def U(x,y):
  return max(x,y)

def I(x,y):
  return min(x,y)

def S(x,y):
  return max(0, x-y)

def expr1(a,b,c):
  return U( I( I(a,b), c),
            S(b,a) )

def expr2(a,b,c):
  return S( b, S( I(a,b), c) )

def all_inputs(n):
  if n == 0:
    return [()]
  else:
    rest = all_inputs(n - 1)
    ret = []
    for r in rest:
      ret.append( (0,) + r)
      ret.append( (1,) + r)
    return ret

if __name__ == "__main__":
  print U(U(0, 0),1)

  all_threes = all_inputs(3)

  for all_three in all_threes:
    assert expr1(*all_three) == expr2(*all_three), "failed on {}".format(all_three)