Figure 1 shows a number grid. The numbers are none negative integers. Design an algorithm that calculates the highest sum of numbers on a path from the top left node. Each step can go down or right to the next available node.

7 8 0 4 5

3 1 4 6

8 7 2

2 5

4

Your program should output the highest sum and the corresponding path.

In our example:

30

D D R D

where D and R represent edges going down and going right, respectively.