





from manim import *






class 					lowercase__ (			__lowerCamelCase       ):

   '''simple docstring'''


   def    UpperCamelCase__						(					self							)				->   List[str]:






       """simple docstring"""
       UpperCamelCase__							:       Any      =   Rectangle(height=0.5,	width=0.5							)
       UpperCamelCase__							:       Any      =   Rectangle(height=0.25,	width=0.25							)
       UpperCamelCase__							:       Dict      =   Rectangle(height=0.46,	width=0.46							).set_stroke(width=0							)

       UpperCamelCase__							:       List[Any]      =   [mem.copy() for i in range(6							)]
       UpperCamelCase__							:       Optional[int]      =   [mem.copy() for i in range(6							)]
       UpperCamelCase__							:       str      =   VGroup(*__magic_name__							).arrange(__magic_name__,	buff=0							)
       UpperCamelCase__							:       List[str]      =   VGroup(*__magic_name__							).arrange(__magic_name__,	buff=0							)
       UpperCamelCase__							:       Tuple      =   VGroup(__magic_name__,	__magic_name__							).arrange(__magic_name__,	buff=0							)
       UpperCamelCase__							:       List[str]      =   Text('''CPU''',	font_size=24							)
       UpperCamelCase__							:       Any      =   Group(__magic_name__,	__magic_name__							).arrange(__magic_name__,	buff=0.5,	aligned_edge=__magic_name__							)
       cpu.move_to([-2.5, -0.5, 0]							)
       self.add(__magic_name__							)

       UpperCamelCase__							:       int      =   [mem.copy() for i in range(4							)]
       UpperCamelCase__							:       str      =   VGroup(*__magic_name__							).arrange(__magic_name__,	buff=0							)
       UpperCamelCase__							:       Tuple      =   Text('''GPU''',	font_size=24							)
       UpperCamelCase__							:       str      =   Group(__magic_name__,	__magic_name__							).arrange(__magic_name__,	buff=0.5,	aligned_edge=__magic_name__							)
       gpu.move_to([-1, -1, 0]							)
       self.add(__magic_name__							)

       UpperCamelCase__							:       str      =   [mem.copy() for i in range(6							)]
       UpperCamelCase__							:       Tuple      =   VGroup(*__magic_name__							).arrange(__magic_name__,	buff=0							)

       UpperCamelCase__							:       Tuple      =   Text('''Model''',	font_size=24							)
       UpperCamelCase__							:       Tuple      =   Group(__magic_name__,	__magic_name__							).arrange(__magic_name__,	buff=0.5,	aligned_edge=__magic_name__							)
       model.move_to([3, -1.0, 0]							)
       self.add(__magic_name__							)

       UpperCamelCase__							:       Union[str, Any]      =   []
       UpperCamelCase__							:       Any      =   []
       UpperCamelCase__							:       List[Any]      =   []

       for i, rect in enumerate(__magic_name__							):
           rect.set_stroke(__magic_name__							)

           UpperCamelCase__							:       Tuple      =   Rectangle(height=0.46 / 4,	width=0.46 / 3							).set_stroke(width=0.0							).set_fill(__magic_name__,	opacity=0.7							)

           if i == 0:
               cpu_target.next_to(cpu_left_col_base[0].get_corner(DOWN + LEFT							),	buff=0.02,	direction=__magic_name__							)
               cpu_target.set_x(cpu_target.get_x() + 0.1							)
           elif i == 3:
               cpu_target.next_to(model_cpu_arr[0],	direction=__magic_name__,	buff=0.0							)
           else:
               cpu_target.next_to(model_cpu_arr[i - 1],	direction=__magic_name__,	buff=0.0							)
           self.add(__magic_name__							)
           model_cpu_arr.append(__magic_name__							)

       self.add(*__magic_name__,	*__magic_name__,	*__magic_name__							)

       UpperCamelCase__							:       Tuple      =   [mem.copy() for i in range(6							)]
       UpperCamelCase__							:       Dict      =   VGroup(*__magic_name__							).arrange(__magic_name__,	buff=0							)

       UpperCamelCase__							:       List[str]      =   Text('''Loaded Checkpoint''',	font_size=24							)
       UpperCamelCase__							:       Optional[Any]      =   Group(__magic_name__,	__magic_name__							).arrange(__magic_name__,	buff=0.5,	aligned_edge=__magic_name__							)
       checkpoint.move_to([3, 0.5, 0]							)

       self.add(__magic_name__							)

       UpperCamelCase__							:       Tuple      =   []
       UpperCamelCase__							:       List[str]      =   []

       for i, rect in enumerate(__magic_name__							):
           UpperCamelCase__							:       Optional[int]      =   fill.copy().set_fill(__magic_name__,	opacity=0.7							)
           target.move_to(__magic_name__							)
           ckpt_arr.append(__magic_name__							)

