In $\triangle ABC$ with integer side lengths,\[\cos A=\frac{11}{16}, \qquad \cos B= \frac{7}{8}, \qquad \text{and} \qquad\cos C=-\frac{1}{4}.\]What is the least possible perimeter for $\triangle ABC$? $\textbf{(A) } 9 \qquad$ $ \textbf{(B) } 12 \qquad$ $ \textbf{(C) } 23 \qquad$ $ \textbf{(D) } 27 \qquad$ $ \textbf{(E) } 44$