Description:
A sequence of $$$n$$$ numbers is called permutation if it contains all numbers from $$$1$$$ to $$$n$$$ exactly once. For example, the sequences [$$$3, 1, 4, 2$$$], [$$$1$$$] and [$$$2,1$$$] are permutations, but [$$$1,2,1$$$], [$$$0,1$$$] and [$$$1,3,4$$$] — are not.
For a permutation $$$p$$$ of even length $$$n$$$ you can make an array $$$b$$$ of length $$$\frac{n}{2}$$$ such that:
- $$$b_i = \max(p_{2i - 1}, p_{2i})$$$ for $$$1 \le i \le \frac{n}{2}$$$
For example, if $$$p$$$ = [$$$2, 4, 3, 1, 5, 6$$$], then:
- $$$b_1 = \max(p_1, p_2) = \max(2, 4) = 4$$$
- $$$b_2 = \max(p_3, p_4) = \max(3,1)=3$$$
- $$$b_3 = \max(p_5, p_6) = \max(5,6) = 6$$$
For a given array $$$b$$$, find the lexicographically minimal permutation $$$p$$$ such that you can make the given array $$$b$$$ from it.
If $$$b$$$ = [$$$4,3,6$$$], then the lexicographically minimal permutation from which it can be made is $$$p$$$ = [$$$1,4,2,3,5,6$$$], since:
- $$$b_1 = \max(p_1, p_2) = \max(1, 4) = 4$$$
- $$$b_2 = \max(p_3, p_4) = \max(2, 3) = 3$$$
- $$$b_3 = \max(p_5, p_6) = \max(5, 6) = 6$$$
A permutation $$$x_1, x_2, \dots, x_n$$$ is lexicographically smaller than a permutation $$$y_1, y_2 \dots, y_n$$$ if and only if there exists such $$$i$$$ ($$$1 \le i \le n$$$) that $$$x_1=y_1, x_2=y_2, \dots, x_{i-1}=y_{i-1}$$$ and $$$x_i<y_i$$$.
Input Format:
The first line of input data contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.
The description of the test cases follows.
The first line of each test case contains one even integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$).
The second line of each test case contains exactly $$$\frac{n}{2}$$$ integers $$$b_i$$$ ($$$1 \le b_i \le n$$$) — elements of array $$$b$$$.
It is guaranteed that the sum of $$$n$$$ values over all test cases does not exceed $$$2 \cdot 10^5$$$.
Output Format:
For each test case, print on a separate line:
- lexicographically minimal permutation $$$p$$$ such that you can make an array $$$b$$$ from it;
- or a number -1 if the permutation you are looking for does not exist.
Note:
The first test case is parsed in the problem statement.