AMC 10 2021a Problem 19

The area of the region bounded by the graph of$$x^2+y^2 = 3|x-y| + 3|x+y|$$is $m+n\pi$, where $m$ and $n$ are integers. What is $m + n$? $\textbf{(A)} ~18 \textbf{(B)} ~27 \textbf{(C)} ~36 \textbf{(D)} ~45 \textbf{(E)} ~54$