2017 AIME II Problem 1

Find the number of subsets of \{1, 2, 3, 4, 5, 6, 7, 8\} that are subsets of neither \{1, 2, 3, 4, 5\} nor \{4, 5, 6, 7, 8\}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.