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