This question is about a brain-teaser puzzle called TopSpin. The puzzle consists of numbered pieces that can be rotated around a tray, and then a wheel that can reverse four numbers at a time. The objective is to put all the numbers in order. We will focus on a much-simplified version that only has four pieces, numbered 1, 2, 3, and 4. From any permutation of these pieces, there are three possible moves: Rotate to the Left: for example, 1234 becomes 2341. Rotate to the Right: for example, 1234 becomes 4123. Swap the two middle pieces: for example 1234 becomes 1324. Using planning techniques from AI, permutations of the pieces such as 1234, 2341, and 4123 are states of the puzzle, and nodes in the search graph. Edges between nodes are labeled with L, R, or S to indicate the moves Left, Right, or Swap. Of course, the moves Left and Right are inverses (a Left followed by a Right brings you back to the same state, and vice-versa); and Swap is its own inverse (a Swap followed by another Swap brings you back to the same state). (a) How many states are in the search graph for this simplified version of TopSpin? (b) Draw part of the graph starting from the state 2134. You should show all nodes and edges within two moves of the start state. 2134 (c) From the start state 2134, you can reach the goal state 1234 with three moves. What is the correct sequence of moves