How many subsets of the set \( \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\} \) have the property that no two of its elements differ by more than 5? For example, count the sets \( \{3\} \), \( \{2, 5, 7\} \), and \( \{5, 6, 7, 8, 9\} \) but not the set \( \{1, 3, 5, 7\} \).

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