2021 AMC 10B Problem 7

In a plane, four circles with radii 1,3,5, and 7 are tangent to line \ell at the same point A, but they may be on either side of \ell. Region S consists of all the points that lie inside exactly one of the four circles. What is the maximum possible area of region S?

\textbf{(A) }24\pi \qquad \textbf{(B) }32\pi \qquad \textbf{(C) }64\pi \qquad \textbf{(D) }65\pi \qquad \textbf{(E) }84\pi

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