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:
'''
5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8
'''

class NotFoundError(Exception):
    def __str__(self):
        return "Lexicograohic sequence nnot found"

def returnNumber(bFinal, a, index):
    for i in range(len(a)):
        # print(a[i], bFinal[index])
        if a[i] > bFinal[index] and a[i] not in bFinal:
            return a[i]
    
    raise NotFoundError()


testCases = int(input())
for t in range(testCases):
    n = int(input())
    b = list(map(int, input().rstrip().split()))

    a = [i for i in range(1, 2*n + 1)]

    bFinal = [None]*2*n

    for i in range(len(b)):
        bFinal[2*i] = b[i]

    for i in b:
        if i in a:
            a.pop(a.index(i))
    
    # print(b)
    # print(a)
    # print(bFinal)

    for i in range(n):
        try:
            bFinal[2*i + 1] = returnNumber(bFinal, a, 2*i)
            # print("bFinal[2*i + 1]= ", bFinal[2*i + 1])
            
        except NotFoundError as e:
            # print(e)
            bFinal = -1
            break
        # print(bFinal)

    if type(bFinal) is list:
        s = ''
        for m in range(len(bFinal)):
            if m == len(bFinal) - 1:
                s = s + str(bFinal[m])
            else:
                s = s + str(bFinal[m]) + ' '
        print(s) 
    else:
        print(-1)