Singular Values & the SVD · Superchallenge problem

Let $C$ be the circulant matrix $C = \begin{pmatrix}1 & 2 & 3 & 4\\4 & 1 & 2 & 3\\3 & 4 & 1 & 2\\2 & 3 & 4 & 1\end{pmatrix}$. Find $\|C - C_1\|_F$ for its best rank-one approximation $C_1$. Give your answer in simplest radical form.