




'''simple docstring'''


from __future__ import annotations
def 	snake_case_					(UpperCamelCase :						List[str]				,		UpperCamelCase :						Optional[int]   ):





							'''simple docstring'''


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

							insert_next(UpperCamelCase				,		n - 1   )
							rec_insertion_sort(UpperCamelCase				,		n - 1   )
def 	snake_case_					(UpperCamelCase :						Union[str, Any]				,		UpperCamelCase :						Any   ):





							'''simple docstring'''


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

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

							insert_next(UpperCamelCase				,		index + 1   )


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







'''simple docstring'''


_snake_case   :   Any     							=	tuple[float, float, float]
_snake_case   :   Optional[int]     							=	tuple[float, float, float]
def 	snake_case_					(UpperCamelCase :						Pointad				,		UpperCamelCase :						Pointad   ):





							'''simple docstring'''


							_a			  =       end_pointa[0] - end_pointa[0]
							_a			  =       end_pointa[1] - end_pointa[1]
							_a			  =       end_pointa[2] - end_pointa[2]
							return (x, y, z)
def 	snake_case_					(UpperCamelCase :						Vectorad				,		UpperCamelCase :						Vectorad   ):





							'''simple docstring'''


							_a			  =       ab[1] * ac[2] - ab[2] * ac[1]  # *i
							_a			  =       (ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
							_a			  =       ab[0] * ac[1] - ab[1] * ac[0]  # *k
							return (x, y, z)
def 	snake_case_					(UpperCamelCase :						Vectorad				,		UpperCamelCase :						int   ):





							'''simple docstring'''


							return tuple(round(UpperCamelCase				,		UpperCamelCase   ) for x in vector   ) == (0, 0, 0)

def 	snake_case_					(UpperCamelCase :						Pointad				,		UpperCamelCase :						Pointad				,		UpperCamelCase :						Pointad				,		UpperCamelCase :						int = 10   ):





							'''simple docstring'''


							_a			  =       create_vector(UpperCamelCase				,		UpperCamelCase   )
							_a			  =       create_vector(UpperCamelCase				,		UpperCamelCase   )
							return is_zero_vector(get_ad_vectors_cross(UpperCamelCase				,		UpperCamelCase   )				,		UpperCamelCase   )

