4. Let us stack 1000 identical cubes to form a 10x10x10 array. Two cubes are called neighbors of each other if they share a face in common. In Step 1 we will label the bottom-south-west cube with a 1. In Step 2 we will label each of the three cubes that are neighbors of the cube in Step 1 with the sum of the labels of its neighbors from Step 1. (Therefore, each cube in Step 2 is also labeled 1.) In Step 3 we label each of the unlabeled cubes with the sum of the labels of its neighbors that were already labelled in Steps 1 or 2. We continue this way in steps, where in Step k we label each of the unlabeled cubes with the sum of the labels of its neighbors that were already labelled in Steps 1 through k-1. This is done until all of the cubes are labelled. (a) How many steps are needed to label all of the cubes? (b) What is the label of the top-north-east unit cube?