# The Triangle

Description

The figure shows a number triangle. Write a program that calculates the highest sum of numbers 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.

Input

Your program is to read from standard input. There are multiple test cases.

For each case, the first line contains an integer N: the number of rows in the triangle. The following N lines describe the data of the triangle. The number of rows in the triangle is > 1 but ≤ 100. The numbers in the triangle, all integers, are between 0 and 99.

For each case, the first line contains an integer N: the number of rows in the triangle. The following N lines describe the data of the triangle. The number of rows in the triangle is > 1 but ≤ 100. The numbers in the triangle, all integers, are between 0 and 99.

Output

Your program is to write to standard output. For each test case, output the highest sum seperated by line break.

Sample Input

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

Sample Output

10 30

Source

Editor

keefo on 2013-12-04 07:24:42