           UpperCamelCase__							:       int      =   target.copy()
           if i < 5:
               cpu_target.move_to(cpu_left_col_base[i + 1]							)
           else:
               cpu_target.move_to(cpu_right_col_base[i - 5]							)
           ckpt_cpu_arr.append(__magic_name__							)
       self.add(*__magic_name__,	*__magic_name__							)

       UpperCamelCase__							:       List[str]      =   Square(side_length=2.2							)
       key.move_to([-5, 2, 0]							)

       UpperCamelCase__							:       List[str]      =   MarkupText(
           f"<b>Key:</b>\n\n<span fgcolor='{YELLOW}'>●</span> Empty Model",	font_size=18,	)

       key_text.move_to([-5, 2.4, 0]							)

       self.add(__magic_name__,	__magic_name__							)

       UpperCamelCase__							:       Any      =   MarkupText(
           f"<span fgcolor='{BLUE}'>●</span> Checkpoint",	font_size=18,	)

       blue_text.next_to(__magic_name__,	DOWN * 2.4,	aligned_edge=key_text.get_left()							)
       self.add(__magic_name__							)

       UpperCamelCase__							:       Dict      =   MarkupText(
           f"Based on the passed in configuration, weights are stored in\na variety of np.memmaps on disk or to a particular device.",	font_size=24,	)
       step_a.move_to([2, 2, 0]							)

       UpperCamelCase__							:       Any      =   [meta_mem.copy() for i in range(6							)]
       UpperCamelCase__							:       int      =   [meta_mem.copy() for i in range(6							)]
       UpperCamelCase__							:       Optional[int]      =   VGroup(*__magic_name__							).arrange(__magic_name__,	buff=0							)
       UpperCamelCase__							:       Union[str, Any]      =   VGroup(*__magic_name__							).arrange(__magic_name__,	buff=0							)
       UpperCamelCase__							:       Union[str, Any]      =   VGroup(__magic_name__,	__magic_name__							).arrange(__magic_name__,	buff=0							)
       UpperCamelCase__							:       Any      =   Text('''Disk''',	font_size=24							)
       UpperCamelCase__							:       List[Any]      =   Group(__magic_name__,	__magic_name__							).arrange(__magic_name__,	buff=0.5,	aligned_edge=__magic_name__							)
       disk.move_to([-4.0, -1.25, 0]							)
       self.play(Write(__magic_name__,	run_time=3							),	Write(__magic_name__,	run_time=1							),	Create(__magic_name__,	run_time=1							)							)

       UpperCamelCase__							:       Union[str, Any]      =   []
       for i, rect in enumerate(__magic_name__							):
           UpperCamelCase__							:       Union[str, Any]      =   rect.copy()
           target.generate_target()
           target.target.move_to(disk_left_col_base[i]							).scale(0.5							)
           animations.append(MoveToTarget(__magic_name__,	run_time=1.5							)							)
       self.play(*__magic_name__							)

       self.play(FadeOut(__magic_name__							)							)

       UpperCamelCase__							:       Optional[int]      =   MarkupText(f"Then, the checkpoint is removed from memory\nthrough garbage collection.",	font_size=24							)
       step_a.move_to([2, 2, 0]							)

       self.play(Write(__magic_name__,	run_time=3							)							)

       self.play(
           FadeOut(__magic_name__,	__magic_name__,	*__magic_name__,	*__magic_name__							),	)

       self.wait()








from __future__ import annotations

from math import gcd




def 	lowerCAmelCase_					(						__UpperCAmelCase:    int	,     __UpperCAmelCase:    int = 2	,     __UpperCAmelCase:    int = 1	,     __UpperCAmelCase:    int = 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(__UpperCAmelCase:    int	,     __UpperCAmelCase:    int	,     __UpperCAmelCase:    int   ) -> int:
        return (pow(__UpperCAmelCase	,     2   ) + step) % modulus

    for _ in range(__UpperCAmelCase   ):
        # These track the position within the cycle detection logic.
        UpperCamelCase__							:       List[Any]      =   seed
        UpperCamelCase__							:       List[str]      =   seed

        while True:
            # At each iteration, the tortoise moves one step and the hare moves two.
            UpperCamelCase__							:       Optional[int]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )
            UpperCamelCase__							:       List[str]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )
            UpperCamelCase__							:       Optional[int]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )

            # 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__							:       Optional[int]      =   gcd(hare - tortoise	,     __UpperCAmelCase   )

            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__							:       List[str]      =   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

  UpperCAmelCase_  							=				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',
  )
  UpperCAmelCase_  							=				parser.parse_args()

  UpperCAmelCase_  							=				pollard_rho(args.num, attempts=args.attempts)
  if divisor is None:
    print(F'''{args.num} is probably prime''')
  else:
    UpperCAmelCase_  							=				args.num // divisor
    print(F'''{args.num} = {divisor} * {quotient}''')

