J. Jackpot
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an integer array $$$a$$$ of $$$2n$$$ integers. In one operation, you can do the following:

  • Choose any two adjacent elements in the array, let's say, $$$a_i$$$ and $$$a_{i+1}$$$. Then, delete them, and add $$$|a_i - a_{i+1}|$$$ to your score.

    Note that the indices are recalculated after the operation.

You are going to perform this operation $$$n$$$ times, deleting all the elements in the end. What is the largest score you can get?

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^5$$$)  — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 2\cdot 10^5$$$).

The second line of each test case contains $$$2n$$$ integers $$$a_1, a_2, \ldots, a_{2n}$$$ ($$$0 \leq a_i \leq 10^9$$$)  — elements of the array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.

Output

For each test case, output a single integer  — the largest possible score you can get after performing the operation $$$n$$$ times.

Example
Input
3
2
42 42 42 42
1
42 69
3
1 2 3 4 5 6
Output
0
27
9
Note

In the first test case, we can choose the first two elements, and delete them, getting score of $$$0$$$, and then choose the remaining two elements, delete them, getting score of $$$0$$$ again.

In the second test case, the only possible operation is to choose both elements and to get score of $$$|42-69| = 27$$$.

In the third test case, we can do the following sequence of operations:

  1. Choose elements $$$3, 4$$$. Delete them, and get a score of $$$1$$$. The array will become $$$[1, 2, 5, 6]$$$.
  2. Choose elements $$$2, 5$$$. Delete them, and get a score of $$$3$$$. The array will become $$$[1, 6]$$$.
  3. Choose elements $$$1, 6$$$. Delete them, and get score of $$$5$$$. The total score is $$$1+3+5 =9$$$.