How many subsets of the set $\{1,2,3,4,5,6,7,8,9,10\}$ are there that does not contain 4 consequtive integers?

$ \textbf{(A)}\ 596 \qquad \textbf{(B)}\ 648 \qquad \textbf{(C)}\ 679 \qquad \textbf{(D)}\ 773 \qquad \textbf{(E)}\ 812$