



from __future__ import annotations

def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			list				,     _SCREAMING_SNAKE_CASE       :			int    ):
				"""simple docstring"""







				if len(_SCREAMING_SNAKE_CASE    ) <= 1 or n <= 1:
								return

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

def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			list				,     _SCREAMING_SNAKE_CASE       :			int    ):
				"""simple docstring"""







				if index >= len(_SCREAMING_SNAKE_CASE    ) or collection[index - 1] <= collection[index]:
								return

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

				insert_next(_SCREAMING_SNAKE_CASE				,     index + 1    )


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





def   lowerCAmelCase__						(							_SCREAMING_SNAKE_CASE       :			Tuple				,     _SCREAMING_SNAKE_CASE       :			Tuple				,     _SCREAMING_SNAKE_CASE       :			Tuple=False    ):
				"""simple docstring"""







				if isinstance(_SCREAMING_SNAKE_CASE				,     _SCREAMING_SNAKE_CASE    ) and isinstance(_SCREAMING_SNAKE_CASE				,     _SCREAMING_SNAKE_CASE    ):
								__a       =		len(set_a.intersection(_SCREAMING_SNAKE_CASE    )    )

								if alternative_union:
												__a       =		len(_SCREAMING_SNAKE_CASE    ) + len(_SCREAMING_SNAKE_CASE    )
								else:
												__a       =		len(set_a.union(_SCREAMING_SNAKE_CASE    )    )

								return intersection / union

				if isinstance(_SCREAMING_SNAKE_CASE				,     (list, tuple)    ) and isinstance(_SCREAMING_SNAKE_CASE				,     (list, tuple)    ):
								__a       =		[element for element in set_a if element in set_b]

								if alternative_union:
												__a       =		len(_SCREAMING_SNAKE_CASE    ) + len(_SCREAMING_SNAKE_CASE    )
												return len(_SCREAMING_SNAKE_CASE    ) / union
								else:
												__a       =		set_a + [element for element in set_b if element not in set_a]
												return len(_SCREAMING_SNAKE_CASE    ) / len(_SCREAMING_SNAKE_CASE    )

								return len(_SCREAMING_SNAKE_CASE    ) / len(_SCREAMING_SNAKE_CASE    )
				return None


if __name__ == "__main__":
						lowerCamelCase__			= {"""a""", """b""", """c""", """d""", """e"""}
						lowerCamelCase__			= {"""c""", """d""", """e""", """f""", """h""", """i"""}
						print(jaccard_similarity(set_a, set_b))
