Selfish shellfish

Probability Level 3

A subset of {1,2,,12}\{1,2,\ldots, 12\} is said to be selfish if it contains its size as an element. How many subsets of {1,2,12}\{1,2,\ldots 12\} have the property that both the subset and its complement is selfish?

Details and assumptions

As an explicit example, the set {3,6,9}\{3,6,9\} is selfish because it contains 3 elements, and contains the element 3.

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