The figure below is a representation of the game that you are about to play. There are $5$ states: A$,$ B$,$ C$,$ D and the goal state. The goal state, when reached, gives $100$ points as a reward. In addition to the goal's points, you get points by moving to different states. The amount of points you get is shown next to the arrows. You start at the state B$.$ To find out the best policy, you use asynchronous value iteration with a decay of $0\mathrm{.}9.$ Answer the following question with proper justification.

i$.$ When you first start playing the game, what action would you take $*$up$,$ down, left, right$)$ at state B$?$

ii$.$ What is the total reward at state B at this time?

iii. Let's say you keep playing until your total values for each state have converged. What actions would you take at state B$?$

iv$.$ What is the total reward atstate B at this time?