For a string of bits $S,$ let $\frac{?}{\text{b}\text{a}\text{r}}(S)$ denote the complementary string obtained by changing all of the $1$ s to $0$ s and all of the $0$ s to $1$ s $($equivalently$,\frac{?}{\text{b}\text{a}\text{r}}(S)=So111111$dots $).$ Show that if the DES key $K$ encrypts $P$ to $C,$ then $\frac{?}{\text{b}\text{a}\text{r}}(K)$ encrypts $\frac{?}{\text{b}\text{a}\text{r}}(P)$ to $\frac{?}{\text{b}\text{a}\text{r}}(C).$