Consider the Job Selection problem from lecture. You will modify the solution to this problem to work for a related problem. In lecture we had the rule that if you work one day you can’t work the next (or previous). In the modified problem you are allowed to work two days in a row but not three days in a row (so if you work 2 days in a row you can’t work the day before these 2 days or the day after). 1. Express the modified problem formally with input and output conditions. 2. State a self-reduction for your problem. Use the self-reduction from lecture as inspiration. 3. State a dynamic programming algorithm based off of your self reduction that computes the maximum earnings. 4. Design a function that recovers the days that must be worked to achieve the maximum earnings. 5. Compute the maximum earnings and the days to work for this input P=[5, 9, 12, 7, 5, 13, 7, 5, 4, 9, 8, 7, 5, 8, 4, 3, 5, 10, 4, 6, 8, 12, 5, 6, 3, 7, 16, 2, 2, 16] 6. What are the worst case time and space requirements of your complete solution?