The $K_{sp}$ of BaF$_2$ is $1.84 \times 10^{-7}$, the $K_{sp}$ of BaSO$_4$ is $1.08 \times 10^{-10}$ and the $K_{sp}$ of BaCO$_3$ is $2.58 \times 10^{-9}$. If all the constituent ions of these salts were present in solution, which salt would precipitate first?