2008 Cayley Problem 25

The average value of (a-b)^2 + (b-c)^2 + (c-d)^2 + (d-e)^2 + (e-f)^2 + (f-g)^2 over all possible arrangements (a,b,c,d,e,f,g) of the seven numbers 1, 2, 3, 11, 12, 13, 14 is

\textbf{(A)}\ 398\quad \textbf{(B)}\ 400\quad \textbf{(C)}\ 396\quad \textbf{(D)}\ 392\quad \textbf{(E)}\ 394

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.