Decomposition of $\Bbb R^n$ as union of countable disjoint closed balls and a null set

This is a problem in Frank Jones's Lebesgue integration on Euclidean space (p.57),

$$\mathbb{R}^n = N \cup \bigcup_{k=1}^\infty \overline{B}_k$$

where $\lambda(N)=0$, and the closed balls are disjoint.

could any one give some hints?