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())
solutions = []
for i in range(t) :
    n = int(input())
    string = str(input())
    st = string.split()
    lst = []
    for j in range(n) :
        lst.append(int(st[j]))
    solution = []
    for j in range(n) :
        solution.append(lst[j])
        number = lst[j]
        ok = 0
        while ok == 0 and number < 2*n :
            number= number +1
            if number not in solution and number not in lst :
                ok =1
        if ok == 1 :
            solution.append(number)
    if len(solution) == 2*n :
        solutions.append(solution)
    else :
        solutions.append([-1])
for i in range(t) :
    for number in solutions[i] :
        print(number, end=" ")
    print()