The least value of the product $xyz$ for which the determinant $\begin{vmatrix} x& 1& 1 \\ 1 & y & 1 \\ 1 & 1 & z \end{vmatrix}$ is non negative, is:

Question

( A ) $-8$
( B ) $-16 \sqrt{2}$
( C ) $-1$
( D ) $-2\sqrt{2}$