from collections import defaultdict





def  _lowerCamelCase					(   a_				: int):
			lowerCamelCase						:str						  =     1
			lowerCamelCase						:Dict						  =     True
			for v in tree[start]:
						if v not in visited:
									ret += dfs(a_)
			if ret % 2 == 0:
						cuts.append(a_)
			return ret





def  _lowerCamelCase					(   ):
			dfs(1)


if __name__ == "__main__":
			A__      ,					A__           =							10, 9
			A__           =							defaultdict(list)
			A__           =							{}
			A__           =							[]
			A__           =							0
			A__           =							[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (10, 8)]
			for u, v in edges:
						tree[u].append(v)
						tree[v].append(u)
			even_tree()
			print(len(cuts) - 1)




import numpy
class   _lowerCAmelCase		:







							def __init__(				self     :    Dict	,					__snake_case     :    numpy.ndarray	,					__snake_case     :    numpy.ndarray		):
										lowerCamelCase						:Dict						  =     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.
										lowerCamelCase						:Dict						  =     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.
										lowerCamelCase						:Dict						  =     numpy.random.rand(
										    4	,					3		)

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

										# Real output values provided.
										lowerCamelCase						:Union[str, Any]						  =     output_array

										# Predicted output values by the neural network.
										# Predicted_output array initially consists of zeroes.
										lowerCamelCase						:List[str]						  =     numpy.zeros(output_array.shape		)







							def 				snake_case  (				self     :    Optional[int]		):
										lowerCamelCase						: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.
										lowerCamelCase						:Any						  =     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.
										lowerCamelCase						:Dict						  =     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 				snake_case  (				self     :    Any		):
										lowerCamelCase						:Union[str, 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		)	,					)
										lowerCamelCase						:Dict						  =     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		)	,					)
										lowerCamelCase						:int						  =     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 				snake_case  (				self     :    Dict	,					__snake_case     :    numpy.ndarray	,					__snake_case     :    int	,					__snake_case     :    bool		):
										for iteration in range(1	,					iterations + 1		):
													lowerCamelCase						:Union[str, Any]						  =     self.feedforward()
													self.back_propagation()
													if give_loss:
																lowerCamelCase						:Tuple						  =     numpy.mean(numpy.square(output - self.feedforward()		)		)
																print(F"Iteration {iteration} Loss: {loss}"		)







							def 				snake_case  (				self     :    Optional[int]	,					__snake_case     :    numpy.ndarray		):
										lowerCamelCase						:int						  =     input_arr

										lowerCamelCase						:Union[str, Any]						  =     sigmoid(
										    numpy.dot(self.array	,					self.input_layer_and_first_hidden_layer_weights		)		)

										lowerCamelCase						:Optional[Any]						  =     sigmoid(
										    numpy.dot(
										        self.layer_between_input_and_first_hidden_layer	,					self.first_hidden_layer_and_second_hidden_layer_weights	,					)		)

										lowerCamelCase						:Optional[int]						  =     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  _lowerCamelCase					(   a_				: numpy.ndarray):
			return 1 / (1 + numpy.exp(-value))





def  _lowerCamelCase					(   a_				: numpy.ndarray):
			return (value) * (1 - (value))





def  _lowerCamelCase					(   ):
			lowerCamelCase						:Optional[Any]						  =     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.
			lowerCamelCase						:int						  =     numpy.array(([0], [1], [1], [0], [1], [0], [0], [1])						,			dtype=numpy.floataa)

			# Calling neural network class.
			lowerCamelCase						:List[Any]						  =     TwoHiddenLayerNeuralNetwork(
			    input_array=a_						,			output_array=a_)

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

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


if __name__ == "__main__":
			example()



