Let f be a function defined on R (the set of all real numbers) such that
$$f'(x) = 2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4$$, for all $$x \in R$$.
If g is a function defined on R with values in the interval $$(0, \infty)$$ such that $$f(x) = \ln (g(x))$$, for all $$x \in R$$,
then the number of points in R at which g has a local maximum is