import doctest
import random


def flatten(lst):
    """
    >>> flatten([[3,2],[1,2]])
    [3, 2, 1, 2]
    """
    return [i for sublst in lst for i in sublst]

def magic_shuffle(deck):
    """
    >>> magic_shuffle([1,2,3,4])
    [1, 3, 2, 4]
    """
    half = len(deck) // 2
    return flatten(zip(deck[:half], deck[half:]))

def after_how_many_is_equal(shuffle_type,start,end):
    """
    >>> after_how_many_is_equal(magic_shuffle,[1,2,3,4],[1,2,3,4])
    2
    """

    start = shuffle_type(start)
    counter = 1
    while start != end:
        start = shuffle_type(start)
        counter += 1
    return counter

def main():
    doctest.testmod()

    print("Length of the deck of cards | Perfect shuffles needed to obtain the same deck back")
    for length in (8, 24, 52, 100, 1020, 1024, 10000):
        deck = list(range(length))
        shuffles_needed = after_how_many_is_equal(magic_shuffle,deck,deck)
        print("{} | {}".format(length,shuffles_needed))


if __name__ == "__main__":
    main()