P1216 [IOI 1994 / USACO1.5] Number Triangles

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.  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 $R$ ($1 \le R \le 1000$), 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.

IOI 1994 Day 1 T1 / USACO Training Section 1.5.