C. Restoring Permutation
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a sequence $b_1, b_2, \ldots, b_n$. Find the lexicographically minimal permutation $a_1, a_2, \ldots, a_{2n}$ such that $b_i = \min(a_{2i-1}, a_{2i})$, or determine that it is impossible.

Input

Each test contains one or more test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$).

The first line of each test case consists of one integer $n$ — the number of elements in the sequence $b$ ($1 \le n \le 100$).

The second line of each test case consists of $n$ different integers $b_1, \ldots, b_n$ — elements of the sequence $b$ ($1 \le b_i \le 2n$).

It is guaranteed that the sum of $n$ by all test cases doesn't exceed $100$.

Output

For each test case, if there is no appropriate permutation, print one number $-1$.

Otherwise, print $2n$ integers $a_1, \ldots, a_{2n}$ — required lexicographically minimal permutation of numbers from $1$ to $2n$.

Example
Input
5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8

Output
1 2
-1
4 5 1 2 3 6
-1
1 3 5 6 7 9 2 4 8 10