def FrameStewartSolution(ndisks,start=1,end=4,pegs=set([1,2,3,4])):
    if ndisks ==0 or start == end: #zero disks require zero moves
        return []
    if  ndisks == 1 and len(pegs) > 1: #if there is only 1 disk it will only take one move
        return ["move(%s,%s)"%(start,end)]
    if len(pegs) == 3:#3 pegs is well defined optimal solution of 2^n-1
        return towers3(ndisks,start,end,pegs)
    if len(pegs) >= 3 and ndisks > 0:
        best_solution = float("inf")
        best_score = float("inf")
        for kdisks in range(1,ndisks):
            helper_pegs = list(pegs.difference([start,end]))
            LHSMoves = FrameStewartSolution(kdisks,start,helper_pegs[0],pegs)
            pegs_for_my_moves = pegs.difference([helper_pegs[0]]) # cant use the peg our LHS stack is sitting on
            MyMoves = FrameStewartSolution(ndisks-kdisks,start,end,pegs_for_my_moves) #misleading variable name but meh
            RHSMoves = FrameStewartSolution(kdisks,helper_pegs[0],end,pegs)#move the intermediat stack to
            if any(move is None for move in [LHSMoves,MyMoves,RHSMoves]):continue #bad path :(
            move_list = LHSMoves + MyMoves + RHSMoves
            if(len(move_list) < best_score):
                best_solution = move_list
                best_score = len(move_list)
        if best_score < float("inf"):
            return best_solution
    #all other cases where there is no solution (namely one peg, or 2 pegs and more than 1 disk)
    return None