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The following table describes a registry of kidney donor / acceptor pairs, where each acceptor and donor has the specified blood type. Mirroring our in-class examples, you may assume that the blood types need to match exactly for a kidney exchange to occur. Pair Donor Acceptor Pair Donor Acceptor AB A A AB 2 O B AB B B A B O A O 1. Construct a graph for this registry. 2. Find all cycles of length 2 or 3 (that is, the cycle has 2 or 3 vertices in it, respectively). Using only these cycles, what is the maximum number of acceptors that can receive kidneys, and whose kidneys do they receive? 3. Is it worth looking for longer cycles? In other words, can we save additional lives by considering longer cycles? Justify your