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

Time Limit: 1 Sec Memory Limit: 128 MB

Submit: 5 Solved: 3

[Submit][Status][Web Board]## 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

[Submit][Status]