AMC 12 2016b Problem 18

What is the area of the region enclosed by the graph of the equation $x^2+y^2=|x|+|y|?$

\textbf{(A)}\ \pi+\sqrt{2} \textbf{(B)}\ \pi+2 \textbf{(C)}\ \pi+2\sqrt{2} \textbf{(D)}\ 2\pi+\sqrt{2} \textbf{(E)}\ 2\pi+2\sqrt{2}