input:                         
  def distinguish_cats_dogs_model() -> Sequential:
      """
      Create a machine learning model in Python using Keras that distinguishes between cats and dogs.
      The model consists of convolutional layers, max pooling layers, dropout layers, and fully connected layers.
      The model is compiled with binary cross-entropy loss and the Adam optimizer, and trained using an image data generator.
      
      >>> model = distinguish_cats_dogs_model()
      >>> model.summary()
      _________________________________________________________________
      Layer (type)                 Output Shape              Param #   
      =================================================================
      conv2d (Conv2D)              (None, 62, 62, 32)        896       
      _________________________________________________________________
      max_pooling2d (MaxPooling2D) (None, 31, 31, 32)        0         
      _________________________________________________________________
      dropout (Dropout)            (None, 31, 31, 32)        0         
      _________________________________________________________________
      conv2d_1 (Conv2D)            (None, 29, 29, 64)        18496     
      _________________________________________________________________
      max_pooling2d_1 (MaxPooling2 (None, 14, 14, 64)        0         
      _________________________________________________________________
      dropout_1 (Dropout)          (None, 14, 14, 64)        0         
      _________________________________________________________________
      conv2d_2 (Conv2D)            (None, 12, 12, 64)        36928     
      _________________________________________________________________
      max_pooling2d_2 (MaxPooling2 (None, 6, 6, 64)          0         
      _________________________________________________________________
      dropout_2 (Dropout)          (None, 6, 6, 64)          0         
      _________________________________________________________________
      flatten (Flatten)            (None, 2304)              0         
      _________________________________________________________________
      dense (Dense)                (None, 128)               295040    
      _________________________________________________________________
      dense_1 (Dense)              (None, 1)                 129       
      =================================================================
      Total params: 351,489
      Trainable params: 351,489
      Non-trainable params: 0
      _________________________________________________________________
      """
      import numpy as np
      import keras
      from keras.layers import Dense, Conv2D, MaxPooling2D, Dropout, Flatten
      from keras.models import Sequential
      from keras.preprocessing.image import ImageDataGenerator
  
      # Create the neural network model
      model = Sequential()
  
      # Input layer
      model.add(Conv2D(32, (3, 3), input_shape = (64, 64, 3), activation = 'relu'))
  
      # Hidden layers
      model.add(MaxPooling2D(pool_size = (2, 2)))
      model.add(Dropout(0.3))
      model.add(Conv2D(64, (3, 3), activation = 'relu'))
      model.add(MaxPooling2D(pool_size = (2, 2)))
      model.add(Dropout(0.3))
      model.add(Conv2D(64, (3, 3), activation = 'relu'))
      model.add(MaxPooling2D(pool_size = (2, 2)))
      model.add(Dropout(0.3))
  
      # Output layer
      model.add(Flatten())
      model.add(Dense(units = 128, activation = 'relu'))
      model.add(Dense(units = 1, activation = 'sigmoid'))
  
      # Compile the model
      model.compile(loss = 'binary_crossentropy', optimizer = 'adam', metrics = ['accuracy'])
  
      return model
output:     # Data augmentation and preprocessing
      train_datagen = ImageDataGenerator(rescale = 1./255, shear_range = 0.2, zoom_range = 0.2, horizontal_flip = True)
      test_datagen = ImageDataGenerator(rescale = 1./255)
  
      training_set = train_datagen.flow_from_directory('dataset/training_set', target_size = (64, 64), batch_size = 32, class_mode = 'binary')
      test_set = test_datagen.flow_from_directory('dataset/test_set', target_size = (64, 64), batch_size = 32, class_mode = 'binary')
  
      # Train the model
      model.fit_generator(training_set, steps_per_epoch = 8000, epochs = 25, validation_data = test_set, validation_steps = 2000)