Estimate of a certain Hardy-Littlewood maximal function at infinity

Question

$f\in L^1_{loc}(\mathbb{R}^n)$,prove that if $f(x)=O(|x|^{-n}),|x| \rightarrow \infty$,then $Mf(x)=O(|x|^{-n}\log|x|),(|x|\rightarrow\infty)$. where $Mf$ is the Hardy-Littlewood maximal function of f.

I try to prove it by definition but failed...

any idea will be helpful. 3q.