4.3. Suppose that you have a regular deck of cards arranged as follows, from top to bottom: Only two operations on the deck are allowed: inshuffing and outshuffling. In both, you begin by cutting the deck exactly in half, taking the top half into your right hand and the bottom into your left. Then you shuffle the two halves together so that the cards are perfectly interlaced; that is, the shuffled deck consists of one card from the left, one from the right, one from the left, one from the right, etc. The top card in the shufled deck comes from the right hand in an outshuffle and from the left hand in an inshuffle. (a) Model this problem as a state machine. (b) Use the Invariant Principle to prove that you cannot make the entire first half of the deck black through a sequence of inshuffles and outshuffles. Note: Discovering a suitable invariant can be difficult! This is the part of a correctness proof that generally requires some insight, and there is no simple recipe for finding invariants. A standard initial approach is to identify a bunch of reachable states and then look for a pattern -some feature that they all share