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