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 math import *
# from sys import stdin,stdout

def binarySearch(arr,x,i):
	l=i
	r=len(arr)-1 
	while l <= r: 
		mid = (l + r)//2; 
		if arr[mid] == x: 
			return mid 
		elif arr[mid] < x: 
			l = mid + 1
		else: 
			r = mid - 1
	return -1

def js(arr,x):
	l=0
	r=len(arr)-1
	ans=-1
	while(l<=r):
		m=(l+r)//2
		if(arr[m]<=x):
			ans=m
			l=m+1
		else:
			r=m-1
	return ans

def jg(arr,x):
	l=0
	r=len(arr)-1
	ans=-1
	while(l<=r):
		m=(l+r)//2
		if(arr[m]>=x):
			ans=m
			r=m-1
		else:
			l=m+1
	return ans

def ceil(a,b):
	if a%b == 0:
		return int(a/b)
	else:
		return (a//b + 1)


def c(s,i,a,b):
	count=0
	for j in range(i,len(s)):
		if(s[i]!=s[j]):
			if(s[i]=="A"):
				count+=a
			else:
				count+=b
			i=j
	if(i<len(s)-1):
		if(s[i]=="A"):
			count+=a
		else:
			count+=b
	return count

for __ in range(int(input())):
	n=int(input())
	ar=list(map(int,input().split()))
	h=[0]*(2*n + 1)
	ans=[0]*(2*n +1)
	for i in range(n):
		h[ar[i]]=1
	for i in range(n):
		ans[2*(i+1)-1]=ar[i]
		f=-1
		for j in range(ar[i],2*n+1):
			if(h[j]==0):
				f=j
				h[j]=1
				break
		if(f==-1):
			break
		else:
			ans[2*(i+1)]=j
	if(f==-1):
		print(-1)
		# print(*ans[1:])
	else:
		print(*ans[1:])