2012 Fermat Problem 15

Oranges are placed in a pyramid-like stack with each layer completely filled. The base is a rectangle that is 5 oranges wide and 7 oranges long. Each orange, above the first layer, rests in a pocket formed by four oranges in the layer below, as shown. The last layer is a single row of oranges. The total number of oranges in the stack is

\textbf{(A)}\ 53\quad \textbf{(B)}\ 80\quad \textbf{(C)}\ 82\quad \textbf{(D)}\ 85\quad \textbf{(E)}\ 105

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 Fermat contests here.