Solve the Towers of Hanoi game for the following graph G=(V,E) with V={Start, Aux 1, Aux2, Aux3, Dest} and E = {(Start,Aux1), (Aux1,Aux2), (Aux2,Aux3), (Aux3,Aux1), (Aux3,Dest)}.

1) Design an algorithm and determine the time and space complexities of moving n disks from Start to Dest.

do not copy other answers in chegg or google because they are not what im looking for. It must have 5 pegs (Start, A1,A2,A3,DEST) and move one peg per time . AKA "Move Disk 1 from A to B" Then "Move Disk 1 from B to C" and verify if the big o is 2n or 3n because im finding different answers everywhere.