C. Optimal Pairing
time limit per test
1 second
memory limit per test
512 megabytes
input
standard input
output
standard output

You're given an array $$$a_1, a_2, \dots, a_n$$$. You need to pair the elements of the array with each other into $$$\frac{n}{2}$$$ pairs. The length of the array $$$n$$$ is an even number.

The cost of a pair $$$(a_i, a_j)$$$ is $$$\max(a_i, a_j)$$$. You need to find the minimum possible sum of costs of the $$$\frac{n}{2}$$$ pairs, over all the possible ways to pair the elements with each other.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ $$$\left(1 \leq n \leq 10^5\right)$$$ — the length of the array.

The second line of each test case contains $$$n$$$ integers $$$a_i$$$ $$$(1 \leq a_i \leq 10^9)$$$ — the array.

It is guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$10^5$$$.

Output

For each test case, output the minimum possible sum of costs of the $$$\frac{n}{2}$$$ pairs in an optimal pairing.

Example
Input
1
8
7 4 3 2 1 5 8 6
Output
20