设 $I=\int_{0}^{\frac{\pi}{4}} \ln (\sin x) \mathrm{d} x, J=\int_{0}^{\frac{\pi}{4}} \ln (\cot x) \mathrm{d} x, K=\int_{0}^{\frac{\pi}{4}} \ln (\cos x) \mathrm{d} x$, 则 $I, J, K$ 的大小关系为( )
A. $I < J < K$.
B. $I < K < J$.
C. $J < I < K$.
D. $K < J < I$.