Alice is using the one-time pad and notices that when her key is all-zeroes ? = 0^?, then Enc(?, ?) = ? and her message is sent in the clear! To avoid this problem, she decides to modify the scheme to exclude the all-zeroes key. That is, the key is now chosen uniformly from {0, 1}^? {0^?}, the set of all ?-bit strings except 0^? . In this way, she guarantees that her plaintext is never sent in the clear. Is this variant still one-time perfectly secure? Justify your answer.