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 functools import reduce
import os
import sys
from math import *
from collections import *
from fractions import *
from bisect import *
from heapq import*
from io import BytesIO, IOBase

input = lambda: sys.stdin.readline().rstrip("\r\n")
def value():return tuple(map(int,input().split()))
def arr():return [int(i) for i in input().split()]
def sarr():return [int(i) for i in input()]
def inn():return int(input())
mo=1000000007
#----------------------------CODE------------------------------#
for _ in range(int(input())):
    n=inn()
    a=arr()
    d=defaultdict(int)
    ans=[]
    for i in a:
        d[i]+=1
    for i in range(n):
        res=a[i]
        for j in range(a[i]+1,2*n+1):
            if(j not in d):
                ans+=[(res,j)]
                d[j]+=1
                break
    flag=0
    for i in range(1,2*n+1):
        if(i not in d):
            flag=1
            break
    if(flag==1):
        print(-1)
    else:
        for i in range(n):
            print(ans[i][0],ans[i][1],end=" ")
        print()