IOI '94 P1 - The Triangle

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Points: 7 (partial)
Time limit: 0.6s
Memory limit: 16M

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

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 \le 100.
  • The numbers in the triangle, all integers, are between 0 and 99.

Input Specification

The first line of input will contain an integer N. The i^{th} of the next N lines will contain i space-separated integers, denoting the values of the triangle.

Output Specification

The highest sum as required by the problem statement.

Sample Input

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

Sample Output

30

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