Consider the number triangle shown below. Write a program that calculates the highest sum

of numbers that can be passed on a route that starts at the top and ends somewhere on

the base. Each step can go either diagonally down to the left or diagonally down to the right.

          7

        3   8

      8   1   0

    2   7   4   4

  4   5   2   6   5

In the sample above, the route from 7 to 3 to 8 to 7 to 5 produces the highest sum: 30.

The first line contains R (1 <= R <= 1000), the number of rows. Each subsequent line contains the

integers for that particular row of the triangle. All the supplied integers are non-negative and

no larger than 100.

A single line containing the largest sum using the traversal specified.