Fredo has an array A consisting of N elements. He wants to divide the array into $N/2$ pairs where each array element comes in exactly one pair. Say that pair i has elements $X_i$ and $Y_i$, he defines S as :

$S = \sum_{i=1}^{N/2} abs(X_i-Y_i)$

He asks you to find the minimum and maximum value of S.

Input Format:

First line consists of an integer T denoting the number of test cases.
Each test case:
First line consists of an integer N denoting the number of elements in the array.
Second line consists of N space separated integers denoting the array elements.

Output Format:
For each test case, print the minimum and maximum sum (space separated). Answer for each test case should come in a new line.

Input Constraints:

$1 \le T \le 10$
$1 \le N \le 10^5$
$-10^9 \le A[i] \le 10^9$
$N \ is \ even$