Migrated from Lutece 186 Number Triangles

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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

The first line contains $R$ ($1\leq R\leq 1000$), 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.

Samples

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

30

Resources

USACO TRAINING selected by rectaflex