# doctors Choice Function if True or hospitals otherwise
def C(L, doctors):
  pass


# Lower Ideal of L
def Li(L):
  lowerIdeal = set()
  for x in AllContracts:
    for y in L:
      if isComparable(x, y) and x <= y:
        lowerIdeal.add(x)
        break
  return lowerIdeal


# Lower Ideal of C(L, doctors)
def C_star(L, doctors):
  return Li(C(L, doctors))


# antitone function U for the choice function C_star(L, doctors)
def U_star(L, doctors):
  u = set()
  for x in AllContracts:
    if x in L:
      u.add(x)
    else:
      L.add(x)
      if x in C_star(L, doctors):
        u.add(x)
      L.remove(x)
  return u


# one mapping of L1 and L2 with antitone function for hospitals/doctors
def f(L1, L2):
  return (U_star(L2, hospitals), U_star(L1, doctors))


def solve(L1, L2):
  nextL1, nextL2 = f(L1, L2)
  if (L1, L2) == (nextL1, nextL2):
    # (L1, L2) is a fixed Point
    return (L1, L2)
  return solve(nextL1, nextL2)