JSB has an integer sequence . He wants to play a game with SHB. 

For each , JSB calculates the median of , denoted by . SHB is given the sequence . Can you help him restore the sequence ?

Recall that the median of three numbers is the second largest one of them.

输入描述:

There are multiple cases. The first line of the input contains a single positive integer , indicating the number of cases.

For each case, the first line of the input contains a single integer , the length of the sequence . The second line contains integers .

It's guaranteed that the sum of  over all cases does not exceed .

输出描述:

For each case print one line containing  integers, indicating the sequence . Your output must satisfy  for each .

If there are multiple valid answers, you may print any of them. If there is no valid answer, print"-1" (without quotes) instead.

4
5
1 2 3
6
1 2 3 4
6
1 2 4 3
6
1 3 4 2

1 1 3 2 3
1 2 1 4 3 4
1 1 4 2 4 3
-1