input: Write a function to design and implement a neural network in Python using Keras to predict the price of a house given a set of features. The function should take an input array of features, train the model, and return the trained model. The model should have an input layer with 3 nodes, two hidden layers with 64 and 32 nodes respectively, and an output layer with a single node. The model should use the 'relu' activation function for the hidden layers and 'linear' activation function for the output layer. The model should be compiled with the 'mse' loss function and the 'adam' optimizer.
  
  assert predict_house_price([0.8, 0.4, 0.7])
  assert predict_house_price([0.9, 0.3, 0.6])
  assert predict_house_price([0.7, 0.5, 0.8])
  assert predict_house_price([0.6, 0.4, 0.5])
  assert predict_house_price([0.5, 0.3, 0.4])
output: 
  def predict_house_price(features):
      from keras.models import Sequential
      from keras.layers import Dense
      
      model = Sequential()
      model.add(Dense(64, input_dim=3, activation='relu'))
      model.add(Dense(32, activation='relu'))
      model.add(Dense(1, activation='linear'))
      
      model.compile(loss='mse', optimizer='adam')
      
      return model
  