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:

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