

"""simple docstring"""




from __future__ import annotations





def       lowercase__						(       snake_case_   :list			,		snake_case_   :int    ):
	# Checks if the entire collection has been sorted
	if len(snake_case_    ) <= 1 or n <= 1:
		return

	insert_next(snake_case_			,		n - 1    )
	rec_insertion_sort(snake_case_			,		n - 1    )





def       lowercase__						(       snake_case_   :list			,		snake_case_   :int    ):
	# Checks order between adjacent elements
	if index >= len(snake_case_    ) or collection[index - 1] <= collection[index]:
		return

	# Swaps adjacent elements since they are not in ascending order
	__UpperCAmelCase		,							__UpperCAmelCase      		= (
	    collection[index],
	    collection[index - 1],
	)

	insert_next(snake_case_			,		index + 1    )


if __name__ == "__main__":
				_lowercase   :	Any												=						input('Enter integers separated by spaces: ')
				_lowercase   :	list[int]												=						[int(num) for num in numbers.split()]
				rec_insertion_sort(number_list, len(number_list))
				print(number_list)


'''simple docstring'''



from itertools import product


def A (__lowerCamelCase :int					,      __lowerCamelCase :int						):
						_lowerCAmelCase    		=					sides_number
						_lowerCAmelCase    		=					max_face_number * dice_number
						_lowerCAmelCase    		=					[0] * (max_total + 1)

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

						return totals_frequencies


def A ():
						_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(__lowerCamelCase					,      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(__lowerCamelCase					,      ndigits=7						)

						return rounded_peter_win_probability


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