Problem: 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 

Solution (in PYTHON3):

Solution:

def solve(num, n):
    res = [None] * (2 * n)
    for i, x in enumerate(num):
        res[i*2] = x

    # use back tracking to fill in x
    used = set(num)

    for i in range(len(num)):
        for x in range(num[i] +1, 2*n + 1):
            if x not in used:
                used.add(x)
                res[2*i + 1] = x
                break

    return ' '.join([str(x) for x in res]) if None not in res else -1


n = int(input())
for _ in range(n):
    l = int(input())
    num = list(map(int, input().split()))
    print(solve(num, l))