2021 AIME II Problem 6

For any finite set S, let |S| denote the number of elements in S. Find the number of ordered pairs (A,B) such that A and B are (not necessarily distinct) subsets of \{1,2,3,4,5\} that satisfy |A| \cdot |B| = |A \cap B| \cdot |A \cup B|

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.