Let \(\mathbb{R}\) be the set of real numbers. Let \(f : \mathbb{R} \to \mathbb{R}\) be a function such that for all real numbers \(x\) and \(y,\)
\(f(x^2) + f(y^2) = [f(x + y)]^2 - 2xy\)
Let
\(S = \sum_{n = -2019}^{2019} f(n)\)
Determine the number of possible values of \(S.\)
