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:
from sys import stdin, gettrace

if not gettrace():
    def input():
        return next(stdin)[:-1]


def main():
    def solve():

        n = int(input())
        bb = [int(a) for a in input().split()]
        avail = [False] + [True] * 2 * n
        for b in bb:
            avail[b] = False
        res = []
        for b in bb:
            if b == n*2:
                print(-1)
                return
            res.append(b)
            c = b+1
            while not avail[c]:
                c+=1
                if c == 2*n+1:
                    print(-1)
                    return
            res.append(c)
            avail[c] = False
        print(' '.join(map(str, res)))

    q = int(input())
    for _ in range(q):
        solve()


if __name__ == "__main__":
    main()