A subset $S$ of the set of integers from 0 to 99 is said to have property $A$ if it is impossible to fill a crossword puzzle with 2 rows and 2 columns using numbers from $S$ (where 0 is written as 00, 1 as 01, and so on). Determine the maximal number of elements in the set $S$ that has property $A$.

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