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 = [int(i) for i in input().split()]
	a = []
	if (not 1 in b) or 2*n in b:
		print("-1")
	else:
		disp = []
		for i in range(1,2*n+1):
			if not i in b:
				disp.append([i, True])
		for i in b:
			min = -1
			a.append(i)
			for j in disp:
				if j[1] and j[0] > i:
					min = j[0]
					j[1] = False
					break
			else:
				print(min)
				break
			a.append(min)
		else:
			print(*a)