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 main(n, b):
	#print("DEBUT")
	tab = [0]*(2*n)
	dispo = [True]*(2*n + 1)
	for i in range(n):
		tab[2*i] = b[i]
		dispo[b[i]] = False
	for i in range(n):
		j = b[i]
		test = True
		while j <= (2*n) and test:
			if not dispo[j]:
				j += 1
			else:
				test = False
				dispo[j] = False
		tab[2*i + 1] = j
	test = True
	for i in range(1, 2*n+1):
		if dispo[i]:
			test = False

	#print("SOLUCE")
	if not test:
		print(-1)
	else:
		mot = ""
		for x in tab:
			mot += str(x) + " "
		print(mot)
	#print("END")

t = int(input())
for _ in range(t):
	n = int(input())
	b = list(map(int, input().split()))
	main(n, b)