






__UpperCAmelCase										=		[[0, 1, 1], [0, 0, 1], [1, 0, 0]]



class 						lowerCamelCase   :







		'''simple docstring'''



		def __init__(							self       ,	_UpperCamelCase     )			->							Tuple:
							UpperCAmelCase_					:   Tuple   =		name
							UpperCAmelCase_					:   Union[str, Any]   =		[]
							UpperCAmelCase_					:   List[str]   =		[]



		def       __UpperCAmelCase    (							self       ,	_UpperCamelCase     )			->							List[Any]:
							self.inbound.append(_UpperCamelCase     )



		def       __UpperCAmelCase    (							self       ,	_UpperCamelCase     )			->							Union[str, Any]:
							self.outbound.append(_UpperCamelCase     )



		def __repr__(							self     )			->							str:
							return f"<node={self.name} inbound={self.inbound} outbound={self.outbound}>"





def   lowercase__   (  __snake_case					:							Union[str, Any]  , __snake_case					:							int=3  , __snake_case					:							Optional[Any]=0.85						):


					'''simple docstring'''


					UpperCAmelCase_					:   int   =		{}
					for node in nodes:
										UpperCAmelCase_					:   str   =		1

					UpperCAmelCase_					:   List[Any]   =		{}
					for node in nodes:
										UpperCAmelCase_					:   Any   =		len(node.outbound						)

					for i in range(__snake_case						):
										print(F"======= Iteration {i + 1} ======="						)
										for _, node in enumerate(__snake_case						):
															UpperCAmelCase_					:   Dict   =		(1 - d) + d * sum(
															    ranks[ib] / outbounds[ib] for ib in node.inbound						)
										print(__snake_case						)




def   lowercase__   (  ):


					'''simple docstring'''


					UpperCAmelCase_					:   Dict   =		list(input('Enter Names of the Nodes: '						).split()						)

					UpperCAmelCase_					:   Optional[Any]   =		[Node(__snake_case						) for name in names]

					for ri, row in enumerate(__snake_case						):
										for ci, col in enumerate(__snake_case						):
															if col == 1:
																				nodes[ci].add_inbound(names[ri]						)
																				nodes[ri].add_outbound(names[ci]						)

					print('======= Nodes ======='						)
					for node in nodes:
										print(__snake_case						)

					page_rank(__snake_case						)


if __name__ == "__main__":
		main()














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))






