Matrices & Systems · Superchallenge problem

Let $A = \begin{pmatrix}1 & 2 & 3 & 4\\4 & 1 & 2 & 3\\3 & 4 & 1 & 2\\2 & 3 & 4 & 1\end{pmatrix}$, which is invertible. Find the sum of all the entries of $A^{-1}$.