please provide answer and explanation in clear manner

The Tower of Hanoi is a puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod. The puzzle begins with the disks stacked on one rod in order of decreasing size, the smallest at the top, thus approximating a conical shape. The objective of the puzzle is to move the entire stack to the last (rightmost) rod, obeying the following rules: - Only one disk may be moved at a time. - Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod. - No disk may be placed on top of a disk that is smaller than it. Source: https://en.wikipedia.org/wiki/Tower of Hanoi As this is a classical puzzle game, feel free to check out online if you have some doubts with regards to the rules. The task is to solve the Tower of Hanoi problem with 4 disks with the fewest moves possible. 1. Propose an admissible heuristic for the Tower of Hanoi problem. Justify why this is a reasonable heuristic (i.e., how does it help us guide the search). 2. Show the proof that the proposed heuristic is admissible. 3. Show how the Greedy Best First search strategy (using the proposed heuristic) builds the search tree by expanding only the first 4 nodes. 4. Show how the A search strategy (using the proposed heuristic) builds the search tree by expanding only the first 4 nodes. For items 3 and 4 , show the search tree, but only expand the first four states to be expanded. Note that by expanding a state n, that means all the successors of n must also appear in the tree. Clearly label the order of the expansion of the first four states. Label the actions and the costs as well