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:
for namber in range(int(input())):
    tmp = input()
    data = list(map(int, input().split()))
    sortdat = sorted(data)
    if sortdat[0] == 1:
        maxlen = 2
        for i in range(1, len(data)):
            if sortdat[i] - sortdat[i - 1] > maxlen:
                print(-1)
                break
            elif sortdat[i] - sortdat[i - 1] == maxlen:
                maxlen = 2
            else:
                maxlen += 2 - sortdat[i] + sortdat[i - 1]
        else:
            out = [False] * (len(data) * 2)
            for j in data:
                out[j - 1] = True
            prn = ''
            for j in data:
                prn += str(j) + ' '
                tmp = j
                while out[tmp]:
                    tmp += 1
                prn += str(tmp + 1) + ' '
                out[tmp] = True
            print(prn)
    else:
        print(-1)