Optimal Strategy for a Coin Game

You are playing a coin game with your friend Ninjax. There are N coins placed in a straight line.

Here are the rules of the game:

1. Each coin has a value associated with it.
 2. The game involves two players taking alternate turns.
 3. On your turn, you may choose a coin from either end of the line and remove it.
 4. The value of the coin you remove is added to your total winnings.

Ninjax, being a good friend, lets you begin the game. Determine the maximum amount you can accumulate in the game if both you and Ninjax play optimally.

Input:

The first line contains an integer T, the number of test cases.
Each test case begins with an integer N (always even), the number of coins.
The second line consists of N space-separated integers representing the values of the coins.

Output:

For each test case, output the maximum amount you can definitely win.

Example:

Input:

2
4
9 5 21 7
4
20 50 5 10

Output:

30
60

Explanation:

In the first test case, choosing optimally yields you a total of 30.
In the second test case, choosing optimally yields you a total of 60.

Constraints:

• 1 <= T <= 10
• 2 <= N <= 103
• 0 <= VALUE <= 105

Note: You do not need to handle input or output directly. Implement the solution logic only.