Project Euler #67: Maximum path sum II

_{This problem is a programming version of Problem 67 from projecteuler.net}

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is . The path is denoted by numbers in bold.

That is, .

Find the maximum total from top to bottom of the triangle given in input.

Input Format

First line contains , the number of testcases. For each testcase:
First line contains , the number of rows in the triangle.
For next lines, 'th line contains numbers.

Constraints

Each element of triangle lies between and (both inclusive).

Output Format

Print the required answer for each testcase on a new line.

Sample Input

Sample Output

23
23