




from itertools import product

def     _SCREAMING_SNAKE_CASE    (							lowercase			: int			,							lowercase			: int  ):


      '''simple docstring'''



      lowerCamelCase_	  =					sides_number
      lowerCamelCase_	  =					max_face_number * dice_number
      lowerCamelCase_	  =					[0] * (max_total + 1)

      lowerCamelCase_	  =					1
      lowerCamelCase_	  =					range(lowercase			,							max_face_number + 1  )
      for dice_numbers in product(lowercase			,							repeat=lowercase  ):
            lowerCamelCase_	  =					sum(lowercase  )
            totals_frequencies[total] += 1

      return totals_frequencies

def     _SCREAMING_SNAKE_CASE    (							):


      '''simple docstring'''



      lowerCamelCase_	  =					total_frequency_distribution(
          sides_number=4			,							dice_number=9  )
      lowerCamelCase_	  =					total_frequency_distribution(
          sides_number=6			,							dice_number=6  )

      lowerCamelCase_	  =					0
      lowerCamelCase_	  =					9
      lowerCamelCase_	  =					4 * 9
      lowerCamelCase_	  =					6
      for peter_total in range(lowercase			,							max_peter_total + 1  ):
            peter_wins_count += peter_totals_frequencies[peter_total] * sum(
                colin_totals_frequencies[min_colin_total:peter_total]  )

      lowerCamelCase_	  =					(4**9) * (6**6)
      lowerCamelCase_	  =					peter_wins_count / total_games_number

      lowerCamelCase_	  =					round(lowercase			,							ndigits=7  )

      return rounded_peter_win_probability


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









from manim import *







class 						A(		UpperCamelCase     ):



 '''simple docstring'''


 def        a__				(       self      :						Optional[Any]						)     ->			List[str]:

       """simple docstring"""






       lowerCamelCase_	  =					Rectangle(height=0.5		,							width=0.5						)
       lowerCamelCase_	  =					Rectangle(height=0.46		,							width=0.46						).set_stroke(width=0						)

       lowerCamelCase_	  =					Rectangle(height=0.25		,							width=0.25						)

       lowerCamelCase_	  =					[mem.copy() for i in range(6						)]
       lowerCamelCase_	  =					[mem.copy() for i in range(6						)]
       lowerCamelCase_	  =					VGroup(*A_						).arrange(A_		,							buff=0						)
       lowerCamelCase_	  =					VGroup(*A_						).arrange(A_		,							buff=0						)
       lowerCamelCase_	  =					VGroup(A_		,							A_						).arrange(A_		,							buff=0						)
       lowerCamelCase_	  =					Text('CPU'		,							font_size=24						)
       lowerCamelCase_	  =					Group(A_		,							A_						).arrange(A_		,							buff=0.5		,							aligned_edge=A_						)
       cpu.move_to([-2.5, -0.5, 0]						)
       self.add(A_						)

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

       lowerCamelCase_	  =					[mem.copy() for i in range(6						)]
       lowerCamelCase_	  =					VGroup(*A_						).arrange(A_		,							buff=0						)

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

       lowerCamelCase_	  =					[]
       lowerCamelCase_	  =					[]

       for i, rect in enumerate(A_						):
             lowerCamelCase_	  =					fill.copy().set_fill(A_		,							opacity=0.8						)
             target.move_to(A_						)
             model_arr.append(A_						)

             lowerCamelCase_	  =					Rectangle(height=0.46		,							width=0.46						).set_stroke(width=0.0						).set_fill(A_		,							opacity=0.8						)
             cpu_target.move_to(cpu_left_col_base[i]						)
             model_cpu_arr.append(A_						)

       self.add(*A_		,							*A_						)

       lowerCamelCase_	  =					[meta_mem.copy() for i in range(6						)]
       lowerCamelCase_	  =					[meta_mem.copy() for i in range(6						)]
       lowerCamelCase_	  =					VGroup(*A_						).arrange(A_		,							buff=0						)
       lowerCamelCase_	  =					VGroup(*A_						).arrange(A_		,							buff=0						)
       lowerCamelCase_	  =					VGroup(A_		,							A_						).arrange(A_		,							buff=0						)
       lowerCamelCase_	  =					Text('Disk'		,							font_size=24						)
       lowerCamelCase_	  =					Group(A_		,							A_						).arrange(A_		,							buff=0.5		,							aligned_edge=A_						)
       disk.move_to([-4, -1.25, 0]						)
       self.add(A_		,							A_						)

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

       lowerCamelCase_	  =					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(A_		,							A_						)

