for x in range(7):
  for y in range(7):
    if (x*x+y*y) % 7 == 1:
      print (x,y)

# output: (0, 1)
# output: (0, 6)
# output: (1, 0)
# output: (2, 2)
# output: (2, 5)
# output: (5, 2)
# output: (5, 5)
# output: (6, 0)

def clockadd(P1,P2):
  x1,y1 = P1
  x2,y2 = P2
  x3 = x1*y2+y1*x2
  y3 = y1*y2-x1*x2
  return x3,y3

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

F7 = F(7)
P1 = (F7(2),F7(5))
P2 = (F7(1),F7(0))
print clockadd(P1,P2)
print clockadd(P2,P1)
P3 = (F7(5),F7(5))
print clockadd(clockadd(P1,P2),P3)
print clockadd(P1,clockadd(P2,P3))

p = 1000003
Fp = F(p)
P = (Fp(1000),Fp(2))
P2 = clockadd(P,P)
print P2
P3 = clockadd(P2,P)
print P3
P4 = clockadd(P3,P)
P5 = clockadd(P4,P)
P6 = clockadd(P5,P)
print P6
print clockadd(P3,P3)