#
def choose(xs, n):
    """
    Computes r choose n, in other words choose n from xs.
    Returns combinations and not permutations.
    """

    if not xs or n == 0:
        return [[]]
    if len(xs) == n:
        return [xs]

    rs = []
    x = xs[0]
    for r in choose(xs[1:], n - 1):
        rs.append([x] + r)
    for r in choose(xs[1:], n):
        rs.append(r)
    return rs


def pairs(xs):
    if len(xs) == 2:
        return [xs]
    r = []
    a = xs[0]
    for b in xs[1:]:
        r.append([a, b])

    return r + pairs(xs[1:])


def can_form_squares(pair):
    xs, ys = pair

    # replace 9s with 6s
    for d, e in [(0, 1), (0, 4), (0, 6), (1, 6),
                 (2, 5), (3, 6), (4, 6), (6, 4), (8, 1)]:
        if d in xs and e in ys:
            continue
        elif e in xs and d in ys:
            continue
        return False
    return True


def euler_090():
    # replace 9s with 6s to handle "up-side down usage of 6" without hassle
    xs = list(range(0, 9)) + [6]

    cs = choose(xs, 6)
    ps = pairs(cs)
    count = 0
    for p in ps:
        if can_form_squares(p):
            count += 1
    return count


if __name__ == "__main__":
    solution = euler_090()
    print("e090.py: " + str(solution))
    assert(solution == 1217)