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:
t=int(input())
while t:
	t-=1
	n=int(input())
	b=list(map(int, input().split()))
	cpy=b[::]
	s=list(set(range(1, 2*n+1)) - set(b))
	s.sort()
	cpy.sort()
	d=dict()
	for val, k in enumerate(cpy):
		d[k]=val
		
	ans=[]
	flag=True
	for i in b:
		val=0
		for j in s:
			if i<j:
				val=j
				s.remove(j)
				break
		if val:
			ans.append(i)
			ans.append(val)
		else:
			flag=False
			break
	if flag:
		print(*ans)
	else:
		print('-1')