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:
for nt in range(int(input())):
	n=int(input())
	b=list(map(int,input().split()))
	d=set(b)
	ansflag=0
	ans=[]
	d1={}
	for i in range(n):
		ans.append(b[i])
		k=1
		flag=0
		#print (ans)
		while True:
			if (b[i]+k)>2*n:
				flag=1
				break
			if b[i]+k not in d and b[i]+k not in d1:
				ans.append(b[i]+k)
				d1[b[i]+k]=1
				break
			else:
				k+=1
		if flag==1:
			print (-1)
			ansflag=1
			break
	if ansflag!=1:
		print (*ans)