





from __future__ import annotations

import math
from itertools import permutations



def 							lowerCAmelCase_				(    A_):

    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5  ,int(math.sqrt(A_) + 1)  ,6):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True



def 							lowerCAmelCase_				(    A_ = 7):
    UpperCamelCase__:					str												=      "".join(str(A_) for i in range(1  ,n + 1))
    UpperCamelCase__:					List[Any]												=      [int("".join(A_)) for i in permutations(A_  ,A_)]
    UpperCamelCase__:					Optional[Any]												=      [num for num in perm_list if is_prime(A_)]
    return max(A_) if pandigitals else 0


if __name__ == "__main__":
    print(f"{solution() = }")








from manim import *




class    _a  (  UpperCamelCase__):

      """simple docstring"""


      def 	UpperCAmelCase_   (						self:	str			):
          '''simple docstring'''


          UpperCamelCase__:					Optional[Any]												=      Rectangle(height=0.5					,  width=0.5			)
          UpperCamelCase__:					Optional[int]												=      Rectangle(height=0.46					,  width=0.46			).set_stroke(width=0			)
          UpperCamelCase__:					List[Any]												=      Rectangle(height=0.25					,  width=0.25			)

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

          UpperCamelCase__:					Dict												=      [mem.copy() for i in range(4			)]
          UpperCamelCase__:					Any												=      VGroup(*__lowerCamelCase			).arrange(__lowerCamelCase					,  buff=0			)
          UpperCamelCase__:					str												=      Text("GPU"					,  font_size=24			)
          UpperCamelCase__:					List[Any]												=      Group(__lowerCamelCase					,  __lowerCamelCase			).arrange(__lowerCamelCase					,  buff=0.5					,  aligned_edge=__lowerCamelCase			)
          gpu.move_to([-1, -1, 0]			)
          self.add(__lowerCamelCase			)

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

          UpperCamelCase__:					Union[str, Any]												=      Text("Model"					,  font_size=24			)
          UpperCamelCase__:					Tuple												=      Group(__lowerCamelCase					,  __lowerCamelCase			).arrange(__lowerCamelCase					,  buff=0.5					,  aligned_edge=__lowerCamelCase			)
          model.move_to([3, -1.0, 0]			)
          self.add(__lowerCamelCase			)

          UpperCamelCase__:					int												=      []
          UpperCamelCase__:					Optional[Any]												=      []

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

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

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

          self.add(*__lowerCamelCase					,  *__lowerCamelCase			)

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

          UpperCamelCase__:					Optional[int]												=      []

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

          self.add(*__lowerCamelCase			)

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

          UpperCamelCase__:					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(__lowerCamelCase					,  __lowerCamelCase			)

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

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

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

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

          for i in range(6			):
              UpperCamelCase__:					List[Any]												=      cpu_disk_arr[i]
              UpperCamelCase__:					Optional[int]												=      rect.copy().set_fill(__lowerCamelCase					,  opacity=0.8			).scale(2.0			)
              cpa.generate_target()
              cpa.target.move_to(model_base[i]			)

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

                  self.remove(
                      *__lowerCamelCase					,  *__lowerCamelCase					,  )

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

          UpperCamelCase__:					Dict												=      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(__lowerCamelCase					,  run_time=3			)			)

          UpperCamelCase__:					List[str]												=      []
          UpperCamelCase__:					Optional[Any]												=      []
          for i in range(6			):
              UpperCamelCase__:					List[str]												=      Arrow(start=__lowerCamelCase					,  end=__lowerCamelCase					,  color=__lowerCamelCase					,  buff=0.5			)
              a.next_to(model_base[i].get_left()					,  __lowerCamelCase					,  buff=0.2			)
              arrows.append(__lowerCamelCase			)
              animations.append(Write(__lowerCamelCase			)			)
          self.play(*__lowerCamelCase			)
          self.wait()

