The sliding-tile puzzle consists of two black tiles, two white tiles, and an empty space (shown as the middle tile in below initial configuration) in some order. Player with black tiles and Player with white tile alternate turns to play against each other in the game. Below are the possible moves for the players and they can choose only one move type in a terminates if a player has not more valid move to play. Game Move #1: A tile may move into an adjacent empty location. Move #2: A tile can hop over one other tile into the empty position. Move #2: 2023/04/around Black Black White with black colored tiles starts the play, construct game tree with utility up to level 3 or only two Max player and one round for Min 8220023/04/09-202 Static Evaluation Value = Utility of MAX player-Utility60-20 Player using below utility function. 9-20/25 for Utility of a player = Reward of 3 if its own game piece is its adjacent & directly reachable + Penalty of -2 if piece is adjacent & of MIN player Reward of +1 if empty position is adjacent & directly reachable directly re ble-directly reachable + a. If pl04/09-2022 White player LUF b. Explain the process for speeding up the min-max search using the generated utility tree with alpha beta pruning. Show each step in the algorithm c. "Optimal reordering of the game tree improves the efficiency of Alpha Beta pruning". Justify this statement with the given above problem as the example for demonstration.