b$.$ Using Nadam optimization and early stopping, train the network on the CIFAR$10$ dataset. You can load it with keras.datasets.cifar$10.$load$\_$data$().$ The dataset is composed of $60,00032\backslash$times $32$pixel color images $(50,000$ for training, $10,000$ for testing$)$ with $10$ classes, so you'll need a softmax output layer with $10$ neurons. Remember to search for the right learning rate each time you change the model's architecture or hyperparameters.

c$.$ Now try adding Batch Normalization and compare the learning curves: Is it converging faster than before? Does it produce a better model? How does it affect training speed?