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

Their are more than one cases. Each case like follows. The first line contains R (1 <= R <= 1000),R=0 means the end, 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

Output

30