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:
import sys
import collections
input = sys.stdin.readline


def main():
    t = int(input())
    for _ in range(t):
        N = int(input())
        B = [int(x) for x in input().split()]
        c = collections.Counter()

        ans = []
        for b in B:
            if c[b] > 0:
                print(-1)
                break
            ans.append(b)
            c[b] += 1
            i = 1
            while c[b + i] != 0 or b + i in B:
                i += 1
            ans.append(b + i)
            c[b + i] += 1
        else:
            for i in range(1, 2 * N + 1):
                if c[i] == 0:
                    print(-1)
                    break
            else:
                print(*ans)

        
        
    

if __name__ == '__main__':
    main()