Problems

# The Triangle

# The Triangle

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.
- The number of rows in the triangle is greater than
**1**but less or equal**100**. - The numbers in the triangle, all integers, are between
**0**and**99**.

#### Input

First given the number of rows in triangle. Next rows describe the triangle itself.

#### Output

Print the maximum sum from top to the base of triangle.

Input example #1

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

Output example #1

30