A finite set \(S\) of positive integers is called cardinal if \(S\) contains the integer \(|S|\), where \(|S|\) denotes the number of distinct elements in \(S\). Let \(f\) be a function from the set of positive integers to itself, such that for any cardinal set \(S\), the set \(f(S)\) is also cardinal. Here \(f(S)\)denotes the set of all integers that can be expressed as \(f(a)\) for some \(a\) in \(S\). Find all possible values of \(f(2024)\).
Note: As an example, \(\{1,3,5\}\) is a cardinal set because it has exactly 3 distinct elements, and the set contains 3 .