




"""simple docstring"""




import numpy

class   UpperCAmelCase_    :
		def __init__(						self				,						UpperCamelCase_				,						UpperCamelCase_       )						->       None:
					__lowercase			:  Any								=       input_array

					# Random initial weights are assigned where first argument is the
					# number of nodes in previous layer and second argument is the
					# number of nodes in the next layer.

					# Random initial weights are assigned.
					# self.input_array.shape[1] is used to represent number of nodes in input layer.
					# First hidden layer consists of 4 nodes.
					__lowercase			:  str								=       numpy.random.rand(
					    self.input_array.shape[1]				,						4       )

					# Random initial values for the first hidden layer.
					# First hidden layer has 4 nodes.
					# Second hidden layer has 3 nodes.
					__lowercase			:  Union[str, Any]								=       numpy.random.rand(
					    4				,						3       )

					# Random initial values for the second hidden layer.
					# Second hidden layer has 3 nodes.
					# Output layer has 1 node.
					__lowercase			:  Dict								=       numpy.random.rand(3				,						1       )

					# Real output values provided.
					__lowercase			:  List[Any]								=       output_array

					# Predicted output values by the neural network.
					# Predicted_output array initially consists of zeroes.
					__lowercase			:  int								=       numpy.zeros(output_array.shape       )
		def 	_lowerCamelCase							(						self       )						->       numpy.ndarray:
					__lowercase			:  Union[str, Any]								=       sigmoid(
					    numpy.dot(self.input_array				,						self.input_layer_and_first_hidden_layer_weights       )       )

					# layer_between_first_hidden_layer_and_second_hidden_layer is the layer
					# connecting the first hidden set of nodes with the second hidden set of nodes.
					__lowercase			:  str								=       sigmoid(
					    numpy.dot(
					        self.layer_between_input_and_first_hidden_layer				,						self.first_hidden_layer_and_second_hidden_layer_weights				,						)       )

					# layer_between_second_hidden_layer_and_output is the layer connecting
					# second hidden layer with the output node.
					__lowercase			:  str								=       sigmoid(
					    numpy.dot(
					        self.layer_between_first_hidden_layer_and_second_hidden_layer				,						self.second_hidden_layer_and_output_layer_weights				,						)       )

					return self.layer_between_second_hidden_layer_and_output
		def 	_lowerCamelCase							(						self       )						->       None:
					__lowercase			:  List[Any]								=       numpy.dot(
					    self.layer_between_first_hidden_layer_and_second_hidden_layer.T				,						2
					    * (self.output_array - self.predicted_output)
					    * sigmoid_derivative(self.predicted_output       )				,						)
					__lowercase			:  Union[str, Any]								=       numpy.dot(
					    self.layer_between_input_and_first_hidden_layer.T				,						numpy.dot(
					        2
					        * (self.output_array - self.predicted_output)
					        * sigmoid_derivative(self.predicted_output       )				,						self.second_hidden_layer_and_output_layer_weights.T				,						)
					    * sigmoid_derivative(
					        self.layer_between_first_hidden_layer_and_second_hidden_layer       )				,						)
					__lowercase			:  Union[str, Any]								=       numpy.dot(
					    self.input_array.T				,						numpy.dot(
					        numpy.dot(
					            2
					            * (self.output_array - self.predicted_output)
					            * sigmoid_derivative(self.predicted_output       )				,						self.second_hidden_layer_and_output_layer_weights.T				,						)
					        * sigmoid_derivative(
					            self.layer_between_first_hidden_layer_and_second_hidden_layer       )				,						self.first_hidden_layer_and_second_hidden_layer_weights.T				,						)
					    * sigmoid_derivative(self.layer_between_input_and_first_hidden_layer       )				,						)

					self.input_layer_and_first_hidden_layer_weights += (
					    updated_input_layer_and_first_hidden_layer_weights
					)
					self.first_hidden_layer_and_second_hidden_layer_weights += (
					    updated_first_hidden_layer_and_second_hidden_layer_weights
					)
					self.second_hidden_layer_and_output_layer_weights += (
					    updated_second_hidden_layer_and_output_layer_weights
					)
		def 	_lowerCamelCase							(						self				,						UpperCamelCase_				,						UpperCamelCase_				,						UpperCamelCase_       )						->       None:
					for iteration in range(1				,						iterations + 1       ):
								__lowercase			:  Optional[int]								=       self.feedforward()
								self.back_propagation()
								if give_loss:
											__lowercase			:  Tuple								=       numpy.mean(numpy.square(output - self.feedforward()       )       )
											print(F"""Iteration {iteration} Loss: {loss}"""       )
		def 	_lowerCamelCase							(						self				,						UpperCamelCase_       )						->       int:
					__lowercase			:  List[Any]								=       input_arr

