Singular Values & the SVD · Hard problem

Let $a = \begin{pmatrix}1\\2\\2\end{pmatrix}$, $b = \begin{pmatrix}0\\4\\0\end{pmatrix}$ and $A = ab^{T} + ba^{T}$. Find the nuclear norm $\|A\|_* = \sum\sigma_i$ of $A$.