5.7 Show that, if the input set has more than two elements, the validity condition given in Section 5.2.2 is not equivalent to requiring that every nonfaulty decision be the input of some processor. In particular, design an algorithm that satisfies the validity condition of Section 5.2.2 but does not guarantee that every nonfaulty decision is the input of some processor. Hint: Consider the exponential message and phase king algorithms when the size of the input set is larger than 2.