for n in range(0,20):
  print n,n%7

# output: 0 0
# output: 1 1
# output: 2 2
# output: 3 3
# output: 4 4
# output: 5 5
# output: 6 6
# output: 7 0
# output: 8 1
# output: 9 2
# output: 10 3
# output: 11 4
# output: 12 5
# output: 13 6
# output: 14 0
# output: 15 1
# output: 16 2
# output: 17 3
# output: 18 4
# output: 19 5

class F7:
  def __init__(self,x):
    self.int = x % 7
  def __str__(self):
    return str(self.int)
  __repr__ = __str__

# examples:
print F7(2)
# output: 2
print F7(6)
# output: 6
print F7(7)
# output: 0
print F7(10)
# output: 3

F7.__add__ = lambda a,b: F7(a.int + b.int)
F7.__sub__ = lambda a,b: F7(a.int - b.int)
F7.__mul__ = lambda a,b: F7(a.int * b.int)

# examples:
print F7(2) + F7(5)
# output: 0
print F7(2) - F7(5)
# output: 4
print F7(2) * F7(5)
# output: 3

F7.__eq__ = lambda a,b: a.int==b.int
F7.__ne__ = lambda a,b: a.int!=b.int

# examples:
print F7(7) == F7(0)
# output: True
print F7(10) == F7(3)
# output: True
print F7(-3) == F7(4)
# output: True
print F7(0) != F7(1)
# output: True
print F7(0) != F7(2)
# output: True
print F7(1) != F7(2)
# output: True
print F7(7) != F7(0)
# output: False
print F7(10) != F7(3)
# output: False
print F7(-3) != F7(4)
# output: False
print F7(0) == F7(1)
# output: False
print F7(0) == F7(2)
# output: False
print F7(1) == F7(2)
# output: False

def F(p):
  # caveat: caller must ensure that p is prime
  class F:
    def __init__(self,x):
      self.int = x % p
    def __str__(self):
      return str(self.int)
    __repr__ = __str__
    def __eq__(a,b):
      return a.int == b.int
    def __ne__(a,b):
      return a.int != b.int
    def __add__(a,b):
      return F(a.int + b.int)
    def __sub__(a,b):
      return F(a.int - b.int)
    def __mul__(a,b):
      return F(a.int * b.int)
    def __div__(a,b):
      # caveat: caller must ensure that b is nonzero
      return a*F(pow(b.int,p-2,p))
  return F

# examples:
F1009 = F(1009)
print F1009(-1) == F1009(1008)
print F1009(6) != F1009(5)
print F1009(101) + F1009(1000) == F1009(92)
print F1009(101) - F1009(1000) == F1009(110)
print F1009(101) * F1009(1000) == F1009(100)
print F1009(101) / F1009(1000) == F1009(213)