Suppose your search space is an »infinite 3D grid« (see figure below), where the starting point is the coordinate (0,0,0), the goal is some point (x,y,z) – represented on the figure is the point (3,2,2) as a possible goal state. (a) What is the branching factor b in this search space? (b) What is the number of (possible) distinct states after k steps of search (for k>0)? (c) Whatisthemaximalnumberofvisitedstatesduringbreadth-first (in relation to the number of steps k)? (d) Ish=|u-x|+|v-y|+|w-z|anadmissibleheuristicforevaluatingthestate(u,v,w)? Explain!