					__lowercase			:  List[Any]								=       sigmoid(
					    numpy.dot(self.array				,						self.input_layer_and_first_hidden_layer_weights       )       )

					__lowercase			:  Tuple								=       sigmoid(
					    numpy.dot(
					        self.layer_between_input_and_first_hidden_layer				,						self.first_hidden_layer_and_second_hidden_layer_weights				,						)       )

					__lowercase			:  Any								=       sigmoid(
					    numpy.dot(
					        self.layer_between_first_hidden_layer_and_second_hidden_layer				,						self.second_hidden_layer_and_output_layer_weights				,						)       )

					return int(self.layer_between_second_hidden_layer_and_output > 0.6       )







def      __UpperCAmelCase     ( __UpperCamelCase	):
			return 1 / (1 + numpy.exp(-value	))







def      __UpperCAmelCase     ( __UpperCamelCase	):
			return (value) * (1 - (value))







def      __UpperCAmelCase     ( ):
			__lowercase			:  List[str]								=       numpy.array(
			    (
			        [0, 0, 0],
			        [0, 0, 1],
			        [0, 1, 0],
			        [0, 1, 1],
			        [1, 0, 0],
			        [1, 0, 1],
			        [1, 1, 0],
			        [1, 1, 1],
			    )	,				dtype=numpy.floataa	,				)

			# True output values for the given input values.
			__lowercase			:  Optional[Any]								=       numpy.array(([0], [1], [1], [0], [1], [0], [0], [1])	,				dtype=numpy.floataa	)

			# Calling neural network class.
			__lowercase			:  Optional[Any]								=       TwoHiddenLayerNeuralNetwork(
			    input_array=__UpperCamelCase	,				output_array=__UpperCamelCase	)

			# Calling training function.
			# Set give_loss to True if you want to see loss in every iteration.
			neural_network.train(output=__UpperCamelCase	,				iterations=10	,				give_loss=__UpperCamelCase	)

			return neural_network.predict(numpy.array(([1, 1, 1])	,				dtype=numpy.floataa	)	)


if __name__ == "__main__":
			example()






"""simple docstring"""





from collections import deque
from math import floor
from random import random
from time import time







class 							SCREAMING_SNAKE_CASE   :






					"""simple docstring"""



					def __init__(			self     :							Union[str, Any]						):
						lowerCAmelCase__      :		List[str]    							=      {}







					def 			__lowerCAmelCase					(			self     :							Optional[Any]  ,lowercase_     :							Optional[Any]  ,lowercase_     :							str  ,lowercase_     :							List[str]=1						):
						if self.graph.get(lowercase_						):
							if self.graph[u].count([w, v]						) == 0:
								self.graph[u].append([w, v]						)
						else:
							lowerCAmelCase__      :		Optional[int]    							=      [[w, v]]
						if not self.graph.get(lowercase_						):
							lowerCAmelCase__      :		Union[str, Any]    							=      []







					def 			__lowerCAmelCase					(			self     :							List[Any]						):
						return list(self.graph						)







					def 			__lowerCAmelCase					(			self     :							Dict  ,lowercase_     :							Tuple  ,lowercase_     :							Tuple						):
						if self.graph.get(lowercase_						):
							for _ in self.graph[u]:
								if _[1] == v:
									self.graph[u].remove(lowercase_						)







					def 			__lowerCAmelCase					(			self     :							int  ,lowercase_     :							Any=-2  ,lowercase_     :							List[Any]=-1						):
						if s == d:
							return []
						lowerCAmelCase__      :		int    							=      []
						lowerCAmelCase__      :		List[Any]    							=      []
						if s == -2:
							lowerCAmelCase__      :		int    							=      list(self.graph						)[0]
						stack.append(lowercase_						)
						visited.append(lowercase_						)
						lowerCAmelCase__      :		int    							=      s

						while True:
							# check if there is any non isolated nodes
							if len(self.graph[s]						) != 0:
								lowerCAmelCase__      :		List[Any]    							=      s
								for node in self.graph[s]:
									if visited.count(node[1]						) < 1:
										if node[1] == d:
											visited.append(lowercase_						)
											return visited
										else:
											stack.append(node[1]						)
											visited.append(node[1]						)
											lowerCAmelCase__      :		Optional[int]    							=      node[1]
											break

