Let DES:$\{0,1{\}}^{64}\{0,1{\}}^{56}\{0,1{\}}^{64}$ be the DES function. Show that

DES$(\frac{?}{\text{b}\text{a}\text{r}}(k),\stackrel{}{x})\frac{?}{b}=ar(DES(k,x))$

for kin$\{0,1{\}}^{56},$xin$\{0,1{\}}^{64},$ where $\stackrel{}{x}$ denotes the bitwise complement of a bit string $x.(25$ points$)$