You are given an array B of length 2N . You have an unknown array A which is sorted and contains distinct elements. You need to find out the array A. B contains all the medians of each prefix and suffix of the array A.

A median is the middle element in a sorted array . [1,2,3,4] has median 2 and [1,3,4] has 3 as median.

Determine whether B is a valid array of some array A. If yes find the array A else print -1.

------ Input Format ------

• The first line of input contains a single integer T denoting the number of test cases. The description of T test cases follows.
• The first line of each test case contains an integer N.
• The second line of each test case contains $2N space-separated integers B_{1}, B_{2}, \dots, B_{N}$.

------ Output Format ------

For each testcase, output the valid array A or -1 if not possible.

------ Constraints ------

$1 ≤ T ≤ 1000$
$1 ≤ N ≤ 10^{5}$
$1 ≤B_{i} ≤10^{6}$
- Sum of N overall testcases won't exceed $2*10^{5}$.

------ subtasks ------

100 points : Original Constraints

----- Sample Input 1 ------
2
3
6 5 5 7 6 6
3
1 2 1 4 2 4
----- Sample Output 1 ------
5 6 7
-1
----- explanation 1 ------
- Test case $1$: Assume the array $A$ be $[5,6,7]$. The medians of the prefix arrays of $A$ are
- $[5]$ = $5$
- $[5,6]$ = $5$
- $[5,6,7]$ = $6$

The medians of the suffix arrays of $A$ are
- $[7]$ = $7$
- $[6,7]$ = $6$
- $[5,6,7]$ = $6$

Hence $B$ contains all the medians above with the element $5$ repeating exactly $2$ times,
$6$ repeating exactly $3$ times and $7$ repeating only once.

• Test case $2$: no valid array $A$ can be found.

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