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:
def foo():
	size=int(input())
	b=list(map(int,input().split()))
	d={}
	biggest=0
	for i in b:
		d[i]=True

	answer=[]
	saved=0
	c=True
	q=[]
	c=True
	for i in b:
		j=1
		while True:
			if not d.get(i+j):
				d[i+j]=True
				break
			else:
				j+=1
		answer.append(i)
		answer.append(i+j)	
		if i+j>2*len(b):
			c=False
	
	if c:
		print(*answer)
	else:
		print(-1)
		
		


t=int(input())
for i in range(t):
	foo()