In this question, we will investigate shallow search, also known as depth-limited search. Depth-limited search is not guaranteed to find the optimal solution to the original problem. The point of this question is to explore some of the (potentially undesirable) behavior of depth-limited search, and to illustrate that the quality of the evaluation function can play a big role in how well depth-limited search performs. Consider the following Pacman configuration, in the board below. At each time step, Pacman can move either West (left) or East (right) and is using limited-depth minimax search (where the minimizing agent does not really do anything) to choose his next move. Pacman is 3 East moves away from the food. We will consider the following state evaluation functions: F1(state) = -−(Number of food pellets left) F2(state) = -−(Number of food pellets left) + 0.5/(distance to closest food pellet + 1); distance to closest food pellet is taken as 0 when no food remains. The search depth referred to in this question corresponds to the depth in a search tree that only considers the maximizer's actions. For example, if the search considers sequences of up to 2 actions by the maximizer, it'd have a search depth of 2. Note that there can be ties (in which case both East or West could be returned by the search). Also, note that a search does not finish when the dots are eaten.