            # check if all the children are visited
							if s == ss:
								stack.pop()
								if len(lowercase_						) != 0:
									lowerCAmelCase__      :		str    							=      stack[len(lowercase_						) - 1]
							else:
								lowerCAmelCase__      :		Union[str, Any]    							=      ss

							# check if se have reached the starting point
							if len(lowercase_						) == 0:
								return visited







					def 			__lowerCAmelCase					(			self     :							Dict  ,lowercase_     :							Optional[Any]=-1						):
						if c == -1:
							lowerCAmelCase__      :		Any    							=      floor(random() * 1_0_0_0_0						) + 1_0
						for i in range(lowercase_						):
							# every vertex has max 100 edges
							for _ in range(floor(random() * 1_0_2						) + 1						):
								lowerCAmelCase__      :		Any    							=      floor(random() * c						) + 1
								if n != i:
									self.add_pair(lowercase_  ,lowercase_  ,1						)







					def 			__lowerCAmelCase					(			self     :							Optional[Any]  ,lowercase_     :							Union[str, Any]=-2						):
						lowerCAmelCase__      :		Tuple    							=      deque()
						lowerCAmelCase__      :		Tuple    							=      []
						if s == -2:
							lowerCAmelCase__      :		Any    							=      list(self.graph						)[0]
						d.append(lowercase_						)
						visited.append(lowercase_						)
						while d:
							lowerCAmelCase__      :		Dict    							=      d.popleft()
							if len(self.graph[s]						) != 0:
								for node in self.graph[s]:
									if visited.count(node[1]						) < 1:
										d.append(node[1]						)
										visited.append(node[1]						)
						return visited







					def 			__lowerCAmelCase					(			self     :							Union[str, Any]  ,lowercase_     :							Optional[Any]						):
						lowerCAmelCase__      :		Optional[Any]    							=      0
						for x in self.graph:
							for y in self.graph[x]:
								if y[1] == u:
									count += 1
						return count







					def 			__lowerCAmelCase					(			self     :							str  ,lowercase_     :							Optional[int]						):
						return len(self.graph[u]						)







					def 			__lowerCAmelCase					(			self     :							List[str]  ,lowercase_     :							List[str]=-2						):
						lowerCAmelCase__      :		Union[str, Any]    							=      []
						lowerCAmelCase__      :		Any    							=      []
						if s == -2:
							lowerCAmelCase__      :		Any    							=      list(self.graph						)[0]
						stack.append(lowercase_						)
						visited.append(lowercase_						)
						lowerCAmelCase__      :		Tuple    							=      s
						lowerCAmelCase__      :		Optional[int]    							=      []

						while True:
							# check if there is any non isolated nodes
							if len(self.graph[s]						) != 0:
								lowerCAmelCase__      :		Optional[Any]    							=      s
								for node in self.graph[s]:
									if visited.count(node[1]						) < 1:
										stack.append(node[1]						)
										visited.append(node[1]						)
										lowerCAmelCase__      :		Dict    							=      node[1]
										break

            # check if all the children are visited
							if s == ss:
								sorted_nodes.append(stack.pop()						)
								if len(lowercase_						) != 0:
									lowerCAmelCase__      :		Union[str, Any]    							=      stack[len(lowercase_						) - 1]
							else:
								lowerCAmelCase__      :		int    							=      ss

							# check if se have reached the starting point
							if len(lowercase_						) == 0:
								return sorted_nodes







					def 			__lowerCAmelCase					(			self     :							List[Any]						):
						lowerCAmelCase__      :		str    							=      []
						lowerCAmelCase__      :		List[str]    							=      []
						lowerCAmelCase__      :		int    							=      list(self.graph						)[0]
						stack.append(lowercase_						)
						visited.append(lowercase_						)
						lowerCAmelCase__      :		List[Any]    							=      -2
						lowerCAmelCase__      :		str    							=      []
						lowerCAmelCase__      :		Optional[Any]    							=      s
						lowerCAmelCase__      :		Union[str, Any]    							=      False
						lowerCAmelCase__      :		Optional[int]    							=      set()

