from itertools import product
from functools import reduce

def ilen(iterable):
    return reduce(lambda sum, element: sum + 1, iterable, 0)

def proditer(xs):
    for i in product(*map(lambda x: range(x + 1), xs)):
      yield i

def is_valid(ds):
    if sum(ds) == 0:
        return False
    elif ((True in map(lambda x: x >= 2, ds)) and (ilen(filter(lambda x: x > 0, ds)) < 2)):
        return False
    else:
        return True

def is_zero(ds):
    return sum(ds) == 0


def pts(xs, prt=[]):
    if is_zero(xs):
        return 0
    out = 0
    for ds in proditer(xs):
        if not is_valid(ds):
            continue
        dff = [x - d for x, d in zip(xs, ds)]
        if sorted(prt + [ds]) != prt + [ds]:
            continue

        if is_zero(dff):
            q = prt + [ds]
            print(q)
            continue
        else:
            out += pts(dff, prt + [ds])
    return out