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C. Restoring Permutation

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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