the original numbers on all 2018 slips?

Let's think step by step and output the final answer within \boxed{}.
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