A measurable map must be constant on every atom of the $\sigma$-field

Let $\Omega=\{1,2,\dots\}$ the set of positive integers and $\mathbf F=\{\phi,\{1\},\{2\},\{1,2\},\{1\}^c,\{2\}^c,\{1,2\}^c,\Omega\}$, where $A^c$ denotes the complement of the set A. Let $R=(-\infty,\infty)$ and $\mathbf B$ the Borel $\sigma$-field of R. Which of the following functions $f$ from $(\Omega,\mathbf F)$ to $(R,\mathbf B)$ is measurable?