5. Every morning, Clarke has to walk from Lexa’s home to her work in Arkadia, and every evening, she walks back. Clarke owns 4 gas masks to protect her from acid fog. Each time she leaves a location, there is an independent probability p that it is currently foggy. If it is foggy when she leaves a location, she will take a gas mask with her to the next location, as long as there is at least one to take. If it isn’t foggy, then she never takes a gas mask with her. (Clarke can be pretty dumb sometimes.) Give a TPM for this problem, where the states are the number of gas masks at the location she is about to leave. (Hint: the location she leaves from changes each time she makes a commute.) (15pt)