2021 Cayley Problem 19

In the diagram, eight circles, each of radius 1, are drawn inside a rectangle. Four of the circles are tangent to two sides of the rectangle and to two other circles. Four of the circles are tangent to one side of the rectangle and to three other circles. A region has been shaded, as shown. It consists of three spaces (each space bounded by a different set of four circles), as well as four of the circles themselves. The area of this region is closest to

\textbf{(A)}\ 12\quad \textbf{(B)}\ 13\quad \textbf{(C)}\ 14\quad \textbf{(D)}\ 15\quad \textbf{(E)}\ 16

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.