2021 AMC 10A 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\qquad\textbf{(B)} ~27\qquad\textbf{(C)} ~36\qquad\textbf{(D)} ~45\qquad\textbf{(E)} ~54

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.