"""simple docstring"""


import numpy






class    a__    :


   def __init__(     self,				_UpperCAmelCase,				_UpperCAmelCase  ):
        '''simple docstring'''



        lowercase__				 =							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__				 =							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__				 =							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__				 =							numpy.random.rand(3,				1  )

        # Real output values provided.
        lowercase__				 =							output_array

        # Predicted output values by the neural network.
        # Predicted_output array initially consists of zeroes.
        lowercase__				 =							numpy.zeros(output_array.shape  )


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        lowercase__				 =							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__				 =							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__				 =							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  ):
        '''simple docstring'''



        lowercase__				 =							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__				 =							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__				 =							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,				_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase  ):
        '''simple docstring'''



        for iteration in range(1,				iterations + 1  ):
             lowercase__				 =							self.feedforward()
             self.back_propagation()
             if give_loss:
                  lowercase__				 =							numpy.mean(numpy.square(output - self.feedforward()  )  )
                  print(F'''Iteration {iteration} Loss: {loss}'''  )


   def 	snake_case__	(     self,				_UpperCAmelCase  ):
        '''simple docstring'''



        lowercase__				 =							input_arr

        lowercase__				 =							sigmoid(
            numpy.dot(self.array,				self.input_layer_and_first_hidden_layer_weights  )  )

        lowercase__				 =							sigmoid(
            numpy.dot(
                self.layer_between_input_and_first_hidden_layer,				self.first_hidden_layer_and_second_hidden_layer_weights,				)  )

        lowercase__				 =							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 					__a   (		A      ):






     '''simple docstring'''



     return 1 / (1 + numpy.exp(-value      ))







def 					__a   (		A      ):






     '''simple docstring'''



     return (value) * (1 - (value))







def 					__a   (		):






     '''simple docstring'''



     lowercase__				 =							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__				 =							numpy.array(([0], [1], [1], [0], [1], [0], [0], [1])    ,				dtype=numpy.floataa      )

     # Calling neural network class.
     lowercase__				 =							TwoHiddenLayerNeuralNetwork(
         input_array=__SCREAMING_SNAKE_CASE    ,				output_array=__SCREAMING_SNAKE_CASE      )

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

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


if __name__ == "__main__":
 example()
"""simple docstring"""


import itertools
import math







def 					__a   (		A      ):






     '''simple docstring'''



     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5    ,				int(math.sqrt(A      ) + 1      )    ,				6      ):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True







def 					__a   (		):






     '''simple docstring'''



     lowercase__				 =							2
     while True:
          if is_prime(A      ):
               yield num
          num += 1







def 					__a   (		A = 1_00_01      ):






     '''simple docstring'''



     return next(itertools.islice(prime_generator()    ,				nth - 1    ,				A      )      )


if __name__ == "__main__":
 print(F'{solution() = }')




