Singular Values & the SVD · Challenge problem

Find the nuclear norm (sum of the singular values) of $C = \begin{pmatrix}1 & 1 & 0 & 0\\0 & 1 & 1 & 0\\0 & 0 & 1 & 1\\1 & 0 & 0 & 1\end{pmatrix}$. Give an exact answer.