code: 
  from __future__ import annotations
  
  
  
  
  
  
  def 						lowerCAmelCase_		(      _snake_case   :						Optional[int]   ,     _snake_case   :						str     )       ->	Any:
  
  
  
  
  
  
  
  	'''simple docstring'''
  
  
  	__magic_name__	:	Union[str, Any]			     =  0
  	__magic_name__	:	List[str]			     =  len(_snake_case     ) - 1
  	while left <= right:
  		__magic_name__	:	Optional[int]			     =  (left + right) // 2
  		if left == right:
  			if sorted_list[middle] < item:
  				__magic_name__	:	Any			     =  middle + 1
  			break
  		elif sorted_list[middle] < item:
  			__magic_name__	:	Optional[Any]			     =  middle + 1
  		else:
  			__magic_name__	:	Tuple			     =  middle - 1
  	sorted_list.insert(_snake_case   ,     _snake_case     )
  	return sorted_list
  
  
  
  
  
  
  def 						lowerCAmelCase_		(      _snake_case   :						Tuple   ,     _snake_case   :						List[Any]     )       ->	Union[str, Any]:
  
  
  
  
  
  
  
  	'''simple docstring'''
  
  
  	__magic_name__	:	str			     =  []
  	while left and right:
  		if left[0][0] < right[0][0]:
  			result.append(left.pop(0     )     )
  		else:
  			result.append(right.pop(0     )     )
  	return result + left + right
  
  
  
  
  
  
  def 						lowerCAmelCase_		(      _snake_case   :						str     )       ->	Tuple:
  
  
  
  
  
  
  
  	'''simple docstring'''
  
  
  	__magic_name__	:	Dict			     =  len(_snake_case     )
  	if length <= 1:
  		return list_ad
  	__magic_name__	:	Optional[int]			     =  length // 2
  	return merge(sortlist_ad(list_ad[:middle]     )   ,     sortlist_ad(list_ad[middle:]     )     )
  
  
  
  
  
  
  def 						lowerCAmelCase_		(      _snake_case   :						list[int]     )       ->	list[int]:
  
  
  
  
  
  
  
  	'''simple docstring'''
  
  
  	if len(_snake_case     ) <= 1:
  		return collection
  	__magic_name__	:	Optional[Any]			     =  []
  	__magic_name__	:	Union[str, Any]			     =  False
  	for i in range(0   ,     len(_snake_case     )   ,     2     ):
  		if i == len(_snake_case     ) - 1:
  			__magic_name__	:	List[str]			     =  True
  		else:
  			if collection[i] < collection[i + 1]:
  				two_paired_list.append([collection[i], collection[i + 1]]     )
  			else:
  				two_paired_list.append([collection[i + 1], collection[i]]     )
  	__magic_name__	:	List[Any]			     =  sortlist_ad(_snake_case     )
  	__magic_name__	:	List[Any]			     =  [i[0] for i in sorted_list_ad]
  	result.append(sorted_list_ad[-1][1]     )
  	if has_last_odd_item:
  		__magic_name__	:	Tuple			     =  collection[-1]
  		__magic_name__	:	Union[str, Any]			     =  binary_search_insertion(_snake_case   ,     _snake_case     )
  	__magic_name__	:	Union[str, Any]			     =  False
  	for i in range(len(_snake_case     ) - 1     ):
  		if result[i] == collection[-1] and has_last_odd_item:
  			__magic_name__	:	int			     =  True
  		__magic_name__	:	Tuple			     =  sorted_list_ad[i][1]
  		# If last_odd_item is inserted before the item's index,
  		# you should forward index one more.
  		if is_last_odd_item_inserted_before_this_index:
  			__magic_name__	:	Optional[Any]			     =  result[: i + 2] + binary_search_insertion(result[i + 2 :]   ,     _snake_case     )
  		else:
  			__magic_name__	:	Dict			     =  result[: i + 1] + binary_search_insertion(result[i + 1 :]   ,     _snake_case     )
  
  	return result
  
  
  if __name__ == "__main__":
  				snake_case				:	str							   =						input("Enter numbers separated by a comma:\n").strip()
  				snake_case				:	str							   =						[int(item) for item in user_input.split(",")]
  				print(merge_insertion_sort(unsorted))
  
  
  
  
  
  
style_context: 
  from __future__ import annotations
  
  snake_case				:	List[str]							   =						"Alexander Joslin"
  
  
  
  
  
  
  def 						lowerCAmelCase_		(      _snake_case   :						int     )       ->	int:
  
  
  
  
  
  
  
  	'''simple docstring'''
  
  
  	if number <= 0:
  		__magic_name__	:	int			     =  F'''n must be greater than 0. Got n = {number}'''
  		raise ValueError(_snake_case     )
  
  	__magic_name__	:	List[str]			     =  [number + 1] * (number + 1)
  
  	# starting position
  	__magic_name__	:	Any			     =  0
  	for i in range(1   ,     _snake_case     ):
  		__magic_name__	:	Optional[int]			     =  min(table[i + 1]   ,     table[i] + 1     )
  		# check if out of bounds
  		if i * 2 <= number:
  			__magic_name__	:	str			     =  min(table[i * 2]   ,     table[i] + 1     )
  		# check if out of bounds
  		if i * 3 <= number:
  			__magic_name__	:	Any			     =  min(table[i * 3]   ,     table[i] + 1     )
  	return table[number]
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  