
'''simple docstring'''

from __future__ import annotations







def 						snake_case__	(      UpperCamelCase			,UpperCamelCase	) ->      Any:
		_UpperCamelCase       : str    =      0
		_UpperCamelCase       : List[str]    =      len(UpperCamelCase__	) - 1
		while left <= right:
				_UpperCamelCase       : str    =      (left + right) // 2
				if left == right:
						if sorted_list[middle] < item:
								_UpperCamelCase       : Dict    =      middle + 1
						break
				elif sorted_list[middle] < item:
						_UpperCamelCase       : Optional[Any]    =      middle + 1
				else:
						_UpperCamelCase       : Any    =      middle - 1
		sorted_list.insert(UpperCamelCase__			,UpperCamelCase__	)
		return sorted_list







def 						snake_case__	(      UpperCamelCase			,UpperCamelCase	) ->      int:
		_UpperCamelCase       : int    =      []
		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 						snake_case__	(      UpperCamelCase	) ->      Union[str, Any]:
		_UpperCamelCase       : Tuple    =      len(UpperCamelCase__	)
		if length <= 1:
				return list_ad
		_UpperCamelCase       : Optional[int]    =      length // 2
		return merge(sortlist_ad(list_ad[:middle]	)			,sortlist_ad(list_ad[middle:]	)	)







def 						snake_case__	(      UpperCamelCase	) ->      List[Any]:

		if len(UpperCamelCase__	) <= 1:
				return collection
		_UpperCamelCase       : Optional[int]    =      []
		_UpperCamelCase       : List[Any]    =      False
		for i in range(0			,len(UpperCamelCase__	)			,2	):
				if i == len(UpperCamelCase__	) - 1:
						_UpperCamelCase       : Optional[int]    =      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]]	)
		_UpperCamelCase       : Tuple    =      sortlist_ad(UpperCamelCase__	)
		_UpperCamelCase       : Optional[int]    =      [i[0] for i in sorted_list_ad]
		result.append(sorted_list_ad[-1][1]	)
		if has_last_odd_item:
				_UpperCamelCase       : Optional[int]    =      collection[-1]
				_UpperCamelCase       : List[str]    =      binary_search_insertion(UpperCamelCase__			,UpperCamelCase__	)
		_UpperCamelCase       : Union[str, Any]    =      False
		for i in range(len(UpperCamelCase__	) - 1	):
				if result[i] == collection[-1] and has_last_odd_item:
						_UpperCamelCase       : Dict    =      True
				_UpperCamelCase       : int    =      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:
						_UpperCamelCase       : Optional[Any]    =      result[: i + 2] + binary_search_insertion(result[i + 2 :]			,UpperCamelCase__	)
				else:
						_UpperCamelCase       : Union[str, Any]    =      result[: i + 1] + binary_search_insertion(result[i + 1 :]			,UpperCamelCase__	)

		return result


if __name__ == "__main__":
	_UpperCAmelCase   :      List[str] 						=  input("""Enter numbers separated by a comma:\n""").strip()
	_UpperCAmelCase   :      int 						=  [int(item) for item in user_input.split(""",""")]
	print(merge_insertion_sort(unsorted))







'''simple docstring'''

from __future__ import annotations

from collections.abc import Iterable
from dataclasses import dataclass
from typing import Any

class 			UpperCAmelCase				:





		"""simple docstring"""





		A__  :   List[str]          =    ('_front', '_back', '_len')

		@dataclass
		class 			UpperCAmelCase				:





				"""simple docstring"""





				A__  :   Any          =    None
				A__  :   Deque._Node | None          =    None
				A__  :   Deque._Node | None          =    None







		class 			UpperCAmelCase				:





				"""simple docstring"""





