def hanoi_iterative(n):
    pegs = {"A": list(range(n, 0, -1)), "B": [], "C": []}
    # Disk 1 always travels the same way round: A, C, B for an odd n, A, B, C for an even n.
    cycle = "ACB" if n % 2 == 1 else "ABC"

    for move in range(1, 2**n):
        smallest_at = cycle[(move // 2) % 3]
        if move % 2 == 1:
            # Odd moves: disk 1 steps on to the next tower in its cycle.
            source, target = smallest_at, cycle[(move // 2 + 1) % 3]
        else:
            # Even moves: the one legal move that leaves disk 1 alone.
            a, b = (peg for peg in "ABC" if peg != smallest_at)
            if not pegs[a] or (pegs[b] and pegs[b][-1] < pegs[a][-1]):
                source, target = b, a
            else:
                source, target = a, b
        disk = pegs[source].pop()
        pegs[target].append(disk)
        print(f"Move disk {disk} from {source} to {target}")


if __name__ == "__main__":
    hanoi_iterative(3)