						while True:
							# check if there is any non isolated nodes
							if len(self.graph[s]						) != 0:
								lowerCAmelCase__      :		List[str]    							=      s
								for node in self.graph[s]:
									if (
									    visited.count(node[1]						) > 0
									    and node[1] != parent
									    and indirect_parents.count(node[1]						) > 0
									    and not on_the_way_back
									):
										lowerCAmelCase__      :		List[Any]    							=      len(lowercase_						) - 1
										while len_stack >= 0:
											if stack[len_stack] == node[1]:
												anticipating_nodes.add(node[1]						)
												break
											else:
												anticipating_nodes.add(stack[len_stack]						)
												len_stack -= 1
									if visited.count(node[1]						) < 1:
										stack.append(node[1]						)
										visited.append(node[1]						)
										lowerCAmelCase__      :		Optional[int]    							=      node[1]
										break

            # check if all the children are visited
							if s == ss:
								stack.pop()
								lowerCAmelCase__      :		str    							=      True
								if len(lowercase_						) != 0:
									lowerCAmelCase__      :		Tuple    							=      stack[len(lowercase_						) - 1]
							else:
								lowerCAmelCase__      :		int    							=      False
								indirect_parents.append(lowercase_						)
								lowerCAmelCase__      :		str    							=      s
								lowerCAmelCase__      :		Tuple    							=      ss

							# check if se have reached the starting point
							if len(lowercase_						) == 0:
								return list(lowercase_						)







					def 			__lowerCAmelCase					(			self     :							int						):
						lowerCAmelCase__      :		Tuple    							=      []
						lowerCAmelCase__      :		Tuple    							=      []
						lowerCAmelCase__      :		Any    							=      list(self.graph						)[0]
						stack.append(lowercase_						)
						visited.append(lowercase_						)
						lowerCAmelCase__      :		List[str]    							=      -2
						lowerCAmelCase__      :		int    							=      []
						lowerCAmelCase__      :		int    							=      s
						lowerCAmelCase__      :		List[Any]    							=      False
						lowerCAmelCase__      :		List[str]    							=      set()

						while True:
							# check if there is any non isolated nodes
							if len(self.graph[s]						) != 0:
								lowerCAmelCase__      :		Optional[int]    							=      s
								for node in self.graph[s]:
									if (
									    visited.count(node[1]						) > 0
									    and node[1] != parent
									    and indirect_parents.count(node[1]						) > 0
									    and not on_the_way_back
									):
										lowerCAmelCase__      :		List[Any]    							=      len(lowercase_						) - 1
										while len_stack_minus_one >= 0:
											if stack[len_stack_minus_one] == node[1]:
												anticipating_nodes.add(node[1]						)
												break
											else:
												return True
									if visited.count(node[1]						) < 1:
										stack.append(node[1]						)
										visited.append(node[1]						)
										lowerCAmelCase__      :		Optional[Any]    							=      node[1]
										break

            # check if all the children are visited
							if s == ss:
								stack.pop()
								lowerCAmelCase__      :		List[str]    							=      True
								if len(lowercase_						) != 0:
									lowerCAmelCase__      :		Dict    							=      stack[len(lowercase_						) - 1]
							else:
								lowerCAmelCase__      :		Union[str, Any]    							=      False
								indirect_parents.append(lowercase_						)
								lowerCAmelCase__      :		Tuple    							=      s
								lowerCAmelCase__      :		Union[str, Any]    							=      ss

							# check if se have reached the starting point
							if len(lowercase_						) == 0:
								return False







					def 			__lowerCAmelCase					(			self     :							Any  ,lowercase_     :							List[Any]=-2  ,lowercase_     :							Union[str, Any]=-1						):
						lowerCAmelCase__      :		Optional[int]    							=      time()
						self.dfs(lowercase_  ,lowercase_						)
						lowerCAmelCase__      :		Any    							=      time()
						return end - begin







					def 			__lowerCAmelCase					(			self     :							Any  ,lowercase_     :							Dict=-2						):
						lowerCAmelCase__      :		List[str]    							=      time()
						self.bfs(lowercase_						)
						lowerCAmelCase__      :		List[Any]    							=      time()
						return end - begin







class 							SCREAMING_SNAKE_CASE   :






