Number triangle opening

A few of my colleagues discussed a topic a few days ago as an example of dynamic planning. I think it is quite classic. Record it.

The general consistency is as follows:

A digital triangle, for example, has multiple paths from the top to the bottom. For each path, add the numbers in the path to get the maximum path of a sum and sum, is an optimal path. Find the optimal path.

5

4 5

4 5 9

9 8 4 8

9 0 7 4 8

0 9 2 4 5 8

Requirements:

Each step of the path can only go from a number to the number on the left or right of the next layer and closest to it.

Input: the first line is an integer N (1 <n <100). The number of rows in the triangle is displayed, and the number triangle is displayed after driving. The number ranges from 0 ~ In the range of 100.

Output: Maximum Sum.