Number Triangle
TimeLimit:1000MS MemoryLimit:32MB
64-bit integer IO format:%I64d
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Problem Description
Consider the number triangle shown below. Write a program that calculates the highest sum of numbers that can be 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.
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In the sample above, the route from 7 to 3 to 8 to 7 to 5 produces the highest sum: 30.
Input
There are multiple test cases.The first line of each test case contains R (1 <= R <= 1000), the number of rows. Each subsequent line contains the integers for that particular row of the triangle. All the supplied integers are non-negative and no larger than 100.
Output
Print a single line containing the largest sum using the traversal specified for each test case.
SampleInput
5 7 3 8 8 1 0 2 7 4 4 4 5 2 6 5
SampleOutput
30