PROBLEM 1 (35 points). NASA's Perseverance Rover has just landed on Mars! You are the scientist now in charge of navigating the rover as it visits locations on the Martian surface to perform experiments. The region that the rover has landed in is modeled as a topographical map represented by an N x N grid. For each point (i,j), there is an associated height hij > 0 and scientific value vi,j for visiting the location. Because we want the rover to run as long as possible, you are also required to conserve energy during navigation and are subsequently forbidden from moving the rover uphill. The Rover's movements can thus be summarized as follows. The rover starts at position (^,^) and is allowed to navigate from positions (i,j) to (i',j') where i' = i +1 and j' =j+1 provided that hij