Consider the following interference graph Let the number of available registers be 3, and let the spill costs be as follows: live range cost (a) (5 points) Give the order we'l color the graph using top-down coloring. (b) (5 points) Give the order we'll color the graph using bottom-up coloring. Use a table similar to what we used in class. Show your work. If you can choose more than one node at a given step, choose the one with the greatest cost. Note: bottom-up doesn't normally have a spill metric to break ties, but I'm adding one to make grading easier