# 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