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 future import print_function,division
# range = xrange
import sys
input = sys.stdin.readline
from bisect import bisect_right
# sys.setrecursionlimit(10**9)
from sys import stdin, stdout

def main():
    for _ in range(int(input())):
        n = int(input())
        l = [int(s) for s in input().split()]
        tot = set(i+1 for i in range(2*n))
        re = sorted(tot - set(l))
        ans = [-1]*(2*n)
        flag = 0
        for i in range(n):
            ans[2*i] = l[i]
            w = bisect_right(re,l[i])
            if w==len(re):
                flag = 1
                break
            ans[2*i+1] = re[w]
            re.remove(re[w])
        if flag:
            print(-1)
        else:
            print(*ans)

if __name__== '__main__':
    main()