## #1563 BagsOfGold

47  1 s   128 MB

## Description

My partner and I have bags of gold, lined up in a row. The bags are different sizes. My partner has offered to split up the gold using the following system: we take turns, each time choosing one bag from either end of the line. She has even generously offered to let me go first -- hmmmmmmmm....
I need software to tell me the total amount of gold that I will get compared to how much my partner will get if I choose first. Of course we will assume that my partner and I are brilliant and always choose in the optimum way.

## Input

The first line of the input gives a number of test cases, T (1 <= T <= 200).
The first line of each case gives a number of bags, N (1 <= N <= 50).
Next line gives N integers, the number of gold in each bag, separated by space. The number of gold in each bag is not greater than 100,000.

## Output

﻿For each test case, output the number how much more gold I will get than my partner.

### Sample Output

2
2
7 2
3
2 7 3
5
-2