Consider the below initial and goal states (three equally acceptable goals are given) of a planning problem and answer the following questions. In this problem the agent can move any labelled tile on top of other labelled tiles or on top of the empty tile (colored gray) and no tiles are allowed to be placed above Height 2 of any column. a. Depict the search tree up to exactly two levels (level-2) and find the heuristic values of all the generated nodes. (Given initial state can be assumed to be on level-0.). H(n)=h1(n)+h2(n) Where, h1(n)= Goal Orientation w.r.t to positioning of tiles labelled "C" \& " A " + Goal Orientation w.r.t to positioning of tiles labelled "B" \& " D " h2(n)= No.of.legal moves possible w.r.t to tiles labelled "A" \& " D " Note for Calculation: For Goal orientation, if tiles labelled "C" \& "A" are placed in same column matching any of the goal states, add a cost of +2, else add a cost of +5. Similarly, if tiles labelled "B" \& "D" are placed in same column matching any of the goal states, add a cost of +2, else add a cost of +5. Here hl (initialstate) =5+5=10 In initial state, the no.of. legal moves for " A " is 0 and that of " D " is 1 (only one allowed move on top of "C"). Here the h2(initialstate) =0+1=1. b. Using the results of sub part a., apply Greedy Best First Search algorithm till first 5 closed list updates. Show the status of OPEN and CLOSE list at each level and find the approximation toward the space complexity of the algorithm