def iterate_partition(pi, f):
    pi_prime = []
    for part in pi:
        d = {part: set() for part in pi}
        for elem in part:
            b = f(elem)
            for part in pi:
                if b in part:
                    d[part].add(elem)
                    break
        for v in d.values():
            if v:
                pi_prime.append(frozenset(v))
    return pi_prime, pi != pi_prime


def print_partition(pi):
    print(list(map(set, pi)))


def main():
    n = 20
    b1 = frozenset(range(1, n))
    b2 = frozenset([20])
    pi = [b1, b2]
    f = lambda x: x + 1 if x < n else x

    print_partition(pi)
    while True:
        pi, changed = iterate_partition(pi, f)
        if not changed:
            break
    print_partition(pi)


if __name__ == "__main__":
    main()