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

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

       lowerCamelCase_	  =					MarkupText(
           f"""Now watch as an input is passed through the model\nand how the memory is utilized and handled."""		,							font_size=24		,							)
       step_a.move_to([2, 2, 0]						)

       self.play(Write(A_						)						)

       lowerCamelCase_	  =					Square(0.3						)
       input.set_fill(A_		,							opacity=1.0						)
       input.set_stroke(width=0.0						)
       input.next_to(model_base[0]		,							A_		,							buff=0.5						)

       self.play(Write(A_						)						)

       input.generate_target()
       input.target.next_to(model_arr[0]		,							direction=A_		,							buff=0.02						)
       self.play(MoveToTarget(A_						)						)

       self.play(FadeOut(A_						)						)

       lowerCamelCase_	  =					Arrow(start=A_		,							end=A_		,							color=A_		,							buff=0.5						)
       a.next_to(model_arr[0].get_left()		,							A_		,							buff=0.2						)

       model_cpu_arr[0].generate_target()
       model_cpu_arr[0].target.move_to(gpu_rect[0]						)

       lowerCamelCase_	  =					MarkupText(
           f"""As the input reaches a layer, the hook triggers\nand weights are moved from the CPU\nto the GPU and back."""		,							font_size=24		,							)
       step_a.move_to([2, 2, 0]						)

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

       lowerCamelCase_	  =					{'run_time': 1, 'fade_in': True, 'fade_out': True, 'buff': 0.02}

       self.play(
           Write(A_						)		,							Circumscribe(model_arr[0]		,							color=A_		,							**A_						)		,							Circumscribe(model_cpu_arr[0]		,							color=A_		,							**A_						)		,							Circumscribe(gpu_rect[0]		,							color=A_		,							**A_						)		,							)
       self.play(MoveToTarget(model_cpu_arr[0]						)						)

       lowerCamelCase_	  =					a.copy()
       for i in range(6						):
             a_c.next_to(model_arr[i].get_right() + 0.02		,							A_		,							buff=0.2						)

             input.generate_target()
             input.target.move_to(model_arr[i].get_right() + 0.02						)

             lowerCamelCase_	  =					AnimationGroup(
                 FadeOut(A_		,							run_time=0.5						)		,							MoveToTarget(A_		,							run_time=0.5						)		,							FadeIn(A_		,							run_time=0.5						)		,							lag_ratio=0.2						)

             self.play(A_						)

             model_cpu_arr[i].generate_target()
             model_cpu_arr[i].target.move_to(cpu_left_col_base[i]						)

             if i < 5:
                   model_cpu_arr[i + 1].generate_target()
                   model_cpu_arr[i + 1].target.move_to(gpu_rect[0]						)
                   if i >= 1:
                         lowerCamelCase_	  =					0.7

                   self.play(
                       Circumscribe(model_arr[i]		,							**A_						)		,							Circumscribe(cpu_left_col_base[i]		,							**A_						)		,							Circumscribe(cpu_left_col_base[i + 1]		,							color=A_		,							**A_						)		,							Circumscribe(gpu_rect[0]		,							color=A_		,							**A_						)		,							Circumscribe(model_arr[i + 1]		,							color=A_		,							**A_						)		,							)
                   if i < 1:
                         self.play(
                             MoveToTarget(model_cpu_arr[i]						)		,							MoveToTarget(model_cpu_arr[i + 1]						)		,							)
                   else:
                         self.play(
                             MoveToTarget(model_cpu_arr[i]		,							run_time=0.7						)		,							MoveToTarget(model_cpu_arr[i + 1]		,							run_time=0.7						)		,							)
             else:
                   model_cpu_arr[i].generate_target()
                   model_cpu_arr[i].target.move_to(cpu_left_col_base[-1]						)
                   input.generate_target()
                   input.target.next_to(model_arr[-1].get_right()		,							RIGHT + 0.02		,							buff=0.2						)

                   self.play(
                       Circumscribe(model_arr[-1]		,							color=A_		,							**A_						)		,							Circumscribe(cpu_left_col_base[-1]		,							color=A_		,							**A_						)		,							Circumscribe(gpu_rect[0]		,							color=A_		,							**A_						)		,							)

                   self.play(MoveToTarget(model_cpu_arr[i]						)						)

             lowerCamelCase_	  =					a_c
             lowerCamelCase_	  =					a_c.copy()

       input.generate_target()
       input.target.next_to(model_base[-1]		,							RIGHT + 0.02		,							buff=0.5						)
       self.play(
           FadeOut(A_						)		,							FadeOut(A_		,							run_time=0.5						)		,							)

       lowerCamelCase_	  =					MarkupText(f"""Inference on a model too large for GPU memory\nis successfully completed."""		,							font_size=24						)
       step_a.move_to([2, 2, 0]						)

       self.play(Write(A_		,							run_time=3						)		,							MoveToTarget(A_						)						)

       self.wait()



