'''simple docstring'''
from manim import *




class _lowerCAmelCase (  snake_case				):







      def     lowerCamelCase__			(     self    ):
        lowercase							:       Dict											=      Rectangle(height=0.5     ,						width=0.5    )
        lowercase							:       Any											=      Rectangle(height=0.46     ,						width=0.46    ).set_stroke(width=0    )
        lowercase							:       Any											=      Rectangle(height=0.25     ,						width=0.25    )

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

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

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

        lowercase							:       List[str]											=      Text('''Model'''     ,						font_size=24    )
        lowercase							:       List[Any]											=      Group(lowercase     ,						lowercase    ).arrange(lowercase     ,						buff=0.5     ,						aligned_edge=lowercase    )
        model.move_to([3, -1.0, 0]    )
        self.add(lowercase    )

        lowercase							:       Optional[int]											=      []
        lowercase							:       int											=      []

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

          lowercase							:       List[str]											=      Rectangle(height=0.46 / 4     ,						width=0.46 / 3    ).set_stroke(width=0.0    ).set_fill(lowercase     ,						opacity=0.7    )

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

        self.add(*lowercase     ,						*lowercase    )

        lowercase							:       Union[str, Any]											=      [meta_mem.copy() for i in range(6    )]
        lowercase							:       Dict											=      [meta_mem.copy() for i in range(6    )]
        lowercase							:       Dict											=      VGroup(*lowercase    ).arrange(lowercase     ,						buff=0    )
        lowercase							:       Union[str, Any]											=      VGroup(*lowercase    ).arrange(lowercase     ,						buff=0    )
        lowercase							:       int											=      VGroup(lowercase     ,						lowercase    ).arrange(lowercase     ,						buff=0    )
        lowercase							:       str											=      Text('''Disk'''     ,						font_size=24    )
        lowercase							:       Dict											=      Group(lowercase     ,						lowercase    ).arrange(lowercase     ,						buff=0.5     ,						aligned_edge=lowercase    )
        disk.move_to([-4.0, -1.25, 0]    )
        self.add(lowercase     ,						lowercase    )

        lowercase							:       Tuple											=      []

        for i in range(6    ):
          lowercase							:       List[Any]											=      fill.copy().set_fill(lowercase     ,						opacity=0.8    )
          target.move_to(disk_left_col_base[i]    ).scale(0.5    )
          cpu_disk_arr.append(lowercase    )

        self.add(*lowercase    )

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

        lowercase							:       int											=      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(lowercase     ,						lowercase    )

        lowercase							:       List[str]											=      MarkupText(
            F"""<span fgcolor='{BLUE}'>●</span> Checkpoint"""     ,						font_size=18     ,						)

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

        lowercase							:       List[Any]											=      MarkupText(F"""The offloaded weights are all sent to the CPU."""     ,						font_size=24    )
        step_a.move_to([2, 2, 0]    )

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

        for i in range(6    ):
          lowercase							:       Dict											=      cpu_disk_arr[i]
          lowercase							:       List[str]											=      rect.copy().set_fill(lowercase     ,						opacity=0.8    ).scale(2.0    )
          cpa.generate_target()
          cpa.target.move_to(model_base[i]    )

          if i == 0:
            rect.set_fill(lowercase     ,						opacity=0.8    )
            rect.generate_target()
            rect.target.move_to(cpu_left_col_base[0]    ).scale(2.0    )

            self.remove(
                *lowercase     ,						*lowercase     ,						)

          else:
            rect.generate_target()
            rect.target.move_to(cpu_left_col_base[i]    ).scale(2.0    )
          self.play(MoveToTarget(lowercase    )     ,						MoveToTarget(lowercase    )     ,						model_base[i].animate.set_stroke(lowercase    )    )
        self.play(FadeOut(lowercase    )    )

        lowercase							:       Tuple											=      MarkupText(
            F"""Finally, hooks are added to each weight in the model\nto transfer the weights from CPU to GPU\n\t\tand back when needed."""     ,						font_size=24     ,						)
        step_a.move_to([2, 2, 0]    )

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

        lowercase							:       Any											=      []
        lowercase							:       List[str]											=      []
        for i in range(6    ):
          lowercase							:       Union[str, Any]											=      Arrow(start=lowercase     ,						end=lowercase     ,						color=lowercase     ,						buff=0.5    )
          a.next_to(model_base[i].get_left()     ,						lowercase     ,						buff=0.2    )
          arrows.append(lowercase    )
          animations.append(Write(lowercase    )    )
        self.play(*lowercase    )
        self.wait()
'''simple docstring'''
def 							__UpperCamelCase   (				__UpperCAmelCase     :				int )       ->  list:
  lowercase							:       Union[str, Any]											=      [True for i in range(n + 1 )]
  lowercase							:       Dict											=      [i - 1 for i in range(n + 1 )]
  lowercase							:       Union[str, Any]											=      []
  for i in range(2   ,      n + 1 ):
    if is_prime[i]:
      primes.append(__UpperCAmelCase )
    for j in range(0   ,      len(__UpperCAmelCase ) ):
      if i * primes[j] >= n:
        break
      lowercase							:       List[str]											=      False

      if i % primes[j] == 0:
        lowercase							:       Optional[Any]											=      totients[i] * primes[j]
        break

      lowercase							:       Union[str, Any]											=      totients[i] * (primes[j] - 1)

  return totients


if __name__ == "__main__":
 import doctest

 doctest.testmod()