

'''simple docstring'''


import numpy as np







def 						SCREAMING_SNAKE_CASE(  UpperCamelCase  )    ->    str:
	return 1 / (1 + np.exp(-vector  ))







def 						SCREAMING_SNAKE_CASE(  UpperCamelCase  )    ->    List[str]:
	return vector * sigmoid(_lowerCamelCase  )


if __name__ == "__main__":
						import doctest

						doctest.testmod()









'''simple docstring'''


class 					lowercase						:


							def __init__(			self)							->				Dict:
								UpperCAmelCase_		:      List[str]       	=					0
								UpperCAmelCase_		:      str       	=					0
								UpperCAmelCase_		:      Union[str, Any]       	=					{}


							def 						_snake_case							(			self    ,			_snake_case)							->				Tuple:
								if vertex not in self.adjacency:
									UpperCAmelCase_		:      Tuple       	=					{}
									self.num_vertices += 1


							def 						_snake_case							(			self    ,			_snake_case    ,			_snake_case    ,			_snake_case)							->				Any:
								self.add_vertex(_snake_case)
								self.add_vertex(_snake_case)

								if head == tail:
									return

								UpperCAmelCase_		:      str       	=					weight
								UpperCAmelCase_		:      Optional[int]       	=					weight


							def 						_snake_case							(			self)							->				Union[str, Any]:
								UpperCAmelCase_		:      Dict       	=					self.get_edges()
								for edge in edges:
									UpperCAmelCase_	,    UpperCAmelCase_	,    UpperCAmelCase_		:      str       	=					edge
									edges.remove((tail, head, weight))
								for i in range(len(_snake_case)):
									UpperCAmelCase_		:      Union[str, Any]       	=					list(edges[i])

								edges.sort(key=lambda _snake_case: e[2])
								for i in range(len(_snake_case) - 1):
									if edges[i][2] >= edges[i + 1][2]:
										UpperCAmelCase_		:      Tuple       	=					edges[i][2] + 1
								for edge in edges:
									UpperCAmelCase_	,    UpperCAmelCase_	,    UpperCAmelCase_		:      List[Any]       	=					edge
									UpperCAmelCase_		:      Any       	=					weight
									UpperCAmelCase_		:      Union[str, Any]       	=					weight


							def __str__(			self)							->				str:
								UpperCAmelCase_		:      int       	=					''
								for tail in self.adjacency:
									for head in self.adjacency[tail]:
										UpperCAmelCase_		:      Dict       	=					self.adjacency[head][tail]
										string += F"""{head} -> {tail} == {weight}\n"""
								return string.rstrip('\n')


							def 						_snake_case							(			self)							->				str:
								UpperCAmelCase_		:      Optional[int]       	=					[]
								for tail in self.adjacency:
									for head in self.adjacency[tail]:
										output.append((tail, head, self.adjacency[head][tail]))
								return output


							def 						_snake_case							(			self)							->				Any:
								return self.adjacency.keys()


							@staticmethod
							def 						_snake_case							(			_snake_case=None    ,			_snake_case=None)							->				Dict:
								UpperCAmelCase_		:      List[str]       	=					Graph()
								if vertices is None:
									UpperCAmelCase_		:      Optional[Any]       	=					[]
								if edges is None:
									UpperCAmelCase_		:      int       	=					[]
								for vertex in vertices:
									g.add_vertex(_snake_case)
								for edge in edges:
									g.add_edge(*_snake_case)
								return g



							class 					lowercase						:


														def __init__(			self)							->				Dict:
															UpperCAmelCase_		:      Tuple       	=					{}
															UpperCAmelCase_		:      str       	=					{}


														def __len__(			self)							->				List[Any]:
															return len(self.parent)


														def 						_snake_case							(			self    ,			_snake_case)							->				Union[str, Any]:
															if item in self.parent:
																return self.find(_snake_case)

															UpperCAmelCase_		:      Any       	=					item
															UpperCAmelCase_		:      List[str]       	=					0
															return item


														def 						_snake_case							(			self    ,			_snake_case)							->				str:
															if item not in self.parent:
																return self.make_set(_snake_case)
															if item != self.parent[item]:
																UpperCAmelCase_		:      Dict       	=					self.find(self.parent[item])
															return self.parent[item]





														def 						_snake_case							(			self    ,			_snake_case    ,			_snake_case)							->				int:
															UpperCAmelCase_		:      List[str]       	=					self.find(_snake_case)
															UpperCAmelCase_		:      List[str]       	=					self.find(_snake_case)

															if roota == roota:
																return roota

															if self.rank[roota] > self.rank[roota]:
																UpperCAmelCase_		:      int       	=					roota
																return roota

															if self.rank[roota] < self.rank[roota]:
																UpperCAmelCase_		:      Dict       	=					roota
																return roota

															if self.rank[roota] == self.rank[roota]:
																self.rank[roota] += 1
																UpperCAmelCase_		:      Any       	=					roota
																return roota
															return None


							@staticmethod
							def 						_snake_case							(			_snake_case)							->				int:
								UpperCAmelCase_		:      Optional[Any]       	=					graph.num_vertices

								UpperCAmelCase_		:      Optional[int]       	=					Graph.UnionFind()
								UpperCAmelCase_		:      int       	=					[]
								while num_components > 1:
									UpperCAmelCase_		:      Any       	=					{}
									for vertex in graph.get_vertices():
										UpperCAmelCase_		:      Optional[Any]       	=					-1

									UpperCAmelCase_		:      List[str]       	=					graph.get_edges()
									for edge in edges:
										UpperCAmelCase_	,    UpperCAmelCase_	,    UpperCAmelCase_		:      List[str]       	=					edge
										edges.remove((tail, head, weight))
									for edge in edges:
										UpperCAmelCase_	,    UpperCAmelCase_	,    UpperCAmelCase_		:      Union[str, Any]       	=					edge
										UpperCAmelCase_		:      Any       	=					union_find.find(_snake_case)
										UpperCAmelCase_		:      Dict       	=					union_find.find(_snake_case)
										if seta != seta:
											if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
												UpperCAmelCase_		:      List[str]       	=					[head, tail, weight]

											if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
												UpperCAmelCase_		:      str       	=					[head, tail, weight]
									for vertex in cheap_edge:
										if cheap_edge[vertex] != -1:
											UpperCAmelCase_	,    UpperCAmelCase_	,    UpperCAmelCase_		:      Any       	=					cheap_edge[vertex]
											if union_find.find(_snake_case) != union_find.find(_snake_case):
												union_find.union(_snake_case    ,			_snake_case)
												mst_edges.append(cheap_edge[vertex])
												UpperCAmelCase_		:      Tuple       	=					num_components - 1
								UpperCAmelCase_		:      int       	=					Graph.build(edges=_snake_case)
								return mst