				A__  :   Any          =    ('_cur',)
				def __init__(    self  ,					_snake_case     )				->    None:
						_UpperCamelCase       : Any    =      cur
				def __iter__(    self     )				->    Deque._Iterator:
						return self




				def _lowercase  (    self     )				->    Any:
						if self._cur is None:
								# finished iterating
								raise StopIteration
						_UpperCamelCase       : List[Any]    =      self._cur.val
						_UpperCamelCase       : List[Any]    =      self._cur.next_node

						return val







		def __init__(    self  ,					_snake_case = None     )				->    None:
				_UpperCamelCase       : Any    =      None
				_UpperCamelCase       : Any    =      None
				_UpperCamelCase       : int    =      0

				if iterable is not None:
						# append every value to the deque
						for val in iterable:
								self.append(_snake_case     )
		def _lowercase  (    self  ,					_snake_case     )				->    None:
				_UpperCamelCase       : List[str]    =      self._Node(_snake_case  ,					_snake_case  ,					_snake_case     )
				if self.is_empty():
						# front = back
						_UpperCamelCase       : Union[str, Any]    =      node
						_UpperCamelCase       : Tuple    =      1
				else:
						# connect nodes
						_UpperCamelCase       : Union[str, Any]    =      node
						_UpperCamelCase       : int    =      self._back
						_UpperCamelCase       : List[Any]    =      node  # assign new back to the new node

						self._len += 1

						# make sure there were no errors
						assert not self.is_empty(), "Error on appending value."
		def _lowercase  (    self  ,					_snake_case     )				->    None:
				_UpperCamelCase       : Optional[Any]    =      self._Node(_snake_case  ,					_snake_case  ,					_snake_case     )
				if self.is_empty():
						# front = back
						_UpperCamelCase       : Union[str, Any]    =      node
						_UpperCamelCase       : Optional[int]    =      1
				else:
						# connect nodes
						_UpperCamelCase       : Tuple    =      self._front
						_UpperCamelCase       : Optional[int]    =      node
						_UpperCamelCase       : List[str]    =      node  # assign new front to the new node

						self._len += 1

						# make sure there were no errors
						assert not self.is_empty(), "Error on appending value."
		def _lowercase  (    self  ,					_snake_case     )				->    None:
				for val in iterable:
						self.append(_snake_case     )
		def _lowercase  (    self  ,					_snake_case     )				->    None:
				for val in iterable:
						self.appendleft(_snake_case     )
		def _lowercase  (    self     )				->    Any:
				assert not self.is_empty(), "Deque is empty."

				_UpperCamelCase       : int    =      self._back
				_UpperCamelCase       : List[Any]    =      self._back.prev_node  # set new back
				# drop the last node - python will deallocate memory automatically
				_UpperCamelCase       : Union[str, Any]    =      None

				self._len -= 1

				return topop.val
		def _lowercase  (    self     )				->    Any:
				assert not self.is_empty(), "Deque is empty."

				_UpperCamelCase       : List[Any]    =      self._front
				_UpperCamelCase       : str    =      self._front.next_node  # set new front and drop the first node
				_UpperCamelCase       : Union[str, Any]    =      None

				self._len -= 1

				return topop.val
		def _lowercase  (    self     )				->    bool:
				return self._front is None
		def __len__(    self     )				->    int:
				return self._len
		def __eq__(    self  ,					_snake_case     )				->    bool:

				if not isinstance(_snake_case  ,					_snake_case     ):
						return NotImplemented

				_UpperCamelCase       : Optional[int]    =      self._front
				_UpperCamelCase       : List[Any]    =      other._front

				# if the length of the dequeues are not the same, they are not equal
				if len(self     ) != len(_snake_case     ):
						return False

				while me is not None and oth is not None:
						# compare every value
						if me.val != oth.val:
								return False
						_UpperCamelCase       : str    =      me.next_node
						_UpperCamelCase       : List[str]    =      oth.next_node

				return True
		def __iter__(    self     )				->    Deque._Iterator:
				return Deque._Iterator(self._front     )




		def __repr__(    self     )				->    str:
				_UpperCamelCase       : str    =      []
				_UpperCamelCase       : Tuple    =      self._front
				while aux is not None:
						# append the values in a list to display
						values_list.append(aux.val     )
						_UpperCamelCase       : List[str]    =      aux.next_node

				return F'''[{', '.join(repr(_snake_case     ) for val in values_list     )}]'''


if __name__ == "__main__":
	import doctest

	doctest.testmod()





