For a polynomial $$g(x)$$ with real coefficients, let mg denote the number of distinct real roots of
$$g(x)$$. Suppose 𝑆 is the set of polynomials with real coefficients defined by

$$S = \left\{(x^{2} − 1)^{2}(a_{0} + a_{1}x + a_{2}x^{2} + a_{3}x^{3}) ∶ a_{0}, a_{1}, a_{2}, a_{3} \epsilon R\right\}$$.

For a polynomial f, let $$f{'}$$ and $$f {'}{'}$$ denote its first and second order derivatives, respectively. Then the minimum possible value of $$(m_{f{'}} + m_{f{'}{'}})$$, where $$f \epsilon S$$, is _____