Cow Bowling
Description
The cows don't use actual bowling balls when
they go bowling. They each take a number (in the range 0..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
The first line contains an integer giving the number of test cases. For each test case, the first line gives a single integer, N, and for 2 <= i <= N+1, line i+1 of the test case contains i space-separated integers that represent row i
of the triangle.
Output
For each test case, your output should give one line of output containing the largest sum achievable using the
traversal rules
Sample Input
1
5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5
Sample Output
30
Hint
Explanation of the sample:
7
*
3 8
*
8 1 0
*
2 7 4 4
*
4 5 2 6 5
The highest score is achievable by traversing
the cows as shown above.
Source
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