Problem 1996. -- Cow Bowling [IOI, 1994]

1996: Cow Bowling [IOI, 1994]

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 5  Solved: 3
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Description

The cows don't use actual bowling balls when they go bowling.  They
each take a number (in the range 1..99), though, and line up in a
standard bowling-pin-like triangle like this:

          7

        3   8

      8   1   0

    2   7   4   4

  4   5   2   6   5

Then the other cows traverse the triangle starting from its tip and
moving "down" to one of the two diagonally adjacent cows until the
"bottom" row is reached.  The cow's score is the sum of the numbers
of the cows visited along the way. The cow with the highest score
wins that frame.

Given a triangle with N (1 <= N <= 350) rows, determine the highest
possible sum achievable.

Input

* Line 1: A single integer, N
* Lines 2..N+1: Line i+1 contains i space-separated integers that
        represent row i of the triangle.

Output

* Line 1: The largest sum achievable using the traversal rules

Sample Input

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

Sample Output

30

HINT

Source

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