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 _ in range(t):
	n = int(input())
	b = list(map(int, input().split()))
	for i in range(n):
		b[i] -= 1
	# print("b: ", b)
	used = [False for _ in range(2*n)]
	for i in range(n):
		used[b[i]] = True
	ans = [0 for i in range(2*n)]
	for i in range(n):
		ans[2*i] = b[i]

	result = True
	for i in range(n):
		found_cand = False
		for cand in range(ans[2*i]+1, 2*n):
			if not used[cand]:
				used[cand] = True
				ans[2*i+1] = cand
				found_cand = True
				break
		if not found_cand:
			result = False

	if not result:
		print(-1)
	else:
		print(" ".join([str(item+1) for item in ans]))



# 	print("ans: ", ans)
	# print("used: ", used)
	# print()