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:
t = int(input())
b_all = list()
for i in range(t):
    n = int(input())
    b_str = input().split(' ')
    b_all.append([int(r) for r in b_str])
results = list()

for b in b_all:
    n = len(b)
    used = [False] * (2*n+1)
    in_res = [False] * (2*n+1)
    bad_seq = False
    for num in b:
        if num > 2*n:
            bad_seq = True
            break
        used[num] = True

    if bad_seq:
        print('-1')
        continue

    res = []
    for j in b:
        res.append(str(j))
        in_res[j] = True
        try:
            false_index = used.index(False, j)
            res.append(str(false_index))
            in_res[false_index] = True
            used[false_index] = True
        except ValueError:
            res = ['-1']
            break
    print(' '.join(res))