input: Write a python function to build and train a neural network using Keras.
  assert build_and_train_model([[1, 3], [1, 4], [2, 4], [3, 1], [4, 1], [4, 2]], [[1], [1], [2], [3], [3], [2]], [[5, 2], [4, 3]]) == [2, 2]
output: def build_and_train_model(X_train, y_train, X_test):
      from keras.models import Sequential
      from keras.layers import Dense
      import numpy as np
  
      # Define the model
      model = Sequential()
      model.add(Dense(10, input_dim=2, activation='relu'))
      model.add(Dense(1))
  
      # Compile the model
      model.compile(optimizer='adam', loss='mean_squared_error')
  
      # Train the model
      model.fit(np.array(X_train), np.array(y_train), epochs=100, verbose=0)
  
      # Make predictions
      predictions = model.predict(np.array(X_test))
  
      # Convert predictions to integers
      return [int(round(pred[0])) for pred in predictions]