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())
	l = list(map(int , input().split(' ')))
	s = set(l)
	l2 = []
	for j in range(1 , 2*n + 1):
		if(j not in s):
			l2.append(j)
	l2.sort()
	done = 0
	for j in range(len(l2)):
		flag = 0
		for k in range(n):
			if(isinstance(l[k] , int) and l2[j] > l[k]):
				l[k] = [l[k] , l2[j]]
				flag = 1
				break
		if(flag == 0):
			print(-1)
			done = 1
			break
		flag = 0
	if(done == 1):
		done = 0
	else:
		for j in range(len(l)):
			print(min(l[j]) , end = ' ')
			print(max(l[j]) , end = ' ')
		print()