Consider this two player game: A number of cubes are placed in one vertical pile on a table between the two players as a start. The two Players then make moves in turns. A move consists of dividing any vertical pile of cubes into two nonempty piles of different sizes. (For example, 6 cubes can be divided into piles of 5 and 1 or 4 and 2, but not 3 and 3). The player who can no longer make a move (all piles are of either one or two cubes, so it can't be divided any more) loses the game. Example: If we start with a pile of 10 cubes then it can be divided (among other choices) into 4 and 6. The second player may choose (also among other choices) to divide the 6 into 5 and 1 (so we have 4 - 5 - 1, note that no order is imposed on the piles, so this is equivalent to: 5-4-1 and 1 - 4 - 5) and so on. a- Draw the complete state space diagram if we start with a pile of 7 cubes as a graph with no repeated nodes b- How many states are in your diagram? C- Suggest a suitable state representation (i.e. name a suitable data structure to represent the state of this game). d- Based on your study of the state space diagram, do you prefer to be the first one to play or the second? (to increase your chances to win)