					"""simple docstring"""



					def __init__(			self     :							Union[str, Any]						):
						lowerCAmelCase__      :		Tuple    							=      {}







					def 			__lowerCAmelCase					(			self     :							List[Any]  ,lowercase_     :							Optional[int]  ,lowercase_     :							Dict  ,lowercase_     :							Any=1						):
						# check if the u exists
						if self.graph.get(lowercase_						):
							# if there already is a edge
							if self.graph[u].count([w, v]						) == 0:
								self.graph[u].append([w, v]						)
						else:
							# if u does not exist
							lowerCAmelCase__      :		List[Any]    							=      [[w, v]]
						# add the other way
						if self.graph.get(lowercase_						):
							# if there already is a edge
							if self.graph[v].count([w, u]						) == 0:
								self.graph[v].append([w, u]						)
						else:
							# if u does not exist
							lowerCAmelCase__      :		int    							=      [[w, u]]







					def 			__lowerCAmelCase					(			self     :							Dict  ,lowercase_     :							Union[str, Any]  ,lowercase_     :							Dict						):
						if self.graph.get(lowercase_						):
							for _ in self.graph[u]:
								if _[1] == v:
									self.graph[u].remove(lowercase_						)
        # the other way round
						if self.graph.get(lowercase_						):
							for _ in self.graph[v]:
								if _[1] == u:
									self.graph[v].remove(lowercase_						)







					def 			__lowerCAmelCase					(			self     :							int  ,lowercase_     :							Optional[int]=-2  ,lowercase_     :							str=-1						):
						if s == d:
							return []
						lowerCAmelCase__      :		Optional[Any]    							=      []
						lowerCAmelCase__      :		Any    							=      []
						if s == -2:
							lowerCAmelCase__      :		Tuple    							=      list(self.graph						)[0]
						stack.append(lowercase_						)
						visited.append(lowercase_						)
						lowerCAmelCase__      :		int    							=      s

						while True:
							# check if there is any non isolated nodes
							if len(self.graph[s]						) != 0:
								lowerCAmelCase__      :		Optional[int]    							=      s
								for node in self.graph[s]:
									if visited.count(node[1]						) < 1:
										if node[1] == d:
											visited.append(lowercase_						)
											return visited
										else:
											stack.append(node[1]						)
											visited.append(node[1]						)
											lowerCAmelCase__      :		List[str]    							=      node[1]
											break

            # check if all the children are visited
							if s == ss:
								stack.pop()
								if len(lowercase_						) != 0:
									lowerCAmelCase__      :		str    							=      stack[len(lowercase_						) - 1]
							else:
								lowerCAmelCase__      :		Dict    							=      ss

							# check if se have reached the starting point
							if len(lowercase_						) == 0:
								return visited







					def 			__lowerCAmelCase					(			self     :							Union[str, Any]  ,lowercase_     :							List[Any]=-1						):
						if c == -1:
							lowerCAmelCase__      :		str    							=      floor(random() * 1_0_0_0_0						) + 1_0
						for i in range(lowercase_						):
							# every vertex has max 100 edges
							for _ in range(floor(random() * 1_0_2						) + 1						):
								lowerCAmelCase__      :		List[str]    							=      floor(random() * c						) + 1
								if n != i:
									self.add_pair(lowercase_  ,lowercase_  ,1						)







					def 			__lowerCAmelCase					(			self     :							Optional[Any]  ,lowercase_     :							List[Any]=-2						):
						lowerCAmelCase__      :		Tuple    							=      deque()
						lowerCAmelCase__      :		List[Any]    							=      []
						if s == -2:
							lowerCAmelCase__      :		Tuple    							=      list(self.graph						)[0]
						d.append(lowercase_						)
						visited.append(lowercase_						)
						while d:
							lowerCAmelCase__      :		Any    							=      d.popleft()
							if len(self.graph[s]						) != 0:
								for node in self.graph[s]:
									if visited.count(node[1]						) < 1:
										d.append(node[1]						)
										visited.append(node[1]						)
						return visited







					def 			__lowerCAmelCase					(			self     :							Any  ,lowercase_     :							Any						):
						return len(self.graph[u]						)







					def 			__lowerCAmelCase					(			self     :							Any						):
						lowerCAmelCase__      :		List[Any]    							=      []
						lowerCAmelCase__      :		int    							=      []
						lowerCAmelCase__      :		List[Any]    							=      list(self.graph						)[0]
						stack.append(lowercase_						)
						visited.append(lowercase_						)
						lowerCAmelCase__      :		Optional[int]    							=      -2
						lowerCAmelCase__      :		List[str]    							=      []
						lowerCAmelCase__      :		Tuple    							=      s
						lowerCAmelCase__      :		Tuple    							=      False
						lowerCAmelCase__      :		Union[str, Any]    							=      set()

