def L():
        global index, tape
        if index: index -= 1
        else: tape.insert(0, 0)

    def R():
        global index, tape
        index += 1
        if index >= len(tape): tape.append(0)

    table = {
     ('A', 0): (1, R, 'B'),
     ('A', 1): (3, L, 'B'),
     ('A', 2): (1, R, 'Z'),
     ('A', 3): (2, R, 'A'),
     ('B', 0): (2, L, 'C'),
     ('B', 1): (3, R, 'B'),
     ('B', 2): (1, L, 'C'),
     ('B', 3): (2, R, 'A'),
     ('C', 0): (3, R, 'B'),
     ('C', 1): (1, L, 'B'),
     ('C', 2): (3, L, 'C'),
     ('C', 3): (2, R, 'C'),
     }

    state = 'A'
    tape = [0]
    index = 0
    while state != 'Z':
        tape[index], direction, state = table[state, tape[index]]
        direction()