Number Triangles

Input file: triangle.in
Output file: triangle.out

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.

It is promised that each number in the triangle is an integer between 0 and 99 inclusive.

The first line in triangle.in contains R (1 <= R <= 100), the number of rows. Each subsequent line contains the integers for that particular row of the triangle. The sample input describes triangle from the example above.

Write a single line to triangle.out with the greatest possible sum that can be obtained following the rules of the problem.

Sample Input

5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5

Sample Output

30
Taken from USA Computing Olympiad 1999, Fall Open Gold