						while True:
							# check if there is any non isolated nodes
							if len(self.graph[s]						) != 0:
								lowerCAmelCase__      :		Union[str, Any]    							=      s
								for node in self.graph[s]:
									if (
									    visited.count(node[1]						) > 0
									    and node[1] != parent
									    and indirect_parents.count(node[1]						) > 0
									    and not on_the_way_back
									):
										lowerCAmelCase__      :		Tuple    							=      len(lowercase_						) - 1
										while len_stack >= 0:
											if stack[len_stack] == node[1]:
												anticipating_nodes.add(node[1]						)
												break
											else:
												anticipating_nodes.add(stack[len_stack]						)
												len_stack -= 1
									if visited.count(node[1]						) < 1:
										stack.append(node[1]						)
										visited.append(node[1]						)
										lowerCAmelCase__      :		Optional[int]    							=      node[1]
										break

            # check if all the children are visited
							if s == ss:
								stack.pop()
								lowerCAmelCase__      :		Optional[int]    							=      True
								if len(lowercase_						) != 0:
									lowerCAmelCase__      :		str    							=      stack[len(lowercase_						) - 1]
							else:
								lowerCAmelCase__      :		Tuple    							=      False
								indirect_parents.append(lowercase_						)
								lowerCAmelCase__      :		Optional[int]    							=      s
								lowerCAmelCase__      :		Optional[int]    							=      ss

							# check if se have reached the starting point
							if len(lowercase_						) == 0:
								return list(lowercase_						)







					def 			__lowerCAmelCase					(			self     :							Optional[Any]						):
						lowerCAmelCase__      :		Optional[Any]    							=      []
						lowerCAmelCase__      :		Union[str, Any]    							=      []
						lowerCAmelCase__      :		Tuple    							=      list(self.graph						)[0]
						stack.append(lowercase_						)
						visited.append(lowercase_						)
						lowerCAmelCase__      :		Dict    							=      -2
						lowerCAmelCase__      :		Union[str, Any]    							=      []
						lowerCAmelCase__      :		Optional[Any]    							=      s
						lowerCAmelCase__      :		Any    							=      False
						lowerCAmelCase__      :		Optional[int]    							=      set()

						while True:
							# check if there is any non isolated nodes
							if len(self.graph[s]						) != 0:
								lowerCAmelCase__      :		str    							=      s
								for node in self.graph[s]:
									if (
									    visited.count(node[1]						) > 0
									    and node[1] != parent
									    and indirect_parents.count(node[1]						) > 0
									    and not on_the_way_back
									):
										lowerCAmelCase__      :		str    							=      len(lowercase_						) - 1
										while len_stack_minus_one >= 0:
											if stack[len_stack_minus_one] == node[1]:
												anticipating_nodes.add(node[1]						)
												break
											else:
												return True
									if visited.count(node[1]						) < 1:
										stack.append(node[1]						)
										visited.append(node[1]						)
										lowerCAmelCase__      :		List[str]    							=      node[1]
										break

            # check if all the children are visited
							if s == ss:
								stack.pop()
								lowerCAmelCase__      :		List[Any]    							=      True
								if len(lowercase_						) != 0:
									lowerCAmelCase__      :		List[str]    							=      stack[len(lowercase_						) - 1]
							else:
								lowerCAmelCase__      :		List[str]    							=      False
								indirect_parents.append(lowercase_						)
								lowerCAmelCase__      :		Optional[int]    							=      s
								lowerCAmelCase__      :		List[Any]    							=      ss

							# check if se have reached the starting point
							if len(lowercase_						) == 0:
								return False







					def 			__lowerCAmelCase					(			self     :							str						):
						return list(self.graph						)







					def 			__lowerCAmelCase					(			self     :							Any  ,lowercase_     :							Optional[int]=-2  ,lowercase_     :							Any=-1						):
						lowerCAmelCase__      :		Dict    							=      time()
						self.dfs(lowercase_  ,lowercase_						)
						lowerCAmelCase__      :		List[str]    							=      time()
						return end - begin







					def 			__lowerCAmelCase					(			self     :							Union[str, Any]  ,lowercase_     :							int=-2						):
						lowerCAmelCase__      :		Dict    							=      time()
						self.bfs(lowercase_						)
						lowerCAmelCase__      :		Any    							=      time()
						return end - begin




