Let $f\left(x\right)$ be a function defined on $R$ such that $f^1\left(x\right)=2010(x-2009)(x-2010{)}^2(x-2011{)}^3(x-2012{)}^4$ for all $x\in \mathrm{R}$. If g is a function defined on $R$ with values in $(0,\mathrm{\infty })$ such that $f\left(x\right)=\ln \left(g\right(x\left)\right)$ for all $x\in \mathrm{R}$. The number of the points in $R$ at which $g$ has a local maximum is _____