IOI'94 - Day 1 - Problem 1: The Triangle

            7
          3   8
        8   1   0
      2   7   4   4
    4   5   2   6   5   (Figure 1)

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Figure 1 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 >1 but <=100.
  
• The numbers in the triangle, all integers, are between 0 and 99.

Input Data

Data about the number of rows in the triangle are first read
from the INPUT.TXT file. In our example, INPUT.TXT appears
as follows:

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

Output Data

The highest sum is written as an integer in the
OUTPUT.TXT file. In our example:

30