# Number Triangles

Time Limit: 1000 ms

Memory Limit: 65535 ms

## Description

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.

## Input

There are several test cases, end by EOF, for each test case:
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.

## Output

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

## Sample Input

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

## Sample Output

30

## Source

USACO SECTION 1.5