设 $f(x)=\left|\begin{array}{ccccc}x+1 & 2 & 3 & \cdots & n \\ 1 & x+2 & 3 & \cdots & n \\ 1 & 2 & x+3 & \cdots & n \\ \vdots & \vdots & \vdots & & \vdots \\ 1 & 2 & 3 & \cdots & x+n\end{array}\right|$
, 则 $f^{(n-1)}(0)=$
A. $\frac{1}{2} n(n+1)$.
B. $\frac{1}{2}(n+1) !$.
C. $n !$.
D. $(n+1)$ !.