def repeat(n, xs):
    return [xs for _ in range(n)]


def sequence(xss, acc):
    if not xss:
        return acc
    return sequence(xss[1:], [a + [x] for x in xss[0] for a in acc])


def is_balanced(xs):
    """ Check if subsets are balanced. That means for every lower number there
    is a higher number that balances it out. """
    ones_balanced, twos_balanced = True, True
    ones, twos = 0, 0
    for x in xs:
        if x == 1:
            ones += 1
            twos -= 1
        elif x == 2:
            ones -= 1
            twos += 1
        if ones < 0:
            ones_balanced = False
        if twos < 0:
            twos_balanced = False
    return ones_balanced or twos_balanced


def euler_106():
    n = 12
    # Generate all possible subsets where both subsets have the same number of
    # elements and at least two elements per subset.
    xs = repeat(n, [0, 1, 2])
    xs = [x for x in sequence(xs, [[]])
          if x.count(1) > 1
          if x.count(1) == x.count(2)]
    return len([1 for x in xs if not is_balanced(x)]) // 2


if __name__ == "__main__":
    solution = euler_106()
    print("e106.py: " + str(solution))
    assert(solution == 21384)