Restoring Permutation

You are given a sequence b_1, b_2, …, b_n. Find the lexicographically minimal permutation a_1, a_2, …, 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 ≤ t ≤ 100).

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

The second line of each test case consists of n different integers b_1, …, b_n — elements of the sequence b (1 ≤ b_i ≤ 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, …, 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

inputFormat

Input

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

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

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

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

outputFormat

Output

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

Otherwise, print 2n integers a_1, …, 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

样例

5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8

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

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