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())
for test in range(t):
    n = int(input())
    b = [int(i) for i in input().split()]
    def solve():
        def minimal(v):
            for i in perm:
                if i > v:
                    return perm.pop(perm.index(i))
            return v
        perm = list(range(1, n * 2 + 1))
        for i in range(n * 2 - 1, -1, -1):
            if perm[i] in b:
                del perm[i]
        msg = ""
        for v in b:
            msg += str(v) + " "
            iplus = minimal(v)
            if iplus > v:
                msg += str(iplus) + " "
            else:
                return "-1"
        return msg
    print(solve())