





from __future__ import annotations

from math import gcd



def 						A_							(	_lowerCAmelCase				,  _lowerCAmelCase = 2				,  _lowerCAmelCase = 1				,  _lowerCAmelCase = 3				,  )		->					int | None:
 # A value less than 2 can cause an infinite loop in the algorithm.
 if num < 2:
  raise ValueError("The input value cannot be less than 2"	)

 # Because of the relationship between ``f(f(x))`` and ``f(x)``, this
 # algorithm struggles to find factors that are divisible by two.
 # As a workaround, we specifically check for two and even inputs.
 #   See: https://math.stackexchange.com/a/2856214/165820
 if num > 2 and num % 2 == 0:
  return 2

 # Pollard's Rho algorithm requires a function that returns pseudorandom
 # values between 0 <= X < ``num``.  It doesn't need to be random in the
 # sense that the output value is cryptographically secure or difficult
 # to calculate, it only needs to be random in the sense that all output
 # values should be equally likely to appear.
 # For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
 # However, the success of Pollard's algorithm isn't guaranteed and is
 # determined in part by the initial seed and the chosen random function.
 # To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
 # where ``C`` is a value that we can modify between each attempt.
 def rand_fn(_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase	) -> int:
  return (pow(_lowerCAmelCase				,  2	) + step) % modulus

 for _ in range(_lowerCAmelCase	):
  # These track the position within the cycle detection logic.
  UpperCamelCase      :   Optional[int]			      =  seed
  UpperCamelCase      :   List[str]			      =  seed

  while True:
   # At each iteration, the tortoise moves one step and the hare moves two.
   UpperCamelCase      :   List[Any]			      =  rand_fn(_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase	)
   UpperCamelCase      :   Tuple			      =  rand_fn(_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase	)
   UpperCamelCase      :   int			      =  rand_fn(_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase	)

   # At some point both the tortoise and the hare will enter a cycle whose
   # length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
   # the tortoise and hare will end up on the same value modulo ``p``.
   # We can detect when this happens because the position difference between
   # the tortoise and the hare will share a common divisor with ``num``.
   UpperCamelCase      :   Tuple			      =  gcd(hare - tortoise				,  _lowerCAmelCase	)

   if divisor == 1:
    # No common divisor yet, just keep searching.
    continue
   else:
    # We found a common divisor!
    if divisor == num:
     # Unfortunately, the divisor is ``num`` itself and is useless.
     break
    else:
     # The divisor is a nontrivial factor of ``num``!
     return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
  UpperCamelCase      :   Any			      =  hare

  # The new step value for the random function can just be incremented.
  # At first the results will be similar to what the old function would
  # have produced, but the value will quickly diverge after a bit.
  step += 1

 # We haven't found a divisor within the requested number of attempts.
 # We were unlucky or ``num`` itself is actually prime.
 return None


if __name__ == "__main__":
    import argparse

    __lowerCamelCase			:	Union[str, Any]					    =	argparse.ArgumentParser()
    parser.add_argument(
        """num""",
        type=int,
        help="""The value to find a divisor of""",
    )
    parser.add_argument(
        """--attempts""",
        type=int,
        default=3,
        help="""The number of attempts before giving up""",
    )
    __lowerCamelCase			:	Dict					    =	parser.parse_args()

    __lowerCamelCase			:	str					    =	pollard_rho(args.num, attempts=args.attempts)
    if divisor is None:
        print(f"""{args.num} is probably prime""")
    else:
        __lowerCamelCase			:	Dict					    =	args.num // divisor
        print(f"""{args.num} = {divisor} * {quotient}""")







import os



def 						A_							(	)		->					Union[str, Any]:
 with open(os.path.dirname(_lowerCAmelCase	) + "/grid.txt"	) as f:
  UpperCamelCase      :   Optional[Any]			      =  []  # noqa: E741
  for _ in range(20	):
   l.append([int(_lowerCAmelCase	) for x in f.readline().split()]	)

  UpperCamelCase      :   str			      =  0

  # right
  for i in range(20	):
   for j in range(17	):
    UpperCamelCase      :   int			      =  l[i][j] * l[i][j + 1] * l[i][j + 2] * l[i][j + 3]
    if temp > maximum:
     UpperCamelCase      :   List[Any]			      =  temp

        # down
  for i in range(17	):
   for j in range(20	):
    UpperCamelCase      :   List[str]			      =  l[i][j] * l[i + 1][j] * l[i + 2][j] * l[i + 3][j]
    if temp > maximum:
     UpperCamelCase      :   List[str]			      =  temp

        # diagonal 1
  for i in range(17	):
   for j in range(17	):
    UpperCamelCase      :   Any			      =  l[i][j] * l[i + 1][j + 1] * l[i + 2][j + 2] * l[i + 3][j + 3]
    if temp > maximum:
     UpperCamelCase      :   Tuple			      =  temp

        # diagonal 2
  for i in range(17	):
   for j in range(3				,  20	):
    UpperCamelCase      :   Tuple			      =  l[i][j] * l[i + 1][j - 1] * l[i + 2][j - 2] * l[i + 3][j - 3]
    if temp > maximum:
     UpperCamelCase      :   List[Any]			      =  temp
  return maximum


if __name__ == "__main__":
    print(solution())
