






from __future__ import annotations




def   lowercase__   (  __snake_case					:							Any  , __snake_case					:							int						):


					'''simple docstring'''


					UpperCAmelCase_					:   Optional[int]   =		0
					UpperCAmelCase_					:   Optional[int]   =		len(__snake_case						) - 1
					while left <= right:
										UpperCAmelCase_					:   Optional[Any]   =		(left + right) // 2
										if left == right:
															if sorted_list[middle] < item:
																				UpperCAmelCase_					:   List[Any]   =		middle + 1
															break
										elif sorted_list[middle] < item:
															UpperCAmelCase_					:   Union[str, Any]   =		middle + 1
										else:
															UpperCAmelCase_					:   Tuple   =		middle - 1
					sorted_list.insert(__snake_case  , __snake_case						)
					return sorted_list




def   lowercase__   (  __snake_case					:							Union[str, Any]  , __snake_case					:							int						):


					'''simple docstring'''


					UpperCAmelCase_					:   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   lowercase__   (  __snake_case					:							Dict						):


					'''simple docstring'''


					UpperCAmelCase_					:   str   =		len(__snake_case						)
					if length <= 1:
										return list_ad
					UpperCAmelCase_					:   List[Any]   =		length // 2
					return merge(sortlist_ad(list_ad[:middle]						)  , sortlist_ad(list_ad[middle:]						)						)




def   lowercase__   (  __snake_case					:							list[int]						):


					'''simple docstring'''


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

					return result


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














def   lowercase__   (  __snake_case					:							int  , __snake_case					:							int  , __snake_case					:							int  , __snake_case					:							int						):


					'''simple docstring'''


					return len_board * len_board_column * row + column




def   lowercase__   (  __snake_case					:							list[list[str]]  , __snake_case					:							str  , __snake_case					:							int  , __snake_case					:							int  , __snake_case					:							int  , __snake_case					:							set[int]  , ):


					'''simple docstring'''


					if board[row][column] != word[word_index]:
										return False

					if word_index == len(__snake_case						) - 1:
										return True

					UpperCAmelCase_					:   Dict   =		[(0, 1), (0, -1), (-1, 0), (1, 0)]
					UpperCAmelCase_					:   Union[str, Any]   =		len(__snake_case						)
					UpperCAmelCase_					:   List[Any]   =		len(board[0]						)
					for direction in traverts_directions:
										UpperCAmelCase_					:   Optional[int]   =		row + direction[0]
										UpperCAmelCase_					:   Optional[int]   =		column + direction[1]
										if not (0 <= next_i < len_board and 0 <= next_j < len_board_column):
															continue

										UpperCAmelCase_					:   Tuple   =		get_point_key(__snake_case  , __snake_case  , __snake_case  , __snake_case						)
										if key in visited_points_set:
															continue

										visited_points_set.add(__snake_case						)
										if exits_word(__snake_case  , __snake_case  , __snake_case  , __snake_case  , word_index + 1  , __snake_case						):
															return True

										visited_points_set.remove(__snake_case						)

					return False




def   lowercase__   (  __snake_case					:							list[list[str]]  , __snake_case					:							str						):


					'''simple docstring'''


					UpperCAmelCase_					:   Any   =		(
					    'The board should be a non empty matrix of single chars strings.'
					)

					UpperCAmelCase_					:   Optional[Any]   =		len(__snake_case						)
					if not isinstance(__snake_case  , __snake_case						) or len(__snake_case						) == 0:
										raise ValueError(__snake_case						)

					for row in board:
										if not isinstance(__snake_case  , __snake_case						) or len(__snake_case						) == 0:
															raise ValueError(__snake_case						)

										for item in row:
															if not isinstance(__snake_case  , __snake_case						) or len(__snake_case						) != 1:
																				raise ValueError(__snake_case						)

    # Validate word
					if not isinstance(__snake_case  , __snake_case						) or len(__snake_case						) == 0:
										raise ValueError(
										    'The word parameter should be a string of length greater than 0.'						)

					UpperCAmelCase_					:   Any   =		len(board[0]						)
					for i in range(__snake_case						):
										for j in range(__snake_case						):
															if exits_word(
															    __snake_case  , __snake_case  , __snake_case  , __snake_case  , 0  , {get_point_key(__snake_case  , __snake_case  , __snake_case  , __snake_case						)}						):
																				return True

					return False


if __name__ == "__main__":
		import doctest

		doctest.testmod()






