Q(1) Given a rope of length n meters, cut the rope in different parts of integer lengths in a way that maximizes product of lengths of all parts. You must make at least one cut. Assume that the length of rope is more than 2 meters. Examples: Input: rope length is 4 (n-4) Output: 2*2 4 (Maximum obtainable product is 2*2) (n -5) Input: rope length is5 Output: 2*3 (Maximum obtainable product is 2*3) Input: rope length is 10 (n 10) Output: 3*3*4 -36 (Maximum obtainable product is 3*3*4) a) Design the recursive sub-problem condition(s) Use your solution in (a) to solve the problem of a rope length input equals 10 (n-10). You have to show the complete solution of the DP steps either by top down or bottom-up approach b) c) What is the running time of your algorithm? Note: your solution must not run in exponential time