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())
for i in range(t):
	n = int(input())
	b = list(map(int,input().split()))
	l = [i+1 for i in range(2*n)]
	q = sorted(b)
	ans = True
	ansList = []
	count = 0
	if q[0]!=1:
		print(-1)
		continue
	for i in range(1,2*n-1):
		if i not in q and i+1 not in q:
			if count == 0:
				ans = False
				break
			else:
				count -= 1
		if i in q and i+1 in q:
			count+=1
	if ans == False:
		print(-1)
	else:
		for i in b:
			ansList.append(i)
			i+=1
			while i<2*n+1:
				if i not in ansList and i not in q:
					ansList.append(i)
					break
				i+=1
		print(*ansList)