Show that DES exhibits a complementation property, i.e., if C = Enc(K, P), then Cc = Enc(Kc, Pc). Here, P is a plaintext, K is the key and C is the ciphertext, and Xc denotes the bitwise complementation of X. Show all steps.
[Hint: Consider the operations that take place in each round of DES encryption; focus on say the i-th round, and carefully analyze how the